We discuss in detail the constraints on the partial compositeness coming from flavour and CP violation in the leptonic sector. In the first part we present a formulation of partial compositeness in terms of a flavour symmetry group and a set of spurions, whose background values specify the symmetry breaking pattern. In such a framework we construct the complete set of dimension-six operators describing lepton flavour violation and CP violation. By exploiting the existing bounds, we derive limits on the compositeness scale in different scenarios, characterised by increasing restrictions on the spurion properties. We confirm that in the most general case the compositeness scale should lie well above 10 TeV. However, if in the composite sector the mass parameters and Yukawa couplings are universal, such a bound can be significantly lowered, without necessarily reproducing the case of minimal flavour violation. The most sensitive processes are decays of charged leptons either of radiative type or into three charged leptons,  If the solution to the gauge hierarchy problem is based on a new symmetry and not on anthropic considerations (for a review see ) or on s}105 TeV  is requiThe latter possibility is empirically supported by the huge hierarchies among fermion masses and fermion mixing angles, which can only be explained by some special dynamics. An effective mechanism suppressing FCNC and CP violation can be introduced by observing that in the electroweak theory the symmetry of the flavour sector is broken only by the Yukawa interactions. Minimal flavour violation (MFV)  is definview see ), or froIn this paper we reconsider the possibility that both the origin of fermion masses and the suppression of FCNC and CP violation are due to the mechanism of partial compositeness (PC) , as realAn appealing realisation of this idea involves anarchic Yukawa couplings in the composite sector. In this case the observed hierarchies between SM fermion masses and mixing angles are entirely due to the elementary–composite mixing terms. This is of particular interest, especially for the lepton sector, since the known pattern of neutrino masses and mixing angles as extracted from neutrino oscillation experiments  seems toP>10 TeV , while tP>25 TeV . This stP>25 TeV .In this paper we focus on the lepton sector. Several studies of lepton flavour violation (LFV) and CP violation in the lepton sector of composite Higgs models have been realised. Most of the analysis have been performed in the context of five-dimensional (5D) models with a warped space-time metric, weakly coupled duals to strongly coupled four-dimensional conformal theories, believed to provide a calculable framework for composite Higgs models. Explicit computations with anarchic Yukawa couplings have been carried out in Refs. –20. Theydered in –24 requidered in –32. A redered in . LFV anddered in , 35 thatIn the present work we recast the framework of PC in terms of a generalised flavour symmetry and a suitable set of relevant spurions, much along the lines of Refs. , 32, 36.The general scope of our analysis is to check whether there are alternative solutions, beyond MFV, to reconcile PC at the TeV scale with the existing bounds on LFV and CP violation. We also wish to verify if the anarchic scenario is completely ruled out or not. By exploiting the effective Lagrangian of our construction and the existing experimental bounds we estimate the limits on the new physics scale in several scenarios, where our spurions are subjected to a series of increasingly restrictive conditions. We confirm that in general the anarchic scenario is not compatible with new physics at the TeV scale and we provide examples of how PC can be realised at the TeV scale, without necessarily resorting to MFV.In the second part of our paper we consider as an explicit model realisation of the flavour symmetry and its breaking pattern the so-called two-site model, first introduced in Ref. . Such a Our paper has the following plan. In Sect. As a first step, we have to choose the flavour symmetry group of our effective theory and its breaking terms. Throughout this paper we will work in the limit of massless neutrinos. The leptons are those of the SM, that is, three copies of It is well known that, if all the spurions First of all we require that our operators are local in the spurions We also assume that the operators are local in the Yukawa couplings Each power of M, singlet under the flavour symmetry group, to describe masses of other composite particles, such as for instance a new set of vector boson resonances. These additional states are coupled to the Higgs doublet and to the heavy fermions with a strong coupling constant Masses of the composite sector are described by the spurions In our operators masses will always appear in negative powers, to allow for decoupling of all the operators with the scale of new physics.With this set of assumptions, the LO operator describing charged lepton masses is still At variance with MFV, spurions with the dimension of a mass are present in our setup and some additional prescriptions are needed:M in Eq. . We streU(1), respectively. The flavour structure of these two operators is the same and we will focus on the combinationsZ boson to leptons, potentially violating both universality, through the diagonal terms, and lepton flavour, through the non-diagonal ones. There is a unique operator trilinear in the Higgs doubletllqq that can contribute to The physical processes we are interested in concern lepton flavour violation in the charged lepton sector as well as the magnetic dipole moments and the electric dipole moments (EDM) of the charged leptons. To this purpose it is convenient to adopt an effective field theory description where the SM Lagrangian is extended by an appropriate set of gauge invariant operators depending on the SM fields :8\documecument}φ . We starmentclass2pt{minimhis type , but theM or M. We call this the heavy fermion (HF) case. When the two scales M and m, c, Our aim is to estimate the Wilson coefficients of these operators, by expressing them in terms of the spurions using the set of rules described above. We expand each Wilson coefficient in powers of the mixings entclass1pt{minimaConcerning the dependence of the operators on the strong coupling constant To facilitate the identification of the relevant Wilson coefficients, it is useful to identify the combinations of spurions that fit the lepton bilinearsentclass1pt{minimaM in the HF case _{ij}$$hi l}^{1,})_{ij}$$C come from the HF column we have llqq operators we haveFinally we consider the contact operators n in Eq. . In thesk is either an additional loop factor Since we are interested in the scenario where In the other regime, s of Eq. , we can Notice that for rom Eqs.  and 28)\documentModel-independent studies of LFV processes have already been done in the literature –55. In tThe amplitudes for these processes get a tree-level contribution from the off-diagonal elements of the electromagnetic dipole operator The diagonal elements of the dipole operators contribute to electric and magnetic dipole moments of the charged leptons. From the present bounds reported in Table (g-2)μ/2 , 5831\doAlso the scalar operator n decays , 59–61. Z decays, but the corresponding limits on the Wilson coefficients, assuming Coming to the vector operators der 10 % . Throughder 10 % , 55. It We collect the corresponding bounds in Table M and c, X, X and We can translate the bounds collected in Tables entclass1pt{minimac, c, X, c, X, X (right-handed compositeness) or If  in Ref. . This cac and We start by taking mentclass2pt{minimd of Eq.  still apIFV scenario:The Yukawa couplingsare negligible and a choice of basis exists wherec, andare simultaneously proportional to the identity matrix.c, c and y:X and X and X and From the discussion in Sect. X and c and X, By exploiting the freedom related to our flavour symmetry, we can provide an alternative, but equivalent, description of the IFV scenario. We can choose a basis where  of Eqs.  and 4)  X and \dX and the mass matrix X is not proportional to the charged lepton Yukawa couplings, but to their square root. Therefore in discussing IFV we consider the general case where X and Within IFV the special case A is any combination of c, X and X and X is motivated by a possible role that the matrix X can play in describing large lepton mixing angles, once neutrino masses are turned on [In IFV no LFV is generated from the Wilson coefficients of the dipole and scalar operators with relation . The trarelation .X, A depends on c, A only in the combinations X and Now we can complete our discussion concerning the Wilson coefficients that are bilinear in the spurions entclass1pt{minimaM or llqq and we expect, in the mass basis:Here and in the rest of this section X, y or y is close to one.We are left with the coefficients that are quadrilinear in A new physics scale lue, Eq. , we needntify in  the domid of Eq. .X or X and In summary, even in the limit of “wrong” Yukawa coupling negligibly small, an anarchic (i)The gauge group is (ii)The fermionic sector of the model includes three families