The New Exponentiated Half Logistic-Harris-G Family of Distributions with Actuarial Measures and Applications

Gayan Warahena-Liyanage, Broderick Oluyede (), Thatayaone Moakofi and Whatmore Sengweni
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Gayan Warahena-Liyanage: Department of Mathematics, University of Dayton, Dayton, OH 45469, USA
Broderick Oluyede: Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye 10071, Botswana
Thatayaone Moakofi: Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye 10071, Botswana
Whatmore Sengweni: Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye 10071, Botswana

Stats, 2023, vol. 6, issue 3, 1-29

Abstract: In this study, we introduce a new generalized family of distributions called the Exponentiated Half Logistic-Harris-G (EHL-Harris-G) distribution, which extends the Harris-G distribution. The motivation for introducing this generalized family of distributions lies in its ability to overcome the limitations of previous families, enhance flexibility, improve tail behavior, provide better statistical properties and find applications in several fields. Several statistical properties, including hazard rate function, quantile function, moments, moments of residual life, distribution of the order statistics and Rényi entropy are discussed. Risk measures, such as value at risk, tail value at risk, tail variance and tail variance premium, are also derived and studied. To estimate the parameters of the EHL-Harris-G family of distributions, the following six different estimation approaches are used: maximum likelihood (MLE), least-squares (LS), weighted least-squares (WLS), maximum product spacing (MPS), Cramér–von Mises (CVM), and Anderson–Darling (AD). The Monte Carlo simulation results for EHL-Harris-Weibull (EHL-Harris-W) show that the MLE method allows us to obtain better estimates, followed by WLS and then AD. Finally, we show that the EHL-Harris-W distribution is superior to some other equi-parameter non-nested models in the literature, by fitting it to two real-life data sets from different disciplines.

Keywords: Harris-G; heavy-tailed; generalized distribution; actuarial measures; maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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