Title: The Harris-G power series class of distributions with applications

Authors: Wellington Fredrick Charumbira; Broderick Oluyede; Fastel Chipepa; Lesego Gabaitiri

Addresses: Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana; Department of Applied Mathematics and Statistics, Faculty of Science and Technology, Midlands State University, P. Bag 9055, Gweru, Zimbabwe ' Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana ' Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana ' Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana

Abstract: This study introduces a novel class of distributions (CoD) called the Harris-G power series (H-GPS) CoD. The model is obtained by compounding the Harris-G distribution with the power series distribution (PSD). Some statistical properties including quantile function, linear representation, distribution of order statistics, moments, probability weighted moments and Rényi entropy are developed. Four special cases including the Harris-log-logistic distribution, Harris-log-logistic logarithmic distribution, Harris-Weibull Poisson distribution and the Harris-Weibull logarithmic distribution are presented. Parameter estimation is done using maximum likelihood estimation technique. A simulation study is carried out for the special case of Harris-Weibull Poisson (H-WP) distribution. Finally the Harris-Weibull Poisson is applied to two real datasets to illustrate the usefulness and applicability of the model.

Keywords: Harris-G; power series; generalised distribution; maximum likelihood estimation; MLE; moments; order statistics; entropy.

DOI: 10.1504/IJMOR.2024.142119

International Journal of Mathematics in Operational Research, 2024 Vol.29 No.2, pp.234 - 257

Received: 17 Apr 2023
Accepted: 22 Apr 2023
Published online: 08 Oct 2024 *

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