A new family of heavy tailed distributions with an application to the heavy tailed insurance loss data

• Published in: Communications in statistics. Simulation and computation Vol. 51; no. 8; pp. 4372 - 4395
• Main Authors: Ahmad, Zubair, Mahmoudi, Eisa, Dey, Sanku
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03.08.2022; Taylor & Francis Ltd
• Subjects: Actuarial measures; Estimation; Heavy tailed distributions; Insurance; Insurance losses; Maximum likelihood estimators; Monte Carlo simulation; Risk management; Statistical analysis; Statistical models; Weibull distribution
• DOI: 10.1080/03610918.2020.1741623
• ISSN: 0361-0918

Heavy tailed distributions play very significant role in the study of actuarial and financial risk management data but the probability distributions proposed to model such data are scanty. Actuaries often search for new and appropriate statistical models to address data related to financial risk problems. In this work, we propose a new family of heavy tailed distributions. Some basic properties of this new family of heavy tailed distributions are obtained. A special sub-model of the proposed family, called a new heavy tailed Weibull model is considered in detail. The maximum likelihood estimators of the model parameters are obtained. A Monte Carlo simulation study is carried out to evaluate the performance of these estimators. Furthermore, some actuarial measures such as value at risk and tail value at risk are calculated. A simulation study based on these actuarial measures is done. Finally, an application of the proposed model to a heavy tailed insurance loss data set is presented.