Title: A new heavy-tailed exponentiated generalised-G family of distributions: properties and applications

Authors: Gomolemo Jacqueline Lekono; Broderick Oluyede; Lesego Gabaitiri

Addresses: Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana ' Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana ' Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana

Abstract: In this paper, we introduce a new family of heavy-tailed distributions called the type-I heavy-tailed exponentiated generalised-G (TIHTEG-G) family of distributions. A special model of the proposed family, namely the type-I heavy-tailed exponentiated generalised-log-logistic (TIHTEG-LLoG) model is studied in detail. Statistical properties of the new family of distributions are presented. These include, among others, the hazard rate function, quantile function, moments, distribution of order statistics and Rényi entropy. The maximum likelihood method of estimation is used for estimating the model parameters and Monte Carlo simulation is conducted to examine the performance of the model. Actuarial measures are also derived and simulation study for these measures is done to show that the proposed TIHTEG-LLoG model is a heavy-tailed model. Real datasets are analysed to illustrate the usefulness of the proposed model.

Keywords: heavy-tailed; exponentiated generalised-G; family of distributions; properties; applications; simulation; actuarial measures.

DOI: 10.1504/IJMOR.2024.136860

International Journal of Mathematics in Operational Research, 2024 Vol.27 No.1, pp.1 - 34

Received: 27 Oct 2022
Accepted: 31 Oct 2022
Published online: 23 Feb 2024 *