Open AccessType-I heavy tailed family with applications in medicine, engineering and insurance
Author(s) -
Wei Zhao,
Saima K. Khosa,
Zubair Ahmad,
Muhammad Aslam,
Ahmed Z. Afify
Publication year - 2020
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0237462
Subject(s) - weibull distribution , deviance (statistics) , statistics , deviance information criterion , mathematics , monte carlo method , maximum likelihood , class (philosophy) , computer science , econometrics , markov chain monte carlo , artificial intelligence
In the present study, a new class of heavy tailed distributions using the T- X family approach is introduced. The proposed family is called type-I heavy tailed family. A special model of the proposed class, named Type-I Heavy Tailed Weibull (TI-HTW) model is studied in detail. We adopt the approach of maximum likelihood estimation for estimating its parameters, and assess the maximum likelihood performance based on biases and mean squared errors via a Monte Carlo simulation framework. Actuarial quantities such as value at risk and tail value at risk are derived. A simulation study for these actuarial measures is conducted, proving that the proposed TI-HTW is a heavy-tailed model. Finally, we provide a comparative study to illustrate the proposed method by analyzing three real data sets from different disciplines such as reliability engineering, bio-medical and financial sciences. The analytical results of the new TI-HTW model are compared with the Weibull and some other non-nested distributions. The Baysesian analysis is discussed to measure the model complexity based on the deviance information criterion.