Open Access

ARTICLE

Modelling Insurance Losses with a New Family of Heavy-Tailed Distributions

Muhammad Arif¹, Dost Muhammad Khan¹, Saima Khan Khosa², Muhammad Aamir¹, Adnan Aslam³, Zubair Ahmad⁴, Wei Gao^5,*

1 Department of Statistics, Abdul Wali Khan University, Mardan, 23200, Pakistan
2 Department of Statistics, Bahauddin Zakariya University, Multan, 60800, Pakistan
3 Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore, 54000, Pakistan
4 Department of Statistics, Yazd University, Yazd, 89175-741, Iran
5 School of Information Science and Technology, Yunnan Normal University, Kunming, 650500, China

* Corresponding Author: Wei Gao. Email:

Computers, Materials & Continua 2021, 66(1), 537-550. https://doi.org/10.32604/cmc.2020.012420

Received 30 June 2020; Accepted 05 August 2020; Issue published 30 October 2020

Abstract

The actuaries always look for heavy-tailed distributions to model data relevant to business and actuarial risk issues. In this article, we introduce a new class of heavy-tailed distributions useful for modeling data in financial sciences. A specific sub-model form of our suggested family, named as a new extended heavy-tailed Weibull distribution is examined in detail. Some basic characterizations, including quantile function and raw moments have been derived. The estimates of the unknown parameters of the new model are obtained via the maximum likelihood estimation method. To judge the performance of the maximum likelihood estimators, a simulation analysis is performed in detail. Furthermore, some important actuarial measures such as value at risk and tail value at risk are also computed. A simulation study based on these actuarial measures is conducted to exhibit empirically that the proposed model is heavy-tailed. The usefulness of the proposed family is illustrated by means of an application to a heavy-tailed insurance loss data set. The practical application shows that the proposed model is more flexible and efficient than the other six competing models including (i) the two-parameter models Weibull, Lomax and Burr-XII distributions (ii) the three-parameter distributions Marshall-Olkin Weibull and exponentiated Weibull distributions, and (iii) a well-known four-parameter Kumaraswamy Weibull distribution.

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