The McDonald half-logistic distribution: Theory and practice

Abstract

Generalizing lifetime distributions is always precious for applied statisticians. We define and study a new continuous model called the McDonald half-logistic distribution to generalize the half-logistic distribution. The new model is quite flexible to analyze positive data. In fact, it can provide better fits than the classical generalized gamma (Stacy, 1992) and exponentiated Weibull (Mudholkar and Srivastava, 1993) models, all of them with the same number of parameters. Explicit expressions for the ordinary and incomplete moments, mean deviations, generating, and quantile functions and Rényi entropy are derived. The estimation of the model parameters is performed by maximum likelihood. The potentiality of the new model is illustrated by means of a real data set. The new distribution can be used as an alternative model to other well-known distributions for modeling positive real data in many areas.

Keywords:

• Entropy
• Exponentiated distribution
• Half-Logistic distribution
• Maximum likelihood
• Mean deviation
• mcDonald-G distribution

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E10
• 65C05