A new two-parameter discrete poisson-generalized Lindley distribution with properties and applications to healthcare data sets

Bivariate Discrete Poisson–Lindley Distributions

“…This distribution was recently introduced by Altun [ 8 ] and is a Poisson mixture when the Poisson parameter follows the new generalized Lindley distribution studied by [ 20 ] with m.g.f. Some properties of this distribution are: …”

“…The main purpose of this paper is to introduce and study two families of bivariate Poisson–Lindley distributions, each with five members, by extending the univariate Poisson–Lindley models examined by [ 4 – 8 ] to the bivariate case. For this purpose, we adopted two widely used procedures, namely the mixing and the generalizing approach.…”

“…3 , bivariate Poisson–Lindley mixtures are derived by assuming that the common parameter in a bivariate Poisson distribution follows a univariate Lindley distribution with one or two parameters. This procedure was used by [ 4 – 8 ] in the univariate case to derive their corresponding Poisson–Lindley models. Furthermore, implementing a characterization theorem proved by Cacoullos and Papageorgiou [ 13 ] relative characterizations are given for the bivariate ( X , Y ) distribution.…”

“…In Sect. 4 , we generalize a bivariate binomial distribution with respect to its exponent, when it follows one of the five univariate Poisson–Lindley distributions derived by [ 4 – 8 ]. Finally, Sect.…”

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

“…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].…”