A generalized gamma model associated with a Bessel function

Sebastian, Nicy

doi:10.1080/10652469.2010.536413

Cited by 13 publications

(15 citation statements)

References 8 publications

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“…Thus if we are looking for a gamma type density but with a thinner tail then one from this family may be appropriate for δ < 0. For more details of the model in (11), see [31] and [33]. When q → 1 − , η = 1 and replace f (t) by t β−1 0 F 1 ( ; β; δt) in pathway fractional integral operator then we are essentially dealing with distribution functions under a gamma Bessel type model in a practical statistical problem.…”

Section: Limiting Approach To Generalized Gamma Bessel Model Via Pathmentioning

confidence: 99%

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Limiting Approach to Generalized Gamma Bessel Model via Fractional Calculus and Its Applications in Various Disciplines

Sebastian

2015

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The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one can list out almost all the extended densities for the pathway parameter q < 1 and q → 1. Here we bring out the idea of thicker or thinner tailed models associated with a gamma type distribution as a limiting case of pathway operator. Applications of this extended gamma model in Statistical Mechanics, input-output models, and solar spectral irradiance modeling etc are established.

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Section: Limiting Approach To Generalized Gamma Bessel Model Via Pathmentioning

confidence: 99%

“…Also I 11 is the special case of reaction rate probability integral in nuclear reaction rate theory, Krätzel integrals in applied analysis etc (see [11], [15], [17], [18]). For the evaluation of this integral and for more details see [31] and [33]. Hence we have the unconditional density…”

Section: Applications In Statistical Mechanicsmentioning

confidence: 99%

Limiting Approach to Generalized Gamma Bessel Model via Fractional Calculus and Its Applications in Various Disciplines

Sebastian

2015

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“…Computational limitations within the Bayesian framework also no longer present a problem to analysing any data set with complex prior assumptions; a generalised prior can therefore be handled with ease in Bayesian inference. As with this prior it is desirable, as mention by Sebastian [6], to consider priors that exhibit flexibility regarding the shape of their tails.…”

Section: Introductionmentioning

confidence: 99%

A gamma-mixture class of distributions with Bayesian application

Niekerk

Bekker

Arashi

2017

Communications in Statistics - Simulation and Computation

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In this paper a subjective Bayesian approach is followed to derive estimators for the parameters of the normal model by assuming a gamma-mixture class of prior distributions, that includes the gamma and the noncentral gamma as special cases. An innovative approach is proposed to find the analytical expression of the posterior density function when a complicated prior structure is ensued. The simulation studies and a real dataset illustrates the modeling advantages of this proposed prior and support some of the findings.

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“…Note that in both the cases, when α → 1, we have Equation (25) and hence it can be considered to be an extended form of Equation (25). This model has wide potential applications in the discipline physical science especially in statistical mechanics, see [27,28]. For fixed values of γ = 2, ρ = 1.2 and a = 1, we can look at the graphs for δ = −0.5, q < 1, δ = 0.5, q < 1 as well as for δ = −0.5, q > 1, δ = 0.5, q > 1.…”

Section: α-Gamma Models Associated With Bessel Functionmentioning

confidence: 99%

“…We can extend the thermonuclear functions given in Equations (28) and (29) to more general classes by replacing e −bx −ρ by 13,34,35]). Thus we consider the general class of reaction rate integrals…”

Section: Extension Of Thermonuclear Functions Through Pathway Modelmentioning

confidence: 99%

An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences

Sebastian

Nair²,

Joseph³

2015

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Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter α, called the pathway parameter, one can connect generalized type-1 beta family of densities, generalized type-2 beta family of densities, and generalized gamma family of densities, in the scalar as well as the matrix cases, also in the real and complex domains. It is shown that when the model is applied to physical situations then the current hot topics of Tsallis statistics and superstatistics in statistical mechanics become special cases of the pathway model, and the model is capable of capturing many stable situations as well as the unstable or chaotic neighborhoods of the stable situations and transitional stages. The pathway model is shown to be connected to generalized information measures or entropies, power law, likelihood ratio criterion or λ−criterion in multivariate statistical analysis, generalized Dirichlet densities, fractional calculus, Mittag-Leffler stochastic process, Krätzel integral in applied analysis, and many other topics in different disciplines. The pathway model enables one to extend the current results on quadratic and bilinear forms, when the samples come from Gaussian populations, to wider classes of populations.Axioms 2015, 4 531

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A generalized gamma model associated with a Bessel function

Cited by 13 publications

References 8 publications

Limiting Approach to Generalized Gamma Bessel Model via Fractional Calculus and Its Applications in Various Disciplines

Limiting Approach to Generalized Gamma Bessel Model via Fractional Calculus and Its Applications in Various Disciplines

A gamma-mixture class of distributions with Bayesian application

An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences

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