A new asymmetric extended family: Properties and estimation methods with actuarial applications

In the present work, a class of distributions, called new extended family of heavy-tailed distributions is introduced. The special sub-models of the introduced family provide unimodal, bimodal, symmetric, and asymmetric density shapes. A special sub-model of the new family, called the new extended heavy-tailed Weibull (NEHTW) distribution, is studied in more detail. The NEHTW parameters have been estimated via eight classical estimation procedures. The performance of these methods have been explored using detailed simulation results which have been ordered, using partial and overall ranks, to determine the best estimation method. Two important risk measures are derived for the NEHTW distribution. To prove the usefulness of the two actuarial measures in financial sciences, a simulation study is conducted. Finally, the flexibility and importance of the NEHTW model are illustrated empirically using two real-life insurance data sets. Based on our study, we observe that the NEHTW distribution may be a good candidate for modeling financial and actuarial sciences data.

Automated summary

In this study, a new extended family of heavy-tailed distributions is introduced, and a specific sub-model called NEHTW distribution is studied in detail. The performance of parameter estimation methods and two risk measures for NEHTW distribution are evaluated using simulation experiments. The empirical results demonstrate that NEHTW distribution is suitable for modeling financial and actuarial sciences data.