Discrete Weibull geometric distribution and its properties

Jayakumar, K.; Babu, M. Girish

doi:10.1080/03610926.2017.1327074

Cited by 17 publications

(10 citation statements)

References 25 publications

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“…DWG distribution (see Jayakumar and Babu [21]) having pmf, and BIC = −2 log L + k log n, where L is the likelihood function evaluated at the maximum likelihood estimates, k is the number of parameters, and n is the sample size. The K − S distance,…”

Section: Applicationmentioning

confidence: 99%

“…By discretizing the continuous distribution, several discrete lifetime distributions are developed in the literature. Some of them are discrete Weibull distribution in Nakagawa and Osaki [2], a second type of discrete Weibull distribution in Stein and Dattero [3], a third type of discrete Weibull distribution in Padgett and Spurrier [4], discrete exponential distribution in Sato et al [5], discrete normal distribution in Roy [6], discrete Rayleigh distribution in Roy [7], discrete Laplace distribution in Inusah and Kozubowski [8], discrete skew-Laplace distribution in Kozubowski and Inusah [9], discrete Burr and discrete Pareto distributions in Krishna and Pundir [10], discrete inverse Weibull distribution in Jazi et al [11], discrete generalized exponential distribution in Gómez-Déniz [12], discrete generalized exponential distribution in Nekoukhou et al [13], discrete gamma distribution in Chakraborty and Chakravarty [14], discrete additive Weibull (AW) distribution in Bebbington et al [15], discrete Lindley distribution in Bakouch et al [16], discrete Gumbel distribution in Chakraborty and Chakravarty [17], exponentiated geometric distribution in Chakraborty and Gupta [18], discrete distribution related to generalized gamma distribution in Chakraborty [19], transmuted geometric distribution in Chakraborty and Bhati [20], discrete Weibull geometric (DWG) distribution in Jayakumar and Babu [21], and so on.…”

Section: Introductionmentioning

confidence: 99%

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Discrete Additive Weibull Geometric Distribution

Jayakumar¹,

Babu²

2019

JSTA

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Discretizing a continuous distribution has received much attention among researchers recently. Discrete analogue of the wellknown continuous distributions such as Normal, Exponential, Weibull, Laplace, Rayleigh, and so on, are available in the literature. In this paper, we introduce a discrete version of the additive Weibull geometric distribution of Elbatal et al. [1]. Discrete Weibull, discrete modified Weibull, discrete Weibull geometric, discrete exponential geometric, discrete Rayleigh distribution, and so on, are sub models of this distribution. We study some properties of the new distribution. The hazard rate function of the new distribution is monotonically increasing or decreasing or bathtub shape based on the values of the shape parameters. The method of maximum likelihood estimation is used for estimating the model parameters. A simulation study is carried out to show the performance of the maximum likelihood estimate of parameters of the new distribution. An application of this distribution to a real data set is also presented.

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Section: Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discrete Additive Weibull Geometric Distribution

Jayakumar¹,

Babu²

2019

JSTA

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“…They discuss several statistical properties and derive discrete analogue of characterization result of continuous logistic distribution. [16] propose weibull-geometric distribution using conditional cdf and study its properties. They discuss discrete Weibull, discrete Rayleigh, and geometric distributions as special cases of their proposed distribution.…”

Section: Introductionmentioning

confidence: 99%

Discretization of the method of generating an expanded family of distributions based upon truncated distributions

et al. 2021

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Discretization translates the continuous functions into discrete version making them more adaptable for numerical computation and application in applied mathematics and computer sciences. In this article, discrete analogues of a generalization method of generating a new family of distributions is provided. Several new discrete distributions are derived using the proposed methodology. A discrete Weibull-Geometric distribution is considered and various of its significant characteristics including moment, survival function, reliability function, quantile function, and order statistics are discussed. The method of Maximum likelihood and the method of moments are used to estimate the model parameters. The performance of the proposed model is probed through a real data set. A comparison of our model with some existing models is also given to demonstrate its efficiency.

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“…In last years a number of researchers worked and introduced some new discrete distributions. Jayakumar and Girish Babu (2017) studies discrete Weibull geometric distribution and its properties.…”

Section: Introductionmentioning

confidence: 99%