of chiral fermions charged under (iii)The Higgs sector consists of a real bidoublet Table In the previous sections, we focussed on PC scenarios for charged leptons from a general perspective, exploiting a spurionic analysis. Now, instead, we consider a specific simplified composite Higgs model, the so-called two-site model . Its relWe are ready now to introduce the Lagrangian of the two-site model:In shown in . Finallym, From the above Lagrangian we can easily recognise the flavour symmetry group of Eq.  and convThe Lagrangians of Eqs. –62) are are62) aThe first line of Eq.  accountsThe second line of Eq.  refers tv / m. These interactions will contribute to The third line of Eq.  describeThe fourth line of Eq.  containsThe fifth line of Eq.  describeThe sixth line of Eq.  refers tConcerning the flavour structure of the various interaction terms, we remember that each Higgs electroweak doublet v occur accompanied by a power of X and Using the rotations  and 65)65) one cBefore discussing LFV in this model we comment on the issues of renormalizability, gauge-invariance and UV sensitivity. The two-site model is a non-renormalizable effective theory and therefore it is valid only up to energies of the order of an UV cut-off  in Ref. , where iThis explicit breaking raises the question of the reliability and consistency of our results. We can always promote our effective Lagrangian to a gauge-invariant theory by interpreting the sources of gauge symmetry breaking as spurions. Providing the spurions with suitable transformation properties under the gauge group we can recover the gauge invariance under the full local group The embedding of the model in a UV completion also shows that it is not consistent to deal with the HF case, within the effective theory. Indeed to keep the masses of the elementary leptons non-vanishing in the HF limit, we have to consider at the same time large In this section we will present our results for the Wilson coefficients of the various LFV operators considered in Sect. h, Z, W) and heavy fermions and (ii) heavy gauge bosons and heavy fermions. Examples of diagrams for the above classes of contributions are shown in Fig. Dipole operators are among the most important operators in the leptonic sector as they generate LFV radiative decays such as mentclass2pt{minimh, Z and W amplitudes, we find that the dominant effects for class (i) are given byIn particular, summing over the of Refs. , 62. As M stands for a common heavy boson mass, The leading effects for class (ii) start from the order mentclasspt{minimaFrom Eq.  one can entclass1pt{minimaSetting entclass1pt{minimaWe discuss now NLO effects arising from class (ii) which are given by:The Yukawa interactions for charged leptons are modified after we integrate out at tree level the heavy fermions. Setting ne boson –65.Z boson interactions with charged leptons are also modified after we integrate out at tree level the heavy fermions. In particular, we find thatThe Contact operators induced by the exchange of heavy gauge bosons can be easily derived starting from the coefficients In this section, we evaluate the most relevant low-energy processes in the charged lepton sector in the context of the two-site model by making use of the Wilson coefficients derived in the previous section. One of the most interesting features of the two-site model is the absence of the Wilson coefficients _Y, N_X)=,2$$\end{Among the most interesting LFV channels are The dipole transition Here we provide the dominant contribution to e of Eq.  to elimim. In Fig. m of the various curves. In the right plot of Fig. m for This is confirmed by our numerical results shown in Fig. A quite similar behaviour is expected for the electron EDM. Indeed, if In Fig. The process of Refs. , 66 and m is shown for different values of m compared to In particular, in the HB scenario  an an98) anm for different values of These expectations are fully confirmed numerically as shown by the right plot of Fig. y of the composite sector is close to unity. In this respect it is interesting to note that while the bound on y, thus making essentially impossible to lower We have reanalysed the bounds on the compositeness scale derived from LFV and CP violation in the lepton sector, in the framework of PC. In the generic case of anarchic Yukawa couplings, such bounds are known to be quite severe, stronger than the analogous bounds from the quark sector and requiring a compositeness scale above 30 TeV. In this work we focussed on the case of vanishing neutrino masses and vanishing “wrong” Yukawa couplings, in the hope of minimising FCNC and CP-violating effects. We performed a general effective operator analysis, where the Wilson coefficients of the relevant dimension-six operators are determined by a flavour symmetry group and by a set of spurions. We have considered all lowest-dimensional operators leading to LFV violation and CP violation that can be constructed with the Higgs doublet and the SM leptons. We have formally expanded the Wilson coefficients in powers of the Yukawa couplings of the composite sector and in powers of the elementary–composite mixing terms. Our expansion includes, for the first time, terms quadrilinear in the elementary–composite mixing We have also derived the low-energy effective Lagrangian relevant to LFV and CP violation in the lepton sector in the two-site model, that includes heavy vector-like fermions as well as heavy spin-one particles. We focussed on the case


There are high functioning and low functioning ballast water treatment systems on board ships. In this study, five systems were analysed so as to methodically examine the operational difficulties for ship crew members while giving important consideration to sustainable environment practices. Multi-criteria analysis, a questionnaire, survey and interviews were used as the research method so as to ascertain and corroborate existing problems on board ships, and the reliability of the systems was calculated. The co-insistency, maintenance and the efficiency of the systems, were shown as being the major problem as there are no systems for tracking ship ballast operations from land. The treatment system that used oxidants was, through multi criteria analysis, evaluated as being the best and was ranked first. However, the survey results showed that the ship’s crew had serious problems with this system which difficult to solve during the ship’s operations with cargo. The deoxygenation system was the most appropriate according to ballast water treatment criteria in the port or at sea. The treatment system which used electrolysis with oxidant was better in terms of efficacy and the treatment system electrolysis with ultra violet light was better in terms of the criterion environment pollution footprint. During further research, it was shown that 7 % of the surveyed crew members had major problems with operating ballast water treatment systems, including the system which was ranked first through multi criteria analysis. They by-passed these systems while continuing to ballast or de-ballast. It was calculated that of the total time needed for the ballast water treatment system operation, 9 % of this time was used for repairs or maintenance of the systems. Some examples are changing a used UV bulb, cleaning the filter or controlling the amount of oxidant which would be discharged into the sea. A conclusion was made and solution was suggested. The study results emphasised taking action in the interest of protecting the natural world, with particular attention being given to environmental protection to support human life. Escherichia coli or Vibrio cholerae and animals such as zebra mussels. In addition, the ballast tanks are often contaminated with invasive species of animals, plants, and bacteria from the previous port. The BWMC  2004 protects the sea environment through regulations regarding future ballast water treatment. Regulations and standards established by the IMO  require treatment limits to be met independently and calls for vessels to carry out monitoring themselves  which is low in oxygen, higher than normal in CO2, and with a lower than normal seawater pH. Some systems employ multiple methods to increase effectiveness. The 2 × filtration + peracetic acid system utilises the method of passing the ballast water through the filters and adding peracetic acid. The filtration + electrolysis + ultraviolet light system provides the method of killing plants, bacteria and animals passing the ballast water through the filter and exposing them to electrolysis and ultraviolet light  have been type approved by flag administrations to meet the requirements of the IMO ballast water convention  method was designed to analyse criteria parameters including an alternative choice of specific criteria. In PROMETHEE I partial ranking, a) prefers the other criteria (b):Multi-criteria analysis can be defined as a decision-making model that consists of a set of solutions (variants to rank or sort by the decision-maker), a set of criteria  and the set value (score) of each variant for each criteria ; this means that:a” would prefer “b” only if:“The