<Para ID="Par1">Motivated by a roundoff problem, we derive new expressions for cumulants of a random variable distributed uniformly on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$0,1, \ldots , n-1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>. Their computational efficiency over a known expression is discussed. Copyright Springer-Verlag Berlin Heidelberg 2015

The Charlier differential series for distribution and density functions is the foundation for the Edgeworth expansions of distribution and density functions of sample estimators. Here, we give two forms of these expansions for multivariate distributions using multivariate Bell polynomials. Two...

We summarize the main results known for the complex normal and complex Wishart, then give the cumulants of the central and noncentral complex Wishart. Their moments are expressed explicitly in terms of multivariate Bell polynomials, believed to be used here for the first time. Multivariate Bