Open Access

ARTICLE

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

Mohammed Elgarhy¹, Amal S. Hassan², Najwan Alsadat³, Oluwafemi Samson Balogun⁴, Ahmed W. Shawki⁵, Ibrahim E. Ragab^6,*

1 Department of Basic Sciences, Higher Institute of Administrative Sciences, Belbeis, 44621, Egypt
2 Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613, Egypt
3 Department of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh, 11587, Saudi Arabia
4 Department of Computing, University of Eastern Finland, Joensuu, 80130, Finland
5 Central Agency for Public Mobilization & Statistics (CAPMAS), Cairo, 11819, Egypt
6 Department of Basic Sciences, Egyptian Institute of Alexandria Academy for Management and Accounting, EIA, Alexandria, 21919, Egypt

* Corresponding Author: Ibrahim E. Ragab. Email:

Computer Modeling in Engineering & Sciences 2025, 142(3), 2547-2583. https://doi.org/10.32604/cmes.2025.058362

Received 10 September 2024; Accepted 08 February 2025; Issue published 03 March 2025

Abstract

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.

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Keywords

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