PROMETHEE II method was particularly well-fitted to this research as it could make decisions from incomparable criteria. PROMETHEE II has been used with success to solve many problems  with type approvals were chosen to be ranked using the PROMETHEE II multi-criteria decision making method:The importance of ecological protection was dealt with in three of the five criteria parameters. All criteria alternatives were analysed according to the following criteria parameters, as shown in Table Guidelines for approval of ballast water management systems—G8 must be taken into consideration for the approval of a ballast water management system. If a certain ballast water technology uses an active substance, then, to comply with the Convention, it should be approved by the IMO in accordance with the Procedure for approval of ballast water management systems that make use of Active Substances—G9, adopted by the MEPC (Marine Environment Protection Committee) in session 53 . As such, the equation for the reliability function R(t)  has the form of:In the Eq. , we can μ frequency of repairs, F redundancy failure detection ratio, Δt time lag/time interval, λ malfunction index.The computing subsystem of some of the ballast water treatment systems on board ships can be found in three states: proper function, procedural failure and non-procedural failure Shooman . ComputiThe Malfunction index is the relation between malfunctioning components and operational components:Pc is the number of components which remained operational after a specified time, and Pf is the number of components which malfunctioned after the specified time of functioning.Redundancy is a characteristic of the quality of the computing system that ensures failure avoidance when one part of the system fails. This is generally ensured through the use of additional software, through the reliability of the two redundant systems working in parallel and with a known malfunction index for these types of devices in predefined ship conditions.It can be assumed that the computing part of the subsystem in the system with two parallel subsystems, one of which is redundant, will be regularly maintained by the operator and through the self-diagnosis function for error removal. In this way, the possibility of malfunction of some ballast water treatment systems on board ships is reduced.The D-Sight computerised visual method or visual projection of PROMETHEE II analysis, as seen in Fig. The criteria parameters contribution to the solutions is shown in five different colours on the figure. The treatment system of electrolysis + oxidant technology was highly successful in this computational analysis with a percentile of 68.1 %. The value of the criteria parameter environmental pollution for the BWTS filtration with electrolysis and UV, was the most important criterion for ranking second with a percentile of 47.5 %. The system 2 × filtration with peracetic acid technology was ranked third with a percentile of 46.25 %. Crucial to its coming in third place was the high quality of its efficacy value, as well as environmental pollution, in terms of criteria parameters. As one of the analysis criteria was the treatment of ballast water in the port or at sea, the deoxygenation system received a percentile of 45 % as it is the only ballast water treatment system which can be used while at sea. The system which was ranked last was the filtration + electrolysis + electrochlorination + waste control system. It can be confirmed that this system has a high value in terms of the efficacy criteria parameter. However, because of its high environmental pollution footprint, as well as the highest number of treatment methods, received a percentile of 43.1 % and was ranked fifth in this multi criteria analysis.Three students from the courses (out of the 51 surveyed) responded to questions 3, 4 and 5 of the questionnaire affirmatively. In the maritime crewing agency, two experienced officers responded affirmatively to questions 3, 4 and 5. Of the 5 ship captains who were surveyed and during the interview confirmed that they had problems with the operating of the BWTS, one of the surveyed captains worked on a ship with an installed BWTS using the treatment method of electrolysis and oxidant.The problem that this chief officer referred to in regards to treatment system that uses electrolysis and oxidants was TRO . The measured TRO can provide an indication of treatment performance but not a direct measure of discharge standards. TRO was a problem for the TRO sensor unit in the deballastation process. Sensors would inhibit the operation of the ballast water treatment system due to the TRO value being too high. As the TRO was not at the required level, the residual TRO level of the treated ballast water was over 0.2 mg/L for the entire time, caused by an improperly dosed neutralizer in the neutralization unit of the system. The additional substance was most probably insufficient to automatically neutralize residual oxidants instantly and the system kept shutting down according to the interviewed chief officer. During the interview, two bridge officers that were surveyed said they were on a ship with an installed system that uses filtration, electrolysis and UV light. They said that it can take from three to three and a half hours to replace a UV bulb in a BWTS with a UV generator. Bulbs burn out often and in the case of a bulb burning out a second time, they by-passed the UV ballast water treatment system due to lack of time for cargo operations. According to another bridge officer who was interviewed for the survey, filters in the BWTS that uses filtration with UV light were a constant problem for one particular ship in a Brazilian port. The system was not able to operate due to filter problems. This problem was also referred to by another bridge officer who was on the ship with installed BWTS that uses filtration and UV light. All of officers interviewed stated that they by-passed the treatment system and continued the ballasting or de-ballasting process to avoid shutdowns. No reports were done at the time. The complete survey results can be found in Table λ = 0.5 to λ = 0.2 (Bakalar λ can only be determined from on board ship operational history which is at present unavailable for ballast water treatment systems. The mean value of the malfunction index was the most optional value in this calculation and it was taken for all systems in common. If the mean is taken as being λ = 0.35 for each of the serially attached subsystems and this value is included in the equation of reliability for 1000 h of work, we can obtain a reliability value for each of the two computing systems individually, where one is redundant:The malfunction index or maintenance failure which cannot be diagnosed and automatically eliminated for these types of devices ranges from  Bakalar . λ can oThe total reliability of the whole computing subsystem as part of the ballast water treatment system on board ships which consists of two units, one of which is software redundant, is:As such, the reliability of this subsystem has been proven according to the analysis of the results of the reliability of the computing system, which is a subsystem of a ballast water treatment system on board ships. The computing subsystem reliability with the possible use of the redundant software is 0.916 or 91.6 %.This paper reviews ballast water treatment systems in three parts regarding data and methods: multi-criteria analysis, survey on real experience, reliability and availability study. According to the multi-criteria analysis results, the electrolysis + oxidant technology treatment system had a high success rate of 68.1 %. Many aspects were relevant and important. The electrolysis management system that uses oxidants was the most appropriate system from an ecological standpoint, while determining the quality of the treated ballast water was the most acceptable from an environmental point of view. The multi-criteria analysis parameters and scenarios did not consider the functional and operational problems of the systems. It can be clearly concluded from the survey result of 7.3 % from all participants and interviews that ship officers by-pass ballast water treatment systems due to lack of time for rectifying malfunctions, failures, maintenance or spare parts replacement in ballast water treatment systems. The survey results indicate that ballast water treatment systems can become faulty and shut down when operation sensors indicate improper function of the sub-systems. Even the system which utilises oxidant, which was successful in the multi criteria analysis, was shown to have many problems regarding controlling oxidants. This implies an unclear future for port environment protection management, where the ballast water is pumped into the harbour in order to load cargo. The research in this paper aids in understanding how important it is to learn more about ballast water treatment system experiences from crewmembers, since the survey of operational experiences from ships has proven that more time would be needed for the maintenance of ballast water management systems. The total calculated reliability of the entire computing subsystem as part of a particular ballast water treatment system on board ships which consists of the two units of which one is software redundant, was 0.916 or 91.6 %. This means that for 8.4 % of the operational time, any of the mentioned systems could be in failure or under repair. This is a significant risk for the operation of ballast water treatment systems. The results of this research are a warning to relevant stakeholders in the maritime industry. If the system does not operate well, or not at all, the price of treatment is higher, as is air and water pollution, and the active substances used, e.g. oxidant residue, become unmanageable and out of control. Environmental hazards need to be managed. One possibility would be a mechanism to monitor ballast water systems operation continually on board ships. A check-up system should be close as possible to real time. Sensors should report malfunctions to the port authorities immediately after any questionable or doubtful performance of ballast water treatment system occur.


