The generalized Pareto distribution is one of the most important distributions in statistics of e... more The generalized Pareto distribution is one of the most important distributions in statistics of extremes as it has wide applications in fields such as finance, insurance, and hydrology. This study proposes two new methods for estimating the shape parameter of the generalized Pareto distribution (GPD). The proposed methods use the shrinkage principle to adapt the existing empirical Bayesian with data-based prior and the likelihood moment method to obtain two estimators. The performance of the proposed estimators is compared with the existing estimators (i.e., maximum likelihood, likelihood moment estimators, etc.) for the shape parameter of the generalized Pareto distribution in a simulation study. The results show that the proposed estimators perform better for small to moderate number of exceedances in estimating shape parameter of the light-tailed distributions and competitive when estimating heavy-tailed distributions. The proposed estimators are illustrated with practical datase...
This study focuses on the use of digits-based test in anomaly detection in presidential elections... more This study focuses on the use of digits-based test in anomaly detection in presidential elections in Ghana. Even though Ghana has conducted several successful elections to elect presidents, the outcomes of the elections have been challenged in courts on allegations of vote rigging and fraud. It has been established in the literature that for an election to be anomaly free, the following should be satisfied: the distribution of voters turn-out, the winners’ share and total valid votes cast in the election should be uni-modal. Therefore, we assess the applicability of both first and second digits-based tests to aid in the detection of possible anomaly in the 2016 and 2020 presidential election results data in Ghana. The Benford frequency distribution and Spearman rank correlation coefficient tests were used for the analysis of data obtained from the Electoral Commission of Ghana. The results show that the observed first digits distributions of valid vote counts for both New Patriotic ...
A novel flexible extension of the Chen distribution is defined and studied in this paper. Relevan... more A novel flexible extension of the Chen distribution is defined and studied in this paper. Relevant statistical properties of the novel model are derived. For the actuarial risk analysis and evaluation, the maximum likelihood, weighted least squares, ordinary least squares, Cramer–von Mises, moments, and Anderson–Darling methods are utilized. For actuarial purposes, a comprehensive simulation study is presented using various combinations to evaluate the performance of the six methods in analyzing insurance risks. These six methods are used in evaluating actuarial risks using insurance claims data. Two applications on bimodal data are presented to highlight the flexibility and relevance of the new distribution. The new distribution is compared to several competing distributions. Actuarial risks are analyzed and evaluated using actuarial data, and the ability to disclose actuarial risks is compared by a comprehensive simulation study, through which actuarial disclosure models are compa...
In this paper, we introduce reduced-bias estimators for the estimation of the tail index of Paret... more In this paper, we introduce reduced-bias estimators for the estimation of the tail index of Pareto-type distributions. This is achieved through the use of a regularised weighted least squares with an exponential regression model for log-spacings of top-order statistics. The asymptotic properties of the proposed estimators are investigated analytically and found to be asymptotically unbiased, asymptotically consistent, and asymptotically normally distributed. Also, the finite sample behaviour of the estimators are studied through a simulation study The proposed estimators were found to yield low bias and mean square errors. In addition, the proposed estimators are illustrated through the estimation of the tail index of the underlying distribution of claims from the insurance industry.
Elections are one of the barometers through which electorates measure the performance of governme... more Elections are one of the barometers through which electorates measure the performance of governments and decide whether to renew their mandate or not. The success of every election goes a long way to strengthen the frontiers of a country's democracy and provide legitimacy for those who hold political power. However, the electoral process of many African countries has been challenged in courts or allegations of fraud and vote rigging are leveled against the winning party or candidate. Therefore, there is the need for a statistical method for checking and validating election results to ascertain fraud and vote rigging claims. Existing validation methods include the Parallel Vote Tabulation methodology. However, some significant disadvantages of this approach are issues of cost, sampling techniques and sample size determination. To overcome these, this study resorts to using the Dirichlet multinomial Bayesian model to compute posterior probabilities of valid votes cast and Bayesian...
