Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Eliwa, Mohamed S.; Alhussain, Ziyad A.; El-Morshedy, Mahmoud

doi:10.3390/math8030358

Cited by 40 publications

(23 citation statements)

References 35 publications

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“…The first data set contains 64 observations, and it refers to numbers of daily cases in Egypt due to COVID-19 infections from 8 March to 10 May, 2020. The data are: 12,33,7,4,8,13,13,17,16,40,30,14,46,29,9,33,39,36,54,39,41,40,33,47,54,69,86,120,85,103,149,128,110,139,95,145,126,125,160,155,168,171,188,112,189,157,169,232,201,227,215,248,260,226,269,358,298,272,348,388...…”

Section: Applications To Biological Real Datamentioning

confidence: 99%

A New Skewed Discrete Model: Properties, Inference, and Applications

Afify¹,

Elmorshedy²,

Eliwa³

2021

Pak.j.stat.oper.res.

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In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and L- moment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences.

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Section: Applications To Biological Real Datamentioning

confidence: 99%

A New Skewed Discrete Model: Properties, Inference, and Applications

Afify¹,

Elmorshedy²,

Eliwa³

2021

Pak.j.stat.oper.res.

Self Cite

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“… [20] introduced the natural discrete Lindley (NDL), and Eliwa et al. [21] introduced the discrete Gompertz Exponential (DGzEx). Gillariose et al.…”

Section: Introductionmentioning

confidence: 99%

The new discrete distribution with application to COVID-19 Data

et al. 2022

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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).

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“…The authors also studied the new Kumaraswamy-Weibull (NKwW) distribution as a special model of the Kumaraswamy-G family. Eliwa et al [ 16 ] introduced a discrete version of the Gompertz-G family. They also examined some of its distributional and reliability properties and discussed three special models in detail.…”

Section: Introductionmentioning

confidence: 99%

Bayesian and Frequentist Inferences on a Type I Half-Logistic Odd Weibull Generator with Applications in Engineering

Elmorshedy

Alshammari

Tyagi

et al. 2021

Entropy

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In this article, we have proposed a new generalization of the odd Weibull-G family by consolidating two notable families of distributions. We have derived various mathematical properties of the proposed family, including quantile function, skewness, kurtosis, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, probability weighted moments, moments of (reversed) residual lifetime, entropy and order statistics. After producing the general class, two of the corresponding parametric statistical models are outlined. The hazard rate function of the sub-models can take a variety of shapes such as increasing, decreasing, unimodal, and Bathtub shaped, for different values of the parameters. Furthermore, the sub-models of the introduced family are also capable of modelling symmetric and skewed data. The parameter estimation of the special models are discussed by numerous methods, namely, the maximum likelihood, simple least squares, weighted least squares, Cramér-von Mises, and Bayesian estimation. Under the Bayesian framework, we have used informative and non-informative priors to obtain Bayes estimates of unknown parameters with the squared error and generalized entropy loss functions. An extensive Monte Carlo simulation is conducted to assess the effectiveness of these estimation techniques. The applicability of two sub-models of the proposed family is illustrated by means of two real data sets.

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Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Cited by 40 publications

References 35 publications

A New Skewed Discrete Model: Properties, Inference, and Applications

A New Skewed Discrete Model: Properties, Inference, and Applications

The new discrete distribution with application to COVID-19 Data

Bayesian and Frequentist Inferences on a Type I Half-Logistic Odd Weibull Generator with Applications in Engineering

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