C) for measuring socioeconomic equality in health and health care using aggregated total population register data. The C is a widely used index when measuring socioeconomic inequality, but previous studies have mainly focused on developing statistical inference for sampled data from population surveys. While data from large population-based or national registers provide complete coverage, registration comprises several sources of error. We simulate confidence intervals for the C with different Monte Carlo approaches, which take into account the nature of the population data. As an empirical example, we have an extensive dataset from the Finnish cause-of-death register on mortality amenable to health care interventions between 1996 and 2008. Amenable mortality has been often used as a tool to capture the effectiveness of health care. Thus, inequality in amenable mortality provides evidence on weaknesses in health care performance between socioeconomic groups. Our study shows using several approaches with different parametric assumptions that previously introduced methods to estimate the uncertainty of the C for sampled data are too conservative for aggregated population register data. Consequently, we recommend that inequality indices based on the register data should be presented together with an approximation of the uncertainty and suggest using a simulation approach we propose. The approach can also be adapted to other measures of equality in health.In this paper, we introduce several statistical methods to evaluate the uncertainty in the concentration index ( A major health policy goal in many countries is to reduce disparities in health and in access to and the quality of health care. Measuring these disparities is a challenge. In order to obtain extensive and precise knowledge of inequalities, comprehensive methods to study equality are necessary. Most studies of equality in health and health care, and most methodological papers, have focused on survey data. Register-based data provide another possible source of data for equality studies. So far, good-quality individual-level administrative data including information on socioeconomic status have been available only in a few countries, such as the Nordic countries, but the importance of such data is likely to increase as better information systems increasingly become available and changes in data privacy regulations will enable broader utilization of the individual-level data in other countries. Register-based data are typically secondary data, i.e., they have not been collected for the purposes of specific studies Sund . AnotherIt is, however, a complicated task to assess the uncertainty in the indicator of interest using population-based data  is a widely used indicator for the quantification of socioeconomic equality in health and in the use of health care  can be used to measure the degree of socioeconomic inequality in health and health care across the distribution of the whole study population , which is a tool to visualize the degree of inequality. When using aggregated data, L(s) plots the cumulative proportion of the health outcome variable against the cumulative proportion of the population (s), ranked by socioeconomic group (SEG) from the least to the most advantaged. The C is defined as twice the area between the diagonal and L(s). In a case of complete equality, the C gets a value of 0. Negative values indicate a disproportionate concentration of the health outcome among those classed as disadvantaged and vice versa. The C is restricted to values between −1 and 1 when the health variable is not binary  of the gth SEG, and y is the mean of the yg across SEGs weighted by the population share fg. The Rg is the relative rank of the SEG, defined as Rg = ∑ γ=1g−1fγ + 0.5 fg and indicates the cumulative proportion of the population up to the midpoint of each group interval. In this study, yg denotes the directly age-standardized amenable mortality rate  of the gth income group: i is the age group, dig is the number of deaths and pig is the population size in the ith age group of the gth SEG, wi is the weight of the age group according to the standard population. The sum of the standard population is 100,000, i.e., ∑ i=1Iwi = 100,000.For aggregated data—in which the groups comprise SEGs and the socioeconomic indicator is measured on an ordinal scale—the quantitative measure of inequality can be estimated asC has also been estimated using a weighted least squares method (WLS) 2. This convenient regression method gives the C, irrespective of whether the principal model assumptions apply, because the regression method is an artificial technique to calculate the C . Kakwani et al. , and one simulates observed age-adjusted rates (yg). As one of the techniques applies the regression method . The number of person years in each income group can be assumed to be rather stable when using register data due to large datasets. Due to fixed proportions, the ranking is fixed in all our simulation techniques when estimating the uncertainty  and this allows modeling variation only in the health outcome variable. Consequently, even though the proportions in each income group are fixed, the uncertainty involved in recording income information is incorporated in our method.C. In addition, the advantage of our approaches is that they aim to model the assumed error of the data and the concentration curve and not the error of the slope parameter of the fitted regression line.The biasing effect of correlation between the rank and the outcome variable is avoided in all our approaches because the standard error is not estimated from the regression model; we simulate the original data to estimate the uncertainty of the σR2(yg/ygy) in Eq.  in the gth income group. We then re-estimated the C by replicating the regression estimation 10,000 times to account for the uncertainty. The lower and upper limits of the 95 % confidence interval of the C were obtained as the 2.5 and 97.5 percentiles of the distribution of the simulated slopes. The median of the distribution of the slopes is equal to the C calculated from the observed dataset, determined by setting the observed values of the dependent variable in Eq. , but naturally it would enlarge the confidence intervals of the C.If there is a reason to assume larger errors (for example due to consistent miscoding of some variable), the variance The second model (denoted as MC rate) assumes that the age-adjusted rates follow normal distributions mentclass2pt{minimC by allowing some variability in the health outcome (events) by income groups and also in the total number of events. Both methods (C. We denote this technique as BIN. The variability is approximated from the observed data with the following assumptions and steps such as:pig (the population size), the denominator of the rate, is held fixed in the simulation. This is based on the assumption that the information on age and person-years in the registers is perfect.The observed observed total number of events in age group i is the sum over income groups ∑ g=1Gdig = Di.The second assumption concerns the events that are treated as being random. The number of events is allowed to vary due to fact that there is some error in the coding of the events (such as causes of deaths). The ig is simulated assuming to follow a binomial distribution dig ∼ B. The denominator Di is the same for all income groups within the same age group. Probabilities ρig (with the constraints that ∑g=1Gρig = 1 and 0 ≤ ρig ≤ 1) are estimated from the observed data The number of events is allowed to vary between income groups within the age group. This is permitted because the income information presumably does not exactly measure the person’s real wealth. It might not describe the real wealth level of a person since all assets are not recorded in the administrative registers. Income is obtained from multiple administrative sources and, in addition, may vary considerably even over a short period. Now, the number of events in group N times; thus, N is