Some Remarks on the Paper “On the q-type Distributions”

Nair, Seema S.; Kattuveettil, A.

doi:10.1007/978-3-642-03325-4_2

Cited by 2 publications

(1 citation statement)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is to be pointed out here that the superstatistics of Beck and Cohen (2003) and Beck (2006) are available from the procedure given above. It goes without saying that only type-2 beta form as given in ( 2) is available from superstatistics considerations, see Seema Nair & Kattuveettil (2010). The conditional density of the random variable θ, given x is the posterior probability density of θ and is given by…”

Section: Multivariate Generalizationsmentioning

confidence: 99%

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

Sebastian

Nair²,

Joseph³

2015

Axioms

View full text Add to dashboard Cite

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

show abstract

Section: Multivariate Generalizationsmentioning

confidence: 99%

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

Sebastian

Nair²,

Joseph³

2015

Axioms

View full text Add to dashboard Cite

show abstract

An Overview of Generalized Gamma Mittag–Leffler Model and Its Applications

Nair

2015

Axioms

View full text Add to dashboard Cite

Recently, probability models with thicker or thinner tails have gained more importance among statisticians and physicists because of their vast applications in random walks, Lévi flights, financial modeling, etc. In this connection, we introduce here a new family of generalized probability distributions associated with the Mittag-Leffler function. This family gives an extension to the generalized gamma family, opens up a vast area of potential applications and establishes connections to the topics of fractional calculus, nonextensive statistical mechanics, Tsallis statistics, superstatistics, the Mittag-Leffler stochastic process, the Lévi process and time series. Apart from examining the properties, the matrix-variate analogue and the connection to fractional calculus are also explained. By using the pathway model of Mathai, the model is further generalized. Connections to Mittag-Leffler distributions and corresponding autoregressive processes are also discussed.

show abstract

Some Remarks on the Paper “On the q-type Distributions”

Cited by 2 publications

References 6 publications

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

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

An Overview of Generalized Gamma Mittag–Leffler Model and Its Applications

Contact Info

Product

Resources

About