Modelling the proportions with excessive endpoints based on a generalized Lindley binomial model

Abstract This paper presents the generalized Lindley binomial (GLB) distribution, a novel probability distribution designed for the analysis of proportional data with excessive endpoints. The study delves into the probabilistic characteristics of the GLB distribution, including the probability mass function and the rth factorial moment function. Estimation of the distribution parameters in the GLB model, both with and without covariates, is addressed using the Fisher scoring algorithm and the EM algorithm. Furthermore, the paper explores techniques for model diagnosis and evaluates the goodness of fit for the proposed GLB model. To illustrate the performance of the derived EM algorithms in parameter estimation, a limited simulation study is conducted for both cases, with and without covariates, in the GLB model. The practical application of the proposed Lindley binomial regression model is demonstrated using the whitefly dataset.