the number of simulated datasets.Simulation step (3) is repeated N sets of age-adjusted rates are calculated using the simulated number of events, the observed person-years at risk from the original dataset, and the weights from the original standard population.Next, N values of the C are calculated using methods  f fN valueIn the next approach, we made more assumptions and developed the MC technique further to model the uncertainty in more detail. A requirement for the independence of the error terms is not needed because this method does not use errors estimated from a regression. It repeats the estimation of the  methods  and 2)  C by allC, we performed more analyses using different assumptions. The fourth model (denoted POIS) is a simulation approach equivalent to BIN except the number of events in the step (3) follows a Poisson distribution dig ∼ Pois(λig) where the parameter λig is the observed number of events in a group ig. Poisson distribution is asymmetrical when the mean is small. However, as the mean becomes large, the distribution becomes more and more symmetric and approaches normal distribution.To test the robustness of the above-mentioned simulation techniques to estimate the confidence interval for the Di is held fixed. The number of deaths is, however, allowed to vary between income groups within each age group. The number of events is simulated from a multinomial distribution with parameters Di and ρ, and mean E{Xig} = Diρig with the constraint that ∑ g=1GXig = Di. The probabilities ρi = {ρi1, …, ρiG} (with constraints ∑ g=1Gρig = 1 and 0 < ρig ≤ 1) are estimated from the observed data In the fifth simulation method (denoted MN), the total number of events within age group Table As an empirical example, we used Finnish register data on deaths amenable to health care interventions. Monitoring socioeconomic inequalities in mortality amenable to health care interventions—which is used to measure health system performance based on certain premature deaths that should not occur if health care works effectively and is timely—provides useful information on changes in differentials in health service utilization and effectiveness  for 20 income groups in 1996–2008. The age- and income-specific rates, i.e., the number of amenable deaths as a proportion of person-years in the follow-up of the corresponding population, were directly age-standardized to the European standard population  version 9.2 to analyze the data.We repeated the simulation approaches 10,000 times in our analyses; thus, p value for linear trend < 0.01), and by 2008, there were 3012 such cases (53 % among men). In 1996, the overall age-standardized rate per 100,000 person-years was 102 among men and 75 among women, and 60 and 50, respectively, in 2008. The average annual population (person-years) at risk was 4789,000 during the follow-up.In Finland in 1996, according to our definition, the total number of deaths considered amenable to health care interventions was 4087, of which 52 % occurred among men. The number of amenable deaths decreased evenly during the follow-up  for each year 1996–2008 among men and women. The concentration index is estimated using data aggregated by 20 income groups. The middle of the vertical line is the C that is calculated from the observed data using the formula or the WLS method and is the same for all three techniques. The solid circle indicates the MC simulation technique. The ends of the vertical line represent the 2.5 and 97.5 percentiles of the Monte Carlo simulated distribution of the C. The second method (indicated with a square) is a basic regression method (REG) carried out applying procedures using a standard statistical software package. We also used the method proposed by Kakwani et al.  in each SEG across certain years (j) and calculating the variance of the rates in each SEG . We used three different sets of years such as: 1) two preceding years and the study year, 2) two preceding years, the study year and two next years, and 3) three preceding years, the study year and three next years. The lengths of the confidence intervals of the C were equivalent with the results shown in Table Additionally, we compared the results of our MC-rate method with empirical results drawn from the data. This was done by calculating the variance from the empirical data by looking at the rates  are meaningful. In this study, we focus on register data, discuss what kind of uncertainties exist when using them, and how to model them when calculating the C. However, several factors can affect the uncertainty complicating this calculation. Even within Europe, countries have register data of different quality , the oorslaer  have sugn et al.  shows usC too conservatively for aggregated register data, since this method does not take into account the extensive dataset underlying the points of the regression. In addition, our simulation methods to estimate confidence intervals for the C have the advantage that the serial correlation between the rank and the outcome variable do not bias results since we do not estimate standard errors using the regression method. The simulation of point estimates avoids this problem since the possible correlation structure between the ranks (of income group) and outcomes  remains approximately the same in the replicates as in the original data. The similar results obtained using slightly different assumptions support the interpretation that serial correlation between the rank and outcome is not an issue in our simulations. Our results also showed that the point estimates and confidence intervals were systematically equivalent using regression or formula methods. Since, by definition, serial correlation is not present using the original formula method, this result means that it is not an issue in our simulations. Furthermore, using the regression method, the error is evaluated mainly based on the size of the error terms in the Eq. ; thOur empirical example of comprehensive Finnish register data on amenable mortality covers the years from 1996 to 2008. Although amenable mortality faces some criticism as a straightforward indicator of the quality of health care, inequalities in amenable mortality illustrate a broad picture of the state of equality in health care as the deaths also cover those groups who do not use or do not have proper access to health services (Nolte and McKee In Finland, register data are generally of high quality (Gissler and Haukka C when assessing equality using grouped register data.In order to achieve an equitable distribution of health and health services between socioeconomic groups, we need a better knowledge of inequalities in health and the use of health services. This requires more precise measures of equality as well as detailed information on indicators for health and health care use. The approaches we introduce in this study for the concentration index can also be adapted to other measures of equality in health, such as the relative index of inequality and the slope index of inequality. With these techniques, it is possible to evaluate comparable confidence intervals for the population estimate on a case-by-case basis. Although the assessment of uncertainty is demanding, our approaches provide substantive better approximation than the regression method or the KWV method. Consequently, we recommend using our simulation technique to estimate the confidence intervals for the


Before The design of this important study included two aspects which resulted in a disadvantage for the medical-therapy group. First, patients had to be informed about the fact that they had a significant stenosis which was left untreated because they had been randomised to the medical-therapy group. It is easy to imagine what kind of effect such knowledge would have if some even mild form of chest pain recurred. The patient would necessarily interpret this as a signal of impending doom and present to the hospital. There he would be treated as a patient with unstable angina and—knowing that he harboured a high-grade stenosis—be immediately brought to the catheterization laboratory. The treating doctor would not hesitate and dilate the stenosis. This would generate an endpoint “urgent revascularisation” in the medical-therapy group. Unfortunately, it would be difficult to design the study in a way that such an effect could be avoided. Only if the medically treated group would undergo a sham procedure —similar The second disadvantage for the medically treated group was due to the fact that the larger number of revascularizations in the medical-therapy group in patients without objective evidence of ischemia probably also triggered additional hard events in the medical-therapy group. PCI not infrequently results in periprocedural elevations of troponin. Such an event, however, was likely counted as an additional hard event  occurring in the group with medical therapy. The authors do not comment on how such events were counted and on the number of events occurring this way.p = 0.01). Interestingly, this “hard” between-group difference had become smaller at 2 years than after 1 year (3.6 vs. 4.3 %). There