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 Gao5,*
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.
Keywords
Cite This Article
M. Arif, D. Muhammad Khan, S. Khan Khosa, M. Aamir, A. Aslam
et al., "Modelling insurance losses with a new family of heavy-tailed distributions,"
Computers, Materials & Continua, vol. 66, no.1, pp. 537–550, 2021.
Citations