Title: The Topp-Leone-Marshall-Olkin-G power series class of distributions: properties and applications

Authors: Peter Tinashe Chinofunga; Broderick Oluyede; Fastel Chipepa

Addresses: 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 Computer Science, Faculty of Sciences, Great Zimbabwe University, P. Bag 125, Masvingo, 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

Abstract: This study introduces a new class of distributions known as the Topp-Leone-Marshall-Olkin-G power series (TLMO-GPS) distribution. TLMO-G family of distributions is compounded with the power series distribution to get TLMO-GPS distribution. Some statistical properties including quantile function, linear representation, order statistics, Rényi entropy, moments and probability weighted moments are developed. Parameter estimation is done using maximum likelihood estimation technique. To establish estimates consistency, we perform Monte Carlo simulation. By utilising real life datasets, the merits of a member of the new class of distributions are demonstrated. Thus, the Topp-Leone-Marshall-Olkin-G class of distributions is shown to be useful and applicable to real life data.

Keywords: Topp-Leone; Marshall-Olkin; generalised distributions; power series; moments; maximum likelihood estimation; goodness-of-fit statistics.

DOI: 10.1504/IJMOR.2024.143392

International Journal of Mathematics in Operational Research, 2024 Vol.29 No.4, pp.441 - 462

Received: 23 May 2023
Accepted: 11 Jun 2023
Published online: 17 Dec 2024 *

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