was no significant between-group difference in the total rates of death and MI (PCI group: 29 patients experiencing death or MI (6.5 %) vs medical group: death or MI in 36 patients . The absolute number of events was 6 deaths in the PCI group and 8 deaths in the medical-therapy group. However, in each group, only 3 of the deaths were cardiac in origin. The number of MIs at the end of year 2 was 26 in the PCI group and 30 in the medical-therapy group . This skewed vision of the results was promoted by the fact that the lack of a significant difference in hard endpoints over the entire time from randomisation up to 2 years  was placed in a table in the appendix whereas the “landmark” analysis was mentioned in the summary of the trial. Heartwire commented that “PCI is superior to medical therapy for the reduction of hard clinical endpoints in patients with stable coronary artery disease”. Such a disinformation policy will most likely create inaccurate brain engrams in readers who necessarily do not have the time to go into much detail when trying to keep abreast with current studies.Instead, attention was focused on the significantly lower rate in the PCI group when the first 7 days were excluded . The difference does only seem to be statistically significant if one ignores the higher rate of MIs and death in the PCI group within the first 7 days after the intervention. However, this “landmark” type of analysis is clinically irrelevant. Third Repeated attacks of angina are of course worrying for the patient and reducing the number of patients with such symptoms is a valuable goal. However, revascularization of all the patients fulfilling the entire criteria for FAME 2 will result in overtreating many of these patients at unnecessary cost to society. Fourth: FAME 2 clearly demonstrates that no harm will be done if revascularization is postponed until the patient has reoccurrence of symptoms with or without some troponin rise.The interventional community should not be enticed by the irrelevant yet highly publicised result of the “landmark” analysis to forget current guideline recommendations for the treatment of patients with stable coronary disease , 7. The


It was underscored that the optimization of policies of preventive maintenance has become a subject of much research. This article proposes a new optimal policy of preventive maintenance for the roller shaft system. It is divided into two main sections. The first proposes a new design of the shaft where the effect of preventive maintenance is integrated, and the second is developing a new control technique adapted to the new design. In this regard, we are interested in the shaft of rollers of the rotary kilns of cement. We have noted the stresses imposed to the axis of the roller. These constraints that have stemmed from the contact between tire and its support rollers. Currently the ultrasonic inspection method of the solid shaft in this situation poses disadvantages, for example, the obligation to stop the rotary Kiln and the difficulty of detecting and sizing defects (fatigue cracks). We propose in this study another approach, we recommend opting for a hollow shaft instead of a solid shaft with a minimum diameter that allows the control system to enter hollow shaft to show for inspection purposes. This will allow preventive control, in operation by the non-destructive technique of ultrasound. The analysis shows the different results of comparison between the axis of full and hollow cylinders, having the same dimensions and the same material and ultimately the most interesting is the same operation. The objective in all industry feature the machines and systems need to increasingly efficient is taking consideration the complex of these structure but the requirements of the security, cost optimization and control of equipment availability makes preventive maintenance in the first of all search work. It must allow to intervene only in the presence of defective elements, minimize repair time and to provide a reliable and easily interpretable diagnosis despite the complexity of the equipment Claire .Although our interest will mainly focus on constitutes a significant component in the maintenance. The rotary kiln is used for the pre-treatment step in the production of Portland and other types of cements.For the rotary kiln, the roller shafts are among the main parts that make up the kiln. They are considered the most important items related to safety because a roller shaft that has damage can directly cause an accident Chapman .To minimize processing time, the maintenance method adopted is that of preventive maintenance with a new design of the roller shaft minimizing its weight to facilitate preventive maintenance. Then, a comparison is made between the current shaft and the one developed by our study using the finite element method (FEM) to know the difference between the two shaft reliability.The kiln is a pipe rests on supporting station rollers  having an inclination of the order of 3.5 % with respect to the horizontal and rotating at speeds between 1.8 and 3.5 r/min , ρ = 7850 kg/m3, E = 2.05E5 MPa, ν = 0.3, Re = 600 MPa, the properties of EN8 are as showcased in Table Angle between tire and roller is 30°.Load component acting on the single roller.We have assumed that the contact between roller and tire raceway is continuous on the total available width of ring raceway .The kiln shell is equipped with bearings and can be considered as simply supported beam. Under normal conditions, the inlet and the outlet of the furnace do not support the shell, therefore the furnace can be taken as a cantilevered beam.To calculate the support reactions, a simplified procedure is used, and certain hypotheses are made: the mixture is distributed symmetrically around the vertical axis of the kiln. This means that load weight of material are evenly distributed over each roller. Figure The roller and the shaft are assembled rigidly. We can consider, in the FE model, that all points shaft of the roller are in contact with the rails, are presented by the area colored red in Fig. The weight of the oven applied on the shaft of efforts rated for attachment to the seat of the roller, Fig. The model was developed using a finite element program. We use an elastic model in large displacements. We mesh the roller shaft with volume elements 228,880. The elements used are from the library of standard components. These are quadratic elements with reduced integration for hexahedra called C3D20R and without reduced integration for tetrahedral elements called C3D10. These elements were chosen primarily for their performance in dynamic simulation , particularly in the critical zones identified Fig. Transverse waves are used to control the critical zones shaft in order to achieve control without dismantling the covers, thrust collar and the oil change for the six rollers and also for their assembly. The transverse ultrasonic waves are generated by a sensor, with a definite angle from the surface of the shaft hole. As shown in the diagram in Fig. The surface of the shaft being circular, it is necessary to control a rotation of a turn (360°) to ensure scanning of controlled set. Also, we will develop a rotary system to support the sensor, which will allow a dramatically shortening the time  technique, when defects are to be sized in terms of amplitude relative to reference reflectors by the DAC technique. The surface condition of the reference block shall be representative of the surface condition of the part to be examined. Unless otherwise specified the reference block shall contain at least three reflectors covering the entire depth range under examination Lavender .The angle beam shall be directed toward the reference reflector (holes or notches) that yields the maximum response in the area of interest. The gain control shall be set so that this response is 80 % ± 5 % of full screen height. This shall be the reference level. The search unit shall then be manipulated, without changing instrument settings, to obtain the maximum responses from the other calibration reflectors at their beam paths to generate the distance amplitude correction curve (DAC).The test sensitivity requires consideration. As mentioned above, the sensitivity level adopted must assure detection of small cracks in the early stages of growth, whilst not causing the over amplification of insignificant signals which would result in the rejection of good components.New inspection system provides information on the position of the defects on their relative importance compared to artificial defects (DAC) and therefore a classification to know the severity of these defects .Therefore, adoption of the change in the outlook and physical design is a factor taking into account the recommended conditions and parameters considered during maintenance.In perspective, it is proposed the integration of the control system to the roller shaft, allowing continuous monitoring of the shaft. Translators can be integrated into the hole of the roller shaft, which will monitor the critical areas that we have identified above. A study is underway to achieve this.


