The heavy-tailed distributions are very useful and play a major role in actuary and financial management problems.Actuaries are often searching for such distributions to provide the best fit to financial and economic ...The heavy-tailed distributions are very useful and play a major role in actuary and financial management problems.Actuaries are often searching for such distributions to provide the best fit to financial and economic data sets.In the current study,a prominent method to generate new distributions useful for modeling heavy-tailed data is considered.The proposed family is introduced using trigonometric function and can be named as the Arcsine-X family of distri-butions.For the purposes of the demonstration,a specific sub-model of the proposed family,called the Arcsine-Weibull distribution is considered.The max-imum likelihood estimation method is adopted for estimating the parameters of the Arcsine-X distributions.The resultant estimators are evaluated in a detailed Monte Carlo simulation study.To illustrate the Arcsine-Weibull two insurance data sets are analyzed.Comparison of the Arcsine-Weibull model is done with the well-known two parameters and four parameters competitors.The competitive models including the Weibull,Lomax,Burr-XII and beta Weibull models.Different goodness of fit measures are taken into account to determine the useful-ness of the Arcsine-Weibull and other considered models.Data analysis shows that the Arcsine-Weibull distribution works much better than competing models in financial data analysis.展开更多
文摘The heavy-tailed distributions are very useful and play a major role in actuary and financial management problems.Actuaries are often searching for such distributions to provide the best fit to financial and economic data sets.In the current study,a prominent method to generate new distributions useful for modeling heavy-tailed data is considered.The proposed family is introduced using trigonometric function and can be named as the Arcsine-X family of distri-butions.For the purposes of the demonstration,a specific sub-model of the proposed family,called the Arcsine-Weibull distribution is considered.The max-imum likelihood estimation method is adopted for estimating the parameters of the Arcsine-X distributions.The resultant estimators are evaluated in a detailed Monte Carlo simulation study.To illustrate the Arcsine-Weibull two insurance data sets are analyzed.Comparison of the Arcsine-Weibull model is done with the well-known two parameters and four parameters competitors.The competitive models including the Weibull,Lomax,Burr-XII and beta Weibull models.Different goodness of fit measures are taken into account to determine the useful-ness of the Arcsine-Weibull and other considered models.Data analysis shows that the Arcsine-Weibull distribution works much better than competing models in financial data analysis.
