Journal of Statistical Theory and Applications

Volume 19, Issue 2, June 2020, Pages 133 - 147

Modeling Vehicle Insurance Loss Data Using a New Member of T-X Family of Distributions

Authors
Zubair Ahmad1, Eisa Mahmoudi1, *, Sanku Dey2, Saima K. Khosa3
1 Department of Statistics, Yazd University, Yazd, Iran
2 Department of Statistics, St. Anthonys College, Shillong, India
3 Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan
*Corresponding author. Email: emahmoudi@yazd.ac.ir
Corresponding Author
Eisa Mahmoudi
Received 16 October 2019, Accepted 14 January 2020, Available Online 28 May 2020.
DOI
https://doi.org/10.2991/jsta.d.200421.001How to use a DOI?
Keywords
Heavy-tailed distributions, Weibull distribution, Insurance losses, Actuarial measures, Monte Carlo simulation, Estimation
Abstract

In actuarial literature, we come across a diverse range of probability distributions for fitting insurance loss data. Popular distributions are lognormal, log-t, various versions of Pareto, log-logistic, Weibull, gamma and its variants and a generalized beta of the second kind, among others. In this paper, we try to supplement the distribution theory literature by incorporating the heavy tailed model, called weighted T-X Weibull distribution. The proposed distribution exhibits desirable properties relevant to the actuarial science and inference. Shapes of the density function and key distributional properties of the weighted T-X Weibull distribution are presented. Some actuarial measures such as value at risk, tail value at risk, tail variance and tail variance premium are calculated. A simulation study based on the actuarial measures is provided. Finally, the proposed method is illustrated via analyzing vehicle insurance loss data.

Copyright
© 2020 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
19 - 2
Pages
133 - 147
Publication Date
2020/05
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.d.200421.001How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Zubair Ahmad
AU  - Eisa Mahmoudi
AU  - Sanku Dey
AU  - Saima K. Khosa
PY  - 2020
DA  - 2020/05
TI  - Modeling Vehicle Insurance Loss Data Using a New Member of T-X Family of Distributions
JO  - Journal of Statistical Theory and Applications
SP  - 133
EP  - 147
VL  - 19
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.200421.001
DO  - https://doi.org/10.2991/jsta.d.200421.001
ID  - Ahmad2020
ER  -