Transmuted logistic-exponential distribution - some new properties, estimation methods and application with infectious disease mortality data

TL;DR

This paper introduces the new Transmuted Logistic-Exponential (NTLE) distribution, explores its properties, compares estimation methods through simulations, and demonstrates its superior fit to infectious disease mortality data over related distributions.

Contribution

The paper derives key properties of NTLE, evaluates multiple estimation methods, and applies the distribution to real data, enhancing its practical utility and understanding.

Findings

NTLE outperforms exponential and logistic-exponential distributions in data fitting.

Multiple estimation methods are compared, identifying the most accurate for NTLE.

Derived properties include entropy, stochastic ordering, and reliability measures.

Abstract

Lately, a New Transmuted Logistic-exponential (NTLE) distribution was introduced and studied as an extension of the Logistic-Exponential Distribution (LED) with wider applicability in lifetime modelling. However, the maximum likelihood estimates (MLE) of NTLE are not in closed form, and the consistency of the estimates was not examined. Furthermore, some other important properties of NTLE, namely the Shannon entropy, R\'enyi entropy, stochastic ordering, mode, stress-strength reliability measure, residual life functions (mean and reverse), incomplete moments, Bonferroni and Lorenz curves are yet to be derived. Motivated by this, we derived and studied these important properties and evaluated the performance of ten estimation methods (Maximum Likelihood, Moments, Least Squares, Weighted Least Squares, Maximum product of Spacings, Anderson-Darling, Cramer-von Mises, percentile estimation, and Maximum Goodness-of-Fit methods) for NTLE parameters via Monte Carlo simulation using bias, mean square error, and root mean square error as evaluation criteria. Real-life infectious mortality data fitted to the distributions showed that NTLE has a better fit compared to its base distributions (Exponential and Logistic-Exponential). This finding contributes valuable insights for researchers and practitioners when selecting the appropriate estimation methods, especially for NTLE and some similar distributions in non-closed form.