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Some properties and applications of probability distributions based on MacDonald function

Oldřich Kropáč (1982)

Aplikace matematiky

In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types x n K n ( x ) , x 0 , x n K n ( x x ) , x 𝐑 and x n + 1 K n ( x ) , x 0 are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and useful applications...

Some properties of beta functions and the distribution for the product of independent beta random variables.

Giorgio Pederzoli (1985)

Trabajos de Estadística e Investigación Operativa

Products of independent beta random variables appear in a large number of problems in multivariate statistical analysis. In this paper we show how a convenient factorial expansion of gamma ratios can be suitably used in deriving the exact density for a product of independent beta random variables. Possible applications of this result for obtaining the exact densities of the likelihood ratio criteria for testing hypotheses in the multinormal case are also pointed out. For the sake of illustration,...

Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathai, A. (2010)

Fractional Calculus and Applied Analysis

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.Mittag-Leffler functions and their generalizations appear in a large variety of problems in different areas. When we move from total differential equations to fractional equations Mittag-Leffler functions come in naturally. Fractional reaction-diffusion problems in physical sciences and general input-output models in other disciplines are some of the examples in this direction. Some basic properties of Mittag-Leffler functions are...

Some results envolving the concepts of moment generating function and affinity between distribution functions. Extension for r k-dimensional normal distribution functions.

Antonio Dorival Campos (1999)

Qüestiió

We present a function ρ (F1, F2, t) which contains Matusita's affinity and expresses the affinity between moment generating functions. An interesting results is expressed through decomposition of this affinity ρ (F1, F2, t) when the functions considered are k-dimensional normal distributions. The same decomposition remains true for other families of distribution functions. Generalizations of these results are also presented.

Stability of characterizations of distribution functions using failure rate functions

Maia Koicheva, Edward Omey (1990)

Aplikace matematiky

Let λ denote the failure rate function of the d , f . F and let λ 1 denote the failure rate function of the mean residual life distribution. In this paper we characterize the distribution functions F for which λ 1 = c λ and we estimate F when it is only known that λ 1 / λ or λ 1 - c λ is bounded.

Statistical applications of order α - β weighted information energy

María Del Carmen Pardo, Julio A. Pardo (1995)

Applications of Mathematics

A statistic using the concept of order α - β weighted information energy introduced by Tuteja et al. (1992) is considered and its asymptotic distribution in a stratified random sampling is obtained. Some special cases are also discussed.

Statistical aspects of associativity for copulas

José M. González-Barrios (2010)

Kybernetika

In this paper we study in detail the associativity property of the discrete copulas. We observe the connection between discrete copulas and the empirical copulas, and then we propose a statistic that indicates when an empirical copula is associative and obtain its main statistical properties under independence. We also obtained asymptotic results of the proposed statistic. Finally, we study the associativity statistic under different copulas and we include some final remarks about associativity...

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