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

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 pro...

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Vydáno v:Communications in statistics. Simulation and computation Ročník 51; číslo 8; s. 4372 - 4395
Hlavní autoři: Ahmad, Zubair, Mahmoudi, Eisa, Dey, Sanku
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Taylor & Francis 03.08.2022
Taylor & Francis Ltd
Témata:
Actuarial measures
Estimation
Heavy tailed distributions
Insurance
Insurance losses
Maximum likelihood estimators
Monte Carlo simulation
Risk management
Statistical analysis
Statistical models
Weibull distribution
ISSN:0361-0918, 1532-4141
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Shrnutí: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.
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ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2020.1741623