On characterizations of the gamma and generalized inverse Gaussian distributions

Chou, Chao-Wei; Huang, Wen-Jang

doi:10.1016/j.spl.2003.11.021

Cited by 21 publications

(18 citation statements)

References 15 publications

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“…It is worth mentioning several related one-dimensional results [3,10] as well as results for random matrices [12,9].…”

Section: Introductionmentioning

confidence: 99%

The Matsumoto–Yor Property and Its Converse on Symmetric Cones

Kołodziejek

2015

J Theor Probab

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The Matsumoto-Yor (MY) property of the generalized inverse Gaussian and gamma distributions has many generalizations. As was observed in Letac and Wesołowski (Ann Probab 28:1371-1383, 2000, the natural framework for the multivariate MY property is symmetric cones; however, they prove their results for the cone of symmetric positive definite real matrices only. In this paper, we prove the converse to the symmetric cone-variate MY property, which extends some earlier results. The smoothness assumption for the densities of respective variables is reduced to continuity only. This enhancement was possible due to the new solution of a related functional equation for real functions defined on symmetric cones.

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“…It is worth mentioning several related one-dimensional results [3,10] as well as results for random matrices [12,9].…”

Section: Introductionmentioning

confidence: 99%

The Matsumoto–Yor Property and Its Converse on Symmetric Cones

Kołodziejek

2015

J Theor Probab

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“…It will be seen that this new distribution is more flexible and is a natural generalization of the IG and the generalized inverse Gaussian (GIG) distributions. It has also been observed that a number of other distributions including those of Chaudhry and Ahmad (1993) and Chou and Huang (2004) are special cases of this distribution. For some discussions on IG and GIG, the interested readers are referred to Jørgensen (1982), Johnson et al (1994), and Chou and Huang (2004), among others.…”

Section: Introductionmentioning

confidence: 94%

“…It has also been observed that a number of other distributions including those of Chaudhry and Ahmad (1993) and Chou and Huang (2004) are special cases of this distribution. For some discussions on IG and GIG, the interested readers are referred to Jørgensen (1982), Johnson et al (1994), and Chou and Huang (2004), among others. In what follows, some characteristics of our newly proposed distribution, including the expressions for the normalizing constant, pdf, cumulative distribution function (cdf), k-th moment, Shannon's entropy and relationships to other probability distributions, are derived.…”

Section: Introductionmentioning

confidence: 94%

A New Family of Distributions Based on the Generalized Pearson Differential Equation with Some Applications

Shakil

Kibria

Singh

2016

AJS

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Recently, a generalization of the Pearson differential equation has appeared in the literature, from which a vast majority of continuous probability density functions (pdf’s) can be generated, known as the generalized Pearson system of continuous probability distributions. This paper derives a new family of distributions based on the generalized Pearson differential equation, which is a natural generalization of the generalized inverse Gaussian distribution. Some characteristics of the new distribution are obtained. Plots for the cumulative distribution function, pdf and hazard function, tables with percentiles and with values of skewness and kurtosis are provided. It is observed that the new distribution is skewed to the right and bears most of the properties of skewed distributions. As a motivation, the statistical applications of the results to a problem of forestry have been provided. It is found that our newly proposed model fits better than gamma, log-normal and inverse Gaussian distributions. Since many researchers have studied the use of the generalized inverse Gaussian distributions in the fields of biomedicine, demography, environmental and ecological sciences, finance, lifetime data, reliability theory, traffic data, etc., we hope the findings of the paper will be useful for the practitioners in various fields of theoretical and applied sciences.

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“…Characterization theorems declare that the existence of a property determines the distribution function, possibly within some family [for more details in characterization theory see, Galambos and Kotz (1978) and Arnold et al (2008)]. Among others, Shanbhag (1970), Telcs et al (1985), Osaki and Li (1988), Nair and Sankaran (1991), Consul (1995), Ahmad (1996), Seshadri and Wesolowski (2001) and Chou and Huang (2004) have characterized some distributions based on conditional moments. Iwase and Hirano (1990) discussed the PIG and its applications.…”

Section: Introductionmentioning

confidence: 99%

“…The PIG has characterized by Kawamura and Iwase (2003). Among others, Latac and Seshadri (1983), Seshadri and Wesolowski (2001) and Chou and Huang (2004) have characterized the GIG [for more details in GIG, see Seshadri (1993)]. Many studies about inverse Gaussian and generalized Gaussian distributions have been carried out in different hypotheses, for examples, Balakrishnan et al (2009) studied the mixture inverse Gaussian distributions and its transformations, moments and applications statistics.…”

Section: Introductionmentioning

confidence: 99%

Characterizations for the Power Inverse Gaussian and Generalized Inverse Gaussian Distributions Based on Conditional Moments

Al-Hossain

2015

Journal of Mathematics and Statistics

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In this study, we characterize the power inverse Gaussian and generalized inverse Gaussian distributions based on recurrence relations for conditional moments in terms of hazard rate functions. Relations for conditional moments of the largest order statistic (upper record value) given the second largest order statistic (upper record value) are derived from these recurrence relations. Characterizations of the inverse Gaussian, reciprocal inverse Gaussian, gamma and reciprocal gamma distributions are obtained as special cases of both the power inverse Gaussian and the generalized inverse Gaussian distributions.

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On characterizations of the gamma and generalized inverse Gaussian distributions

Cited by 21 publications

References 15 publications

The Matsumoto–Yor Property and Its Converse on Symmetric Cones

The Matsumoto–Yor Property and Its Converse on Symmetric Cones

A New Family of Distributions Based on the Generalized Pearson Differential Equation with Some Applications

Characterizations for the Power Inverse Gaussian and Generalized Inverse Gaussian Distributions Based on Conditional Moments

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