Poisson Xgamma distribution: A discrete model for count data analysis

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

“…Te dataset is reported in [24]. Te data observations are: 1,5,6,11,12,19,20,22,23,31,37,46,54,60, and 66. Some basic descriptive measures (mean, variance, and dispersion index) are 27.533, 431.98, and 15.689, respectively.…”

“…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].…”

Poisson XLindley Distribution for Count Data: Statistical and Reliability Properties with Estimation Techniques and Inference

“…Rashid [ 4 ] introduced a count data model that combines the negative binomial and Kumaraswamy distributions and used it for modeling biological data sets. Some more discrete distributions are Poisson–Ishita distribution by Hassan et al [ 5 ]; Poisson–Ailamujia distribution by Hassan et al [ 6 ]; Poisson Xgamma distribution by Para et al [ 7 ]; Poisson quasi-Lindley distribution by Grine and Zeghdoudi [ 8 ]; discrete Gompertz-G family by Eliwa et al [ 9 ]; discrete extension to three-parameter Lindley model by Eliwa et al [ 10 ]; two-parameter exponentiated discrete Lindley distribution by El-Morshedy et al [ 11 ]; Eliwa and El-Morshedy [ 12 ]; discrete Burr–Hatke distribution by El-Morshedy et al [ 13 ]; discrete Weibull Marshall–Olkin family by Gillariose et al [ 14 ]; and discrete Ramos–Louzada model by Eldeeb et al [ 15 ].…”