A Comparative Study Between Two Discrete Lindley Distributions

Abstract

The methods to generate a probability function from a probability density function has long been used in recent years. In general, the discretization process produces probability functions that could be alternatives to traditional distributions used in the analysis of count data as geometric, Poisson and negative binomial distributions. The discretization also avoids the use of a continuous distribution in the analysis of strictly discrete data. In this paper, using the method based on an infinite series, proposed by , we studied an alternative discrete Lindley distribution to those studies in Bakouch et al. (2014). For both distributions, a simulation study is carried out to examine the bias and mean squared error for the maximum likelihood estimators of the parameters as well the coverage probability and the length of coverage probability. For the discrete Lindley distribution obtained by infinite series method, we present the analytical expression for bias reduction of the maximum likelihood estimator. Some examples using real data from the literature show the potential of these distributions. Despite the discretization methods are quite different, the resulting distributions are interchangeable, however the distribution generated by an infinite series has simple mathematical expressions and can be used directly to count data in the presence of covariates.

A distribuição Half-Normal generalizada discreta: uma distribuição alternativa na análise de dados de contagem

“…Este método foi proposto por Nakagawa e Osaki (1975) e tem como principal característica a preservação da expressão da função de sobrevivência original em sua parte inteira (Kemp, 2004;Chakraborty, 2015). Alguns exemplos de distribuições discretas geradas por este método são: a distribuição Weibull discreta (Nakagawa e Osaki, 1975), a distribuição Weibull geométrica discreta (Bracquemond e Gaudoin, 2003), a distribuição Gumbel discreta (Chakraborty e Chakravarty, 2014), a distribuição gama discreta (Chakraborty e Chakravarty, 2012), a distribuição Lindley discreta (Gómez-Déniz e Calderín-Ojeda, 2011; Bakouch et al, 2014;Oliveira et al, 2017), a distribuição Rayleigh inversa discreta (Hussain e Ahmad, 2014), a distribuição Weibull inversa discreta (Aghababaei Jazi et al, 2010), a distribuição Maxwell discreta (Krishna e Pundir, 2007), e as distribuições Burr e Pareto discretas (Krishna e Pundir, 2009;.…”