Transmuted power function distribution revisited: simulation study and important lessons on starting values and local maxima

Volume 18, Issue 4, pp 250--258 https://dx.doi.org/10.22436/jnsa.018.04.03

Publication Date: July 11, 2025 Submission Date: April 23, 2025 Revision Date: May 29, 2025 Accteptance Date: June 24, 2025

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Authors

I. C. Geraldo - Laboratoire d’Analyse, de Modélisations Mathématiques et Applications (LAMMA), Département de Mathématiques, Faculté des Sciences, Université de Lomé, 1 B.P. 1515 Lomé 1, Togo.

Abstract

In this paper, we consider the transmuted power function distribution (TPFD), an important flexible distribution with applications in lifetime modelling. In past studies, maximum likelihood (ML) was recommended as the best method to use for estimating the parameters of the TPFD. We study the ML estimation problem from a novel computational angle by making a comprehensive study in R software using some of the best optimization algorithms. This study enables us to draw some important lessons on some of the computational aspects sometimes neglected in solving maximum likelihood estimation problems.

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Keywords

• Numerical optimization
• iterative method
• maximum likelihood
• parameter estimation
• probability distributions

MSC

•  60E05
•  62F10
•  62F30

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