A Heavy Tailed Model Based on Power XLindley Distribution with Actuarial Data Applications

Accurately modeling heavy-tailed data is critical across applied sciences, particularly in finance, medicine, and actuarial analysis. This work presents the heavy-tailed power XLindley distribution (HTPXLD), a unique heavy-tailed distribution. Adding one more parameter to the power XLindley distribution improves this new distribution, especially when modeling leptokurtic lifetime data. The suggested density provides greater flexibility with asymmetric forms and different degrees of peakedness. Its statistical features, like the quantile function, moments, extropy measures, incomplete moments, stochastic ordering, and stress-strength parameters, are explored. We further investigate its use in actuarial science through the computation of pertinent metrics, such as value-at-risk, tail value-at-risk, tail variance, and tail variance premium. To obtain the point and interval parameter estimates, we use the maximum likelihood estimation approach. We do many simulation tests to evaluate the performance of our proposed estimator. Metrics like bias, relative bias, mean squared error, root mean squared error, average interval length, and coverage probability will be used in these tests to assess the estimator’s performance. To illustrate the practical value of our proposed model, we apply it to analyze three real-world datasets. We then compare its performance to established competing models, highlighting its advantages.