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Information Matrix for Beta Distributions

Aryal, Gokarna, Nadarajah, Saralees (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 33C90, 62E99.The Fisher information matrix for three generalized beta distributions are derived.

N-dimensional measures of dependence.

Edward F. Wolff (1980)

Stochastica

In recent joint papers with B. Schweizer, we used the notion of a copula to introduce a family of symmetric, nonparametric measures of dependence of two random variables. Here, we present n-dimensional extensions of these measures and of Spearman's ro. We study them vis-a-vis appropriate higher dimensional analogues of Rényi's axioms for measures of dependence, determine relations among them, and in some cases establish reduction formulae for their computation.

On fine properties of mixtures with respect to concentration of measure and Sobolev type inequalities

Djalil Chafaï, Florent Malrieu (2010)

Annales de l'I.H.P. Probabilités et statistiques

Mixtures are convex combinations of laws. Despite this simple definition, a mixture can be far more subtle than its mixed components. For instance, mixing gaussian laws may produce a potential with multiple deep wells. We study in the present work fine properties of mixtures with respect to concentration of measure and Sobolev type functional inequalities. We provide sharp Laplace bounds for Lipschitz functions in the case of generic mixtures, involving a transportation cost diameter of the mixed...

On formulae for central moments of counting distributions

Katarzyna Steliga, Dominik Szynal (2015)

Applicationes Mathematicae

The aim of this article is to give new formulae for central moments of the binomial, negative binomial, Poisson and logarithmic distributions. We show that they can also be derived from the known recurrence formulae for those moments. Central moments for distributions of the Panjer class are also studied. We expect our formulae to be useful in many applications.

On functional measures of skewness

Renata Dziubińska, Dominik Szynal (1996)

Applicationes Mathematicae

We introduce a concept of functional measures of skewness which can be used in a wider context than some classical measures of asymmetry. The Hotelling and Solomons theorem is generalized.

On the product of triangular random variables

Mridula Garg, Sangeeta Choudhary, Saralees Nadarajah (2009)

Applicationes Mathematicae

We derive the probability density function (pdf) for the product of three independent triangular random variables. It involves consideration of various cases and subcases. We obtain the pdf for one subcase and present the remaining cases in tabular form. We also indicate how to calculate the pdf for the product of n triangular random variables.

On the use of difference of two proportions

Saralees Nadarajah (2009)

Applicationes Mathematicae

Differences of two proportions occur most frequently in biomedical research. However, as far as published work is concerned, only approximations have been used to study the distribution of such differences. In this note, we derive the exact probability distribution of the difference of two proportions for seven flexible beta type distributions. The expressions involve several well known special functions. The use of these results with respect to known approximations is illustrated.

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