Modelling of extreme events has always been of interest in fields such as hydrology and meteorology. However, after the recent global financial crises, appropriate models for modelling of such rare events leading to these crises have become quite essential in the finance and risk management fields. This paper models the extreme values of the Ghana stock exchange all-shares index (2000–2010) by applying the extreme value theory (EVT) to fit a model to the tails of the daily stock returns data. A conditional approach of the EVT was preferred and hence an ARMA-GARCH model was fitted to the data to correct for the effects of autocorrelation and conditional heteroscedastic terms present in the returns series, before the EVT method was applied. The Peak Over Threshold approach of the EVT, which fits a Generalized Pareto Distribution (GPD) model to excesses above a certain selected threshold, was employed. Maximum likelihood estimates of the model parameters were obtained and the model’s goodness of fit was assessed graphically using Q–Q, P–P and density plots. The findings indicate that the GPD provides an adequate fit to the data of excesses. The size of the extreme daily Ghanaian stock market movements were then computed using the value at risk and expected shortfall risk measures at some high quantiles, based on the fitted GPD model. Recently, an issue of concern to most risk managers and financial analysts are the events that occur under certain extreme market conditions. This refers to events which have the tendency to produce huge and unexpected losses that could affect and also probably lead to bankruptcies and consequently, systemic risk Gavril . Hence, What makes the EVT very appealing is the fact that the nature of the asymptotic distribution does not necessarily depend on the exact distribution of returns. DuMouchel  succinctAs the estimation of these rare events involve the estimation of extreme quantiles, risk measures such as the value at risk (VaR) and expected shortfall (ES) have been found to be more appropriate compared to the others which rely on the entire distribution since they capture the quantile risks in the tails of the distribution Harlow .This paper therefore models the Ghana all-shares stock index using the EVT method and further computes the risk measures associated with the Ghanaian stock market, under the EVT framework.There have been very few studies investigating the tail behaviour of the returns of the Ghana Stock Exchange indices and also computing the resulting market risks using the VaR or the expected shortfall approaches.The main motivation behind this paper is the need to examine the performance of the EVT method in the analysis of the Ghanaian stock market. This paper thus contributes to empirical evidence of the research into the behaviour of the extreme returns of financial series in Africa and specifically in Ghana.The rest of the paper is organized as follows: “F(x), and a predetermined threshold u, the interest here is in that of the distribution of the exceedances or the values of x above the threshold u, given that u is in fact exceeded. Thus an exceedance occurs when F.The Peak over Threshold approach (POT) of the EVT is described at this stage. For a set of observations Hence, since u, the estimation of its distribution is quite straightforward. However, estimation of the portion above u with distribution Clearly, as the bulk of the observations lie in the area 0–u becomes large, the distribution function of the exceedances over the threshold has approximately a Generalized Pareto Distribution (GPD).Theorem Pickands : If the F, and also a predetermined high threshold u, the conditional excess distribution function Hence, for a large class of underlying distribution functions  Kellezi  indicatex by defining u = 0 and Also, it is possible to express the GPD as a function of have Eq.  as4\docuUsually, attention is restricted to the study of the shape parameter In a bid to estimate the market risks associated with holding financial positions on the Ghana stock market, the VaR and expected shortfall (ES) frameworks are considered.The VaR of a financial portfolio at a confidence level, X models the negative returns on a certain financial portfolio with a corresponding cdf F, then the VaR at the p-th quantile is given byF.Alternatively, if a random variable F(x), and a predetermined threshold u, the conditional excess distribution function For a set of observations F(x) can be written asHence, with some fairly simple algebra, the form of n as the total number of observations and u, the expression Given x = y + u is given byAlso, the expression for the GPD written in terms of Therefore, the tail estimate can be written asp under the GPD approach is obtained by inverting expression above to obtain the inverse function of The estimate of the VaR with a given probability The expected shortfall can be described as the expected value of the size of the loss exceeding the VaR with some level of probability on the condition that the loss actually exceeds the VaR. It can thus be expressed asThis expression can further be written asFrom the definition of the mean excess function of the GPD with distribution function F and some high threshold u, the expected shortfall can similarly be described by considering the u, the mean excess function is given byRecall that if X follows a GPD with threshold Note that for a high threshold value Hence it can be shown that The expected Shortfall under the GPD framework is therefore estimated byThe study employed secondary data obtained from the Ghana Stock Exchange (GSE). It consists of 2226 daily closing prices of GSE all-shares index spanning the years 2000–2010. This index is computed by the GSE based on the values of stocks of each of the companies listed on the stock exchange. Thus it represents a measure of the overall performance of the stock market. The GSE was incorporated in July 1989 and is presently the principal stock exchange of Ghana. It currently has 40 equity listings from 35 companies, mostly Ghanaian, 1 corporate bond, 3 government bonds, and 1 preference share. The exchange is dominated by the manufacturing and brewing industries, followed by the banking sector. The other listings are in the mining, insurance and petroleum sectors. The GSE index was recognised in 1993 as the sixth best performing index among emerging stock markets, with an appreciation in capital by 116 %. By gaining 124.3 % in its index level in 1994, it became the best performing market among all emerging stock markets GSE . The marFurthermore, as indicated by UN , an impoAlso, Benimadhu  revealedIt was observed in 2004 that with the listing of Ashanti Goldfields Company (AGC) now AngloGold Ashanti, a highly liquid company, the stock exchange index appreciated by 124.3 %. Every stock market operates in an economy and hence, happenings in the economy affect the performance of the market. For the Ghana stock market, the main factor which significantly affects its performance is the general elections held after every 4 years. As can be noticed from Fig. t, t and Since the financial market usually only provides the raw data of the realized values of the various financial indices, the daily log-returns, which for the purpose of this paper, will