Another generalization of the geometric distribution

Gómez–Déniz, Emilio

doi:10.1007/s11749-009-0169-3

Cited by 99 publications

(45 citation statements)

References 26 publications

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“…This family is defined by adding a parameter to a baseline distribution, giving more flexibility to model various type of data. In the last few years, several authors proposed Marshall-Olkin models to extend well-known distributions (see, for example, , Zhang and Xie 2007, Ristic´ et al 2007, Ghitany and Kotz 2007, Gómez-Déniz 2010. In this article, we derive various structural properties of the Marshall-Olkin extended-F distribution not explored before including simple expansions for the density function and explicit expressions for the moments, moments of the order statistics and Rénvy entropy.…”

Section: Discussionmentioning

confidence: 97%

General results for the Marshall and Olkin's family of distributions

Barreto‐Souza

Lemonte

Cordeiro

2013

An. Acad. Bras. Ciênc.

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Marshall and Olkin (1997) introduced an interesting method of adding a parameter to a wellestablished distribution. However, they did not investigate general mathematical properties of their family of distributions. We provide for this family of distributions general expansions for the density function, explicit expressions for the moments and moments of the order statistics. Several especial models are investigated. We discuss estimation of the model parameters. An application to a real data set is presented for illustrative purposes.

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Section: Discussionmentioning

confidence: 97%

General results for the Marshall and Olkin's family of distributions

Barreto‐Souza

Lemonte

Cordeiro

2013

An. Acad. Bras. Ciênc.

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“…In addition, the EGG distribution reduces to the GG distribution when γ = 1. Several properties of the GG(α, θ) distribution are obtained for the case 0 < α < 1; see [6]. We will study several properties of the EGG(α, θ, γ) distribution in this case.…”

Section: Three-parameter Egg Distributionmentioning

confidence: 96%

Exponentiated generalized geometric distribution: A new discrete distribution

Bidram¹,

Roozegar²,

Nekoukhou³

2015

HJMS

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In this paper, a new three-parameter extension of the generalized geometric distribution of [6] is introduced. The new discrete distribution belongs to the resilience parameter family and handles a decreasing, increasing, upside-down and bathtub-shaped hazard rate function. The new distributions can also be considered as discrete analogs of some recent continuous distributions belonging to the known Marshall-Olkin family. Here, some basic statistical and mathematical properties of the new distribution are studied. In addition, estimation of the unknown parameters, a simulated example and an application of the new model are illustrated.

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“…This data set in which considers the results of ten shots fired from a rifle at each of 100 targets has been displayed in Table 3. Gómez-Déniz (2010) used these data in order to study its generalization of the geometric distribution. Here, we compare the capacity of the DBR distribution with some of its rival models in discrete data modeling.…”

Section: Applicationmentioning

confidence: 99%

“…In addition, the two-parameter discrete generalized exponential distribution of a second type (DGE 2 ) of Nekoukhou et al (2013) which is a generalization of the geometric distribution, p y = (1 − p)p y , is also fitted to these data. The EDW distribution and its special case, GDR distribution, and also generalized geometric (GG) distribution of Gómez-Déniz (2010) are other rival models. The distributions in Table 4 are considered, briefly, in the Appendix.…”

Section: Applicationmentioning

confidence: 99%

The Beta-Rayleigh Distribution on the Lattice of Integers

Nekoukhou¹

2016

JSRI

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Abstract. In this paper, a discrete analog of the beta-Rayleigh distribution is studied. This new distribution contains the generalized discrete Rayleigh and discrete Rayleigh distributions as special sub-models. Some distributional and moment properties of the new discrete distribution as well as its order statistics are discussed. We will see that the hazard rate function of the new model can be increasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and, finally, the model with a real data set is examined.

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Another generalization of the geometric distribution

Abstract: Branching process, Discretizing, Failure rate, Fitting, Geometric distribution, 60E05, 62E99, 60J80,

Cited by 99 publications

References 26 publications

General results for the Marshall and Olkin's family of distributions

General results for the Marshall and Olkin's family of distributions

Exponentiated generalized geometric distribution: A new discrete distribution

The Beta-Rayleigh Distribution on the Lattice of Integers

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