Modelling and Reliability Analysis of the Two-Parameter Lindley-Binomial Distribution

Abstract

The primary purpose of this research is to describe the two-parameter Lindley Binomial (LB2) distribution, a newprobability distribution applicable for the proportion data analysis, specifically in the simulation, real data, and reliability analysis setting. The shape of probability mass function and some probabilistic properties of the proposed distribution, including generating functions are derived. The method of moment, maximum likelihood estimation, and the expectation maximization algorithm are used for parameter estimation. Goodness of fit of the proposed distribution is assessed by using it on a real dataset. This research also investigates the age-specific prevalence and risk pattern of Hepatitis B virus (HBV) infected within the dataset. It is compared with the binomial, beta-binomial, and negative binomial distributions for its performance. The results show that the proposed distribution has some advantages over previous models and therefore is advantageous in analyzing proportional data. Additionally, the two-parameter Lindley Binomial distribution is fit to the data to evaluate the reliability function, hazard rate function, inverted hazard rate function, and mean residual life (MRL) by age group. The findings demonstrate substantial differences of HBV positive between various age demographics with great public health implications