The new discrete distribution with application to COVID-19 Data

Abstract

This research aims to model the COVID-19 in different countries, including Italy, Puerto Rico, and Singapore. Due to the great applicability of the discrete distributions in analyzing count data, we model a new novel discrete distribution by using the survival discretization method. Because of importance Marshall- Olkin family and the inverse Toppe-Leone distribution, both of them were used to introduce a new discrete distribution called Marshall–Olkin inverse Toppe-Leone distribution, this new distribution namely the new discrete distribution called discrete Marshall- Olkin Inverse Toppe-Leone (DMOITL). This new model posses only two parameters, also many properties have been obtained such as reliability measures and moment functions. The classical method as likelihood method and Bayesian estimation methods are applied to estimate the unknown parameters of DMOITL distributions. The Monte–Carlo simulation procedure is carried out to compare the maximum likelihood and Bayesian estimation methods. The highest posterior density (HPD) confidence intervals are used to discuss credible confidence intervals of parameters of new discrete distribution for the results of the Markov Chain Monte Carlo technique (MCMC).

Generating Optimal Discrete Analogue of the Generalized Pareto Distribution under Bayesian Inference with Applications

“…Table 4 summarizes the values of goodness-of-fit measures when comparing the DGPD with nine different discrete models, including those with one, two, and three parameters. The competitive models are discrete Marshal Olkin inverted Topp-Leone (DMOITL), which is introduced in [37], Discrete Burr (DB), which is introduced in [38], discrete Weibull (DW), which is introduced in [39], discrete inverse Weibull (DIW), which is obtained in [40], negative binomial NB in [41], Poisson, discrete generalized exponential (DGE), which is introduced in [42], discrete alpha power inverse Lomax (DAPIL) in [19], and discrete Lindley (DL) in [43].…”

“…These data comprise daily new deaths. The data are as follows: 52, 26, 36, 63, 52, 37,35,28,17,21,31,30,10,56,40,14,28,42,24,21,28,22,12,31,24,14,13,25,12,7,13,20,23,9,11,13,3,7,10,21,15,17,5,7,22,24,15,19,18,16,5,20,27. The data are available on the Worldometer website at [36].…”

A Generalized Form of Power Transformation on Exponential Family of Distribution with Properties and Application

“…The second data set is the survival times of 72 guinea pigs which are observed and reported by Elbatal et al (2013). The third data sets represent the COVID-19 data set from Italy, recorded between 13 June and 12 August 2021, studied by Almetwally et al [2022]. The observed data sets are presented below: First Data set: 1 ,4 ,4 ,7, 11, 13, 15, 15, 17, 18, 19, 19, 20, 20, 22, 23, 28, 29, 31, 32, 36, 37, 47, 48, 49, 50, 54, 54, 55, 59, 59, 61, 61, 66, 72, 72, 75, 78, 78, 81, 93, 96, 99, 108, 113, 114 ,120, 120, 120, 123, 124, 129, 131, 137, 145, 151, 156, 171, 176, 182, 188, 189, 195, 203, 208, 215, 217, 217, 217, 224, 228, 233, 255, 271, 275, 275, 275, 286, 291, 312, 312, 312, 315, 326, 326, 329, 330, 336, 338 ,345, 348, 354, 361, 364, 369, 378, 390, 457, 467, 498 17,21,31,30,10,56,40,14,28,42,24,21,28,22,12,31,24,14,13,25,12,7,13,20,23,9,11,13,3,7,10,21,15,17,5,7,22,24,15,19,18,…”

Information Approach for Change Point Analysis of EGGAPE Distribution and Application to COVID-19 Data

“…e parameter estimates for a, b, α, λ are obtained by equating equations ( 22)- (25) to zero and solving the system of nonlinear equations.…”

“…In this section, we introduced application to COVID-19 data for Italy, UK, and Mexico. More studies analyzed COVID-19 data [17,[23][24][25][26][27][28][29][30].…”