A Study on Zografos-Balakrishnan Log-Normal Distribution

Abstract

In this article, we studied a generalization of the log-normal distribution called Zografos-Balakrishnan log-normal distribution and investigate its various important properties and functions including moments, quantile function, various reliability measures, Rényi entropy, and some inequality measures. The estimation of unknown parameters is discussed by the methods of maximum likelihood, and the Bayesian technique and their simulation studies are also carried out. The applicability of the distribution is illustrated utilizing a real dataset. A likelihood ratio test is utilized for testing the efficiency of the third parameter. The effectiveness of this model for the dataset is also established using the parametric bootstrap approach.

Keywords

• Zografos-Balakrishnan-G family
• reliability measures
• maximum likelihood estimation
• Bayesian estimation
• bootstrap confidence interval
• likelihood ratio test