New methods to define heavy-tailed distributions with applications to insurance data

被引：54

作者：

Ahmad, Zubair ^{[1
]}

Mahmoudi, Eisa ^{[1
]}

Hamedani, G. G. ^{[2
]}

Kharazmi, Omid ^{[3
]}

机构：

[1] Yazd Univ, Dept Stat, POB 89175-741, Yazd, Iran

[2] Marquette Univ, Dept Math & Stat Sci, Milwaukee, WI 53233 USA

[3] Vali E Asr Univ Rafsanjan, Dept Stat, Fac Sci, Rafsanjan, Iran

来源：

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE | 2020年 / 14卷 / 01期

关键词：

Weibull distribution; heavy-tailed distributions; characterizations; Monte Carlo simulation; actuarial measures; medical care insurance data; vehicle insurance data; Bayesian estimation; FITTING INSURANCE; FINITE MIXTURES; FAMILY;

D O I：

10.1080/16583655.2020.1741942

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Heavy-tailed distributions play an important role in modelling data in actuarial and financial sciences. In this article, nine new methods are suggested to define new distributions suitable for modelling data with an heavy right tail. For illustrative purposes, a special sub-model is considered in detail. Maximum likelihood estimators of the model parameters are obtained and a Monte Carlo simulation study is carried out to assess the behaviour of the estimators. Furthermore, some actuarial measures are calculated. A simulation study based on these actuarial measures is done. The usefulness of the proposed model is proved empirically by means of two real data sets. Finally, Bayesian analysis and performance of Gibbs sampling for the data sets are also carried out.

引用

页码：359 / 382

页数：24

共 33 条

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