A new class of generalized logistic distribution

Abstract

The logistic distribution and the S-shaped pattern of its cumulative distribution and quantile functions have been extensively used in many different spheres affecting human life. By far, the most well-known application of logistic distribution is in the logistic regression that is used for modeling categorical response variables. The exponentiated-exponential logistic distribution, a generalization of the logistic distribution, is obtained using the technique proposed by Alzaatreh et al. (2013) of mixing two distributions, hereafter called the EEL distribution. This distribution subsumes various types of logistic distribution. The structural analysis of the distribution in this paper includes limiting behavior, quantiles, moments, mode, skewness, kurtosis, order statistics, the large sample distributions of the sample maximum and the sample minimum, and the distribution of the sample median. For illustrative purposes, a real-life data set is considered as an application of the EEL distribution.

KEYWORDS:

• Distribution of the sample extremums
• Exponentiated-exponential logistic distribution
• Logistic distribution
• Reliability parameter
• Sample median
• Shannon’s entropy
• T-X families of distributions

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E
• 62F

Acknowledgements

The authors are grateful to the referee and the Editor whose comments and suggestions greatly improved the article.