be used interchangeably with returns, were derived as followsThis paper applies the extreme value theory (EVT) approach in analysing extreme returns of the Ghana stock exchange all-shares index over the period 2000–2010. An in-depth analysis of the extreme value methodology applied to the high frequency (daily) Ghana stock data is presented in this section. The yearly progression of the data is illustrated by means of logarithmic time series plot. Furthermore, the volatility of the financial returns over the period is examined. The establishment of the presumption of financial returns having fat tails is made from an examination of the histogram of returns. Various risk measures are then computed and discussed.Table Figure Figure Furthermore, Phillips-Perron and Augmented Dickey-Fuller unit root tests were performed to check for stationarity and it was found that the returns data is fairly stationary.In order to apply the Extreme Value method to any data, it is a strong requirement for the data to be independent and identically distributed (iid). Hence, a Box-Ljung (lag = 8) test for autocorrelation was performed. The test revealed the presence of significant autocorrelation in the returns series. Furthermore, a Lagrangian Multiplier (LM) test performed to examine the data for the presence of autoregressive conditional heteroscedastic (ARCH) effects also indicated the presence of significant ARCH effects in the data  approach of the EVT is the selection of appropriate threshold levels for the tails of the distribution. This was performed graphically in this study by the use of hill plots, shape parameter plots and mean excess plots.Figure Upon examination of the shape parameter plots in Fig. u = 0.8 is selected for the right tail and u = 0.15 for the left tail. These points are represented by the faint green vertical lines on the graphs. It can be noticed that in both cases, the graphs are relatively stable up to the points selected and from there a slight kink is observed above which the graphs exhibit slight variations even though the slopes remain positive. Furthermore, these selected thresholds fall in the ranges determined by the hill plots and shape parameter plots.Finally, Fig. There were 169 observations above the selected threshold left for modelling for the right tail and 303 observations left above the threshold in the left tail. These were considered enough for a GPD fit since they are more than 10 % of the total observations in each of the tails. It can be also seen that for the threshold selected within the ranges indicated, the curves above the threshold have an upward slope and will therefore be well approximated by the Generalized Pareto Distribution (GPD) with positive shape parameters.Table  Tajvidi . The staFigure The Probability (PP) plots of the goodness of fit of the GPD models on the empirical excesses are presented in Fig. The results obtained by fitting the empirical quantiles of excesses against the quantiles of the fitted GPD models in quantile–quantile (Q–Q) plots are displayed in Fig. The graphs of the density plots exhibited in Fig. Figure Table For the higher quantiles, the results show that with a probability of 0.005, i.e. 99.5 % level of confidence, the daily market gains will not exceed 5.51 %. The expected daily market gains if the level 5.51 % is exceeded is 14.794 %. Similarly, the expected daily market losses will not exceed 5.215 % at a probability of 0.005 and an expected loss of 10.062 % is obtained if the losses exceed that level. Furthermore, at 99.9 % level of confidence i.e. probability of 0.001, the daily market gains will not exceed 15.021 % and if it does exceed that level, the expected daily market gain is 40.773 %. On the other hand, the daily market losses will not exceed 11.54 % with an expected daily market loss of 21.464 % if the losses do exceed 11.54 %.Alternatively, the results above may be interpreted in terms of holding an investment position (short or long position) on the stock market. For the lower quantile, the daily loss associated with holding a long position on the market is at most 1.34 % with a probability of 0.05 and in the case where it is exceeded, a loss of 3.08 % is expected. Conversely, the daily gain associated with holding a short position on the market will not exceed 1.39 % with a corresponding expected gain of 3.55 % in the situation where the gain exceeds 1.39 %. For the higher quantile, with a probability of 0.001 (i.e. 99.9 % level of confidence), a holder of a long position may experience daily losses not in excess of 11.54 % and if the losses do exceed 11.54 %, the expected losses will be 21.46 %, and the holder of a short position may experience a daily gain not exceeding 15.02 % with a probability of 0.001 and in the event it does, the expected gain observed will be 40.77 %.This paper employs the VaR in determining the best and worst case scenarios of the market value of the Ghana stock exchange all-shares index over one trading day, at a given level of confidence. Hence the above results imply that for an investment of $1 million in the market, the expected gains will not exceed $13,900, with a 95 % confidence level, over one trading day. On the other hand, the worst daily loss on the investment will not exceed $13,400. Also, with a 99.9 % level of confidence, a $1 million investment in the market will yield a daily gain not in excess of $150,200 and a daily loss not exceeding $115,400.These results indicate that for an investment in the Ghana stock market, the possibility of losses is lower than the possibility of gains. This is in contrast with findings from the work of Gilli and Kellezi  who founThe main aim of the paper was to empirically examine the application of the EVT methodology in the Ghanaian stock market by applying it to the Ghana stock exchange all-shares indices. The results of the study showed that the daily returns of the Ghana stock exchange all-shares index data was from a distribution with fat-tails and asymmetric in nature and hence the extreme value (EVT) model provided a better fit to the tails of the distribution of returns. As a result of the observed volatility in the daily returns data, the conditional EVT approach was preferred for the study. A similar realization was made by Polakow and Seymour  when theAndjelic et al.  concludeIt was further indicated by Gencay and Selcuk  that EVTConsequently, value at risk (VaR) and expected shortfall (ES) risk measures were computed at some high quantiles from incorporating the GPD models of the tails of the distribution of daily Ghanaian stock returns. They revealed that in the Ghanaian stock market, the VaR and ES associated with the left tail or long investment position increased more significantly as the quantiles increased as compared to the right tail or short investment position, except for the last quantile (99.9th) for which the right tail had a more significant increase in the VaR and ES.Quismorio  indicateTo conclude, this study revealed that the Peak over Threshold approach of the extreme value theory, which fits a Generalized Pareto Distribution to extremes above a certain threshold, can be very efficient in the modeling of extreme events and assessing the size of potential extreme risks, particularly in the stock market.