In this paper, we propose a reduced-bias estimator of the EVI for Pareto-type tails (heavy-tailed... more In this paper, we propose a reduced-bias estimator of the EVI for Pareto-type tails (heavy-tailed) distributions. This is derived using the weighted least squares method. It is shown that the estimator is unbiased, consistent and asymptotically normal under the second-order conditions on the underlying distribution of the data. The finite sample properties of the proposed estimator are studied through a simulation study. The results show that it is competitive to the existing estimators of the extreme value index in terms of bias and Mean Square Error. In addition, it yields estimates of γ > 0 that are less sensitive to the number of top-order statistics, and hence, can be used for selecting an optimal tail fraction. The proposed estimator is further illustrated using practical datasets from pedochemical and insurance.
In this paper, non-life insurance claims were modelled under the three parameter discrete general... more In this paper, non-life insurance claims were modelled under the three parameter discrete generalised Pareto distribution. Data from the National Insurance Commission of Ghana on reported and settled claims were considered for the period 2012-2016. The maximum likelihood estimation principle was adopted in fitting the discrete Pareto distribution to the yearly and aggregated data. The estimation involved two steps. Firstly, the $\mu$ and $(\mu+1)$ frequency method of \citet{Prieto2014} was modified to suit the characteristics of the data under study. Secondly, a bootstrap algorithm was implemented to obtain the standard errors of the estimators of the parameters of the discrete generalised Pareto distribution. The performance of the discrete generalised Pareto distribution is compared to the negative binomial distribution in modelling the non-life insurance claims data using the information criteria of Akaike and Bayesian. The results show that the discrete generalised Pareto distri...
In many statistical problems, several estimators are usually available for interval estimation of... more In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a high coverage probability close to the nominal level and a shorter interval length. However, these two concepts are in opposition to each other: high and low coverages are associated with longer and shorter interval lengths respectively. Some methods, such as bootstrap calibration, modify the nominal level to improve the coverage and thereby allow the selection of intervals based on interval lengths only. Nonetheless, these methods are computationally expensive. In this paper, we propose an index which offers an easy to compute approach of comparing confidence interval estimators based on a compromise between the coverage probability and the confidence interval length. We illustrate that the confidence interval index has range of values within the n...
The generalized Pareto distribution is one of the most important distributions in statistics of e... more The generalized Pareto distribution is one of the most important distributions in statistics of extremes as it has wide applications in fields such as finance, insurance, and hydrology. This study proposes two new methods for estimating the shape parameter of the generalized Pareto distribution (GPD). The proposed methods use the shrinkage principle to adapt the existing empirical Bayesian with data-based prior and the likelihood moment method to obtain two estimators. The performance of the proposed estimators is compared with the existing estimators (i.e., maximum likelihood, likelihood moment estimators, etc.) for the shape parameter of the generalized Pareto distribution in a simulation study. The results show that the proposed estimators perform better for small to moderate number of exceedances in estimating shape parameter of the light-tailed distributions and competitive when estimating heavy-tailed distributions. The proposed estimators are illustrated with practical datase...
This study focuses on the use of digits-based test in anomaly detection in presidential elections... more This study focuses on the use of digits-based test in anomaly detection in presidential elections in Ghana. Even though Ghana has conducted several successful elections to elect presidents, the outcomes of the elections have been challenged in courts on allegations of vote rigging and fraud. It has been established in the literature that for an election to be anomaly free, the following should be satisfied: the distribution of voters turn-out, the winners’ share and total valid votes cast in the election should be uni-modal. Therefore, we assess the applicability of both first and second digits-based tests to aid in the detection of possible anomaly in the 2016 and 2020 presidential election results data in Ghana. The Benford frequency distribution and Spearman rank correlation coefficient tests were used for the analysis of data obtained from the Electoral Commission of Ghana. The results show that the observed first digits distributions of valid vote counts for both New Patriotic ...
A novel flexible extension of the Chen distribution is defined and studied in this paper. Relevan... more A novel flexible extension of the Chen distribution is defined and studied in this paper. Relevant statistical properties of the novel model are derived. For the actuarial risk analysis and evaluation, the maximum likelihood, weighted least squares, ordinary least squares, Cramer–von Mises, moments, and Anderson–Darling methods are utilized. For actuarial purposes, a comprehensive simulation study is presented using various combinations to evaluate the performance of the six methods in analyzing insurance risks. These six methods are used in evaluating actuarial risks using insurance claims data. Two applications on bimodal data are presented to highlight the flexibility and relevance of the new distribution. The new distribution is compared to several competing distributions. Actuarial risks are analyzed and evaluated using actuarial data, and the ability to disclose actuarial risks is compared by a comprehensive simulation study, through which actuarial disclosure models are compa...
In this paper, we introduce reduced-bias estimators for the estimation of the tail index of Paret... more In this paper, we introduce reduced-bias estimators for the estimation of the tail index of Pareto-type distributions. This is achieved through the use of a regularised weighted least squares with an exponential regression model for log-spacings of top-order statistics. The asymptotic properties of the proposed estimators are investigated analytically and found to be asymptotically unbiased, asymptotically consistent, and asymptotically normally distributed. Also, the finite sample behaviour of the estimators are studied through a simulation study The proposed estimators were found to yield low bias and mean square errors. In addition, the proposed estimators are illustrated through the estimation of the tail index of the underlying distribution of claims from the insurance industry.
Elections are one of the barometers through which electorates measure the performance of governme... more Elections are one of the barometers through which electorates measure the performance of governments and decide whether to renew their mandate or not. The success of every election goes a long way to strengthen the frontiers of a country's democracy and provide legitimacy for those who hold political power. However, the electoral process of many African countries has been challenged in courts or allegations of fraud and vote rigging are leveled against the winning party or candidate. Therefore, there is the need for a statistical method for checking and validating election results to ascertain fraud and vote rigging claims. Existing validation methods include the Parallel Vote Tabulation methodology. However, some significant disadvantages of this approach are issues of cost, sampling techniques and sample size determination. To overcome these, this study resorts to using the Dirichlet multinomial Bayesian model to compute posterior probabilities of valid votes cast and Bayesian...
In this paper, we propose a reduced-bias estimator of the EVI for Pareto-type tails (heavy-tailed... more In this paper, we propose a reduced-bias estimator of the EVI for Pareto-type tails (heavy-tailed) distributions. This is derived using the weighted least squares method. It is shown that the estimator is unbiased, consistent and asymptotically normal under the second-order conditions on the underlying distribution of the data. The finite sample properties of the proposed estimator are studied through a simulation study. The results show that it is competitive to the existing estimators of the extreme value index in terms of bias and Mean Square Error. In addition, it yields estimates of γ > 0 that are less sensitive to the number of top-order statistics, and hence, can be used for selecting an optimal tail fraction. The proposed estimator is further illustrated using practical datasets from pedochemical and insurance.
In this paper, non-life insurance claims were modelled under the three parameter discrete general... more In this paper, non-life insurance claims were modelled under the three parameter discrete generalised Pareto distribution. Data from the National Insurance Commission of Ghana on reported and settled claims were considered for the period 2012-2016. The maximum likelihood estimation principle was adopted in fitting the discrete Pareto distribution to the yearly and aggregated data. The estimation involved two steps. Firstly, the $\mu$ and $(\mu+1)$ frequency method of \citet{Prieto2014} was modified to suit the characteristics of the data under study. Secondly, a bootstrap algorithm was implemented to obtain the standard errors of the estimators of the parameters of the discrete generalised Pareto distribution. The performance of the discrete generalised Pareto distribution is compared to the negative binomial distribution in modelling the non-life insurance claims data using the information criteria of Akaike and Bayesian. The results show that the discrete generalised Pareto distri...
In many statistical problems, several estimators are usually available for interval estimation of... more In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a high coverage probability close to the nominal level and a shorter interval length. However, these two concepts are in opposition to each other: high and low coverages are associated with longer and shorter interval lengths respectively. Some methods, such as bootstrap calibration, modify the nominal level to improve the coverage and thereby allow the selection of intervals based on interval lengths only. Nonetheless, these methods are computationally expensive. In this paper, we propose an index which offers an easy to compute approach of comparing confidence interval estimators based on a compromise between the coverage probability and the confidence interval length. We illustrate that the confidence interval index has range of values within the n...
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Papers by Richard Minkah