New methods to define heavy-tailed distributions with applications to insurance data. Issue 1 (1st January 2020)

• Record Type: Journal Article
• Authors: Ahmad, Zubair; Mahmoudi, Eisa; Hamedani, G. G.; Kharazmi, Omid
• Is Part Of: Journal of Taibah University for science. Volume 14:Issue 1(2020)
• Page Start: 359
• Page End: 382
• Publication Date: 2020-01-01
• Subjects: Weibull distribution -- heavy-tailed distributions -- characterizations -- Monte Carlo simulation -- actuarial measures -- medical care insurance data -- vehicle insurance data -- Bayesian estimation; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1080/16583655.2020.1741942
• Languages: English
• ISSNs: 1658-3655

Abstract

Abstract : 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.