Theory of Barnes Beta distributions

Theory of Barnes Beta distributions

A new family of probability distributions βM,N , M = 0 · · ·N, N ∈ N on the unit interval (0, 1] is defined by the Mellin transform. The Mellin transform of βM,N is characterized in terms of products of ratios of Barnes multiple gamma functions, shown to satisfy a functional equation, and a Shintani-type infinite product factorization. The distribution log βM,N is infinitely divisible. If M < N...

Contributions to the Theory of the Barnes Function

This paper presents a family of new integral representations and asymptotic series of the multiple gamma function. The numerical schemes for high-precision computation of the Barnes gamma function and Glaisher's constant are also discussed.

Generalized beta-generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entrop...

Beta Bessel distributions

Three new distributions on the unit interval [0,1] are introduced which generalize the standard beta distribution. These distributions involve the Bessel function. Expression is derived for their shapes, particular cases, and the nthmoments. Estimation by themethod of maximum likelihood and Bayes estimation are discussed. Finally, an application to consumer price indices is illustrated to show ...

Bivariate Beta Distributions and Beyond