The McDonald Lindley-Poisson Distribution

Abstract

We propose the McDonald Lindley-Poisson distribution and derive some of its mathematical properties including explicit expressions for moments, generating and quantile functions, mean deviations, order statistics and their moments. Its model parameters are estimated by maximum likelihood. A simulation study investigates the performance of the estimates. The new distribution represents a more flexible model for lifetime data analysis than other existing models as proved empirically by means of two real data sets.

Discrete Extension of Poisson Distribution for Overdispersed Count Data: Theory and Applications

“…Tis data set was reported by Karlis and Xekalaki [26]. Te data observations are as follows: rep(0, 16), rep (1,13), rep (2,14), rep (3,9), rep (4,11), rep (5,13), rep (6,8), rep (7,4), rep(8, 9), rep (9,6), rep (10,3), rep (11,4), rep (12,6), rep (15,4), rep(16, 1), rep(20, 1), and rep(43, 1). Te extremes and outliers are spotted from the box and violin plots in Figure 9, and it is found that some extreme and outlier observations were reported.…”

“…Compounding a discrete probability distribution continuously is a useful approach for developing fexible distributions to analyze the overdispersed count data sets. In statistical literature, many distributions have been proposed, studied, and used for modeling of overdispersed count observations, such as Poisson Lindley [1], discrete Weibull [2], discrete Burr and Pareto [3], discrete inverse Weibull [4], discrete Lindley [5], discrete Poisson xgamma [6], Poisson Ailamujia [7], discrete Burr-Hatke [8], discrete Bilal [9], exponentiated discrete Lindley [10], discrete Type-IIhalf-logistic exponential [11], discrete inverted Topp-Leone [12] and discrete Ramus-Louzada [13], twoparameter discrete Poisson-generalized Lindley [14], McDonald Lindley-Poisson [15], Poisson-modifcation of quasi Lindley [16], Poisson XLindley [17], discrete power Ailamujia [18], discrete moment exponential [19], Poisson moment exponential [20], and discrete exponential generalized-G class [21].…”

A Study on One-Parameter Entropy-Transformed Exponential Distribution and Its Application

“…Considerable efforts have been done to construct new distributions for survival data. However, there still remain many problems involving real data, which are not contemplated by existing probability models (Percontini, Gomes-Silva, da Silva and Handique, 2021). Suppose a random variable c follow an exponential distribution and its probability density function (P.D.F) and cumulative distribution function (C.D.F) are given by; f (c) = φe −φc and F (c) = 1 − e −φc , for all c ≥ 0 and φ > 0…”