Type I heavy-tailed family of generalized Burr III distributions: properties, actuarial measures, regression and applications

Wilbert Nkomo; Broderick Oluyede; Fastel  Chipepa

doi:https://doi.org/10.59139/stattrans-2025-006

Type I heavy-tailed family of generalized Burr III distributions: properties, actuarial measures, regression and applications

Wilbert Nkomo Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Botswana & Department of Applied Statistics, Manicaland State University of Applied Sciences, Zimbabwe ORCID:https://orcid.org/0009-0006-0277-3981 , Broderick Oluyede Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Botswana ORCID:https://orcid.org/0000-0002-9945-2255 , Fastel Chipepa Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Botswana ORCID:https://orcid.org/0000-0001-6854-8740 Statistics in Transition new series, vol. 26, 2025, 1, pages: 93-115 Published online: 10 March 2025 https://doi.org/10.59139/stattrans-2025-006 Citation: Nkomo W., Oluyede B., Chipepa F., 2025. Type I heavy-tailed family of generalized Burr III distributions: properties, actuarial measures, regression and applications. Statistics in Transition new series, 26(1), pp. 93-115. https://doi.org/10.59139/stattrans-2025-006

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ABSTRACT

This study introduces a new family of distributions (FoD) called type I heavy-tailed odd Burr III-G (TI-HT-OBIII-G) distribution. Several statistical properties of the family are derived along with actuarial risk measures. The maximum likelihood estimation (MLE) approach is adopted in the parameter estimation process. The estimates are evaluated centered on mean square errors and average bias via the Monte Carlo simulation framework. A regression model is formulated and the residual analysis is investigated. Members of the new FoD are applied to heavy-tailed data sets and compared to some well-known competing heavytailed distributions. The practicality, flexibility and importance of the new distribution in modeling is empirically proven using three data sets.

KEYWORDS

type I heavy-tailed-G, odd Burr III-G, parameter estimation, regression, actuarial measures.

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