@Article{cmc.2020.012420,
AUTHOR = {Muhammad Arif, Dost Muhammad Khan, Saima Khan Khosa, Muhammad Aamir, Adnan Aslam, Zubair Ahmad, Wei Gao},
TITLE = {Modelling Insurance Losses with a New Family of Heavy-Tailed Distributions},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {66},
YEAR = {2021},
NUMBER = {1},
PAGES = {537--550},
URL = {http://www.techscience.com/cmc/v66n1/40463},
ISSN = {1546-2226},
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.},
DOI = {10.32604/cmc.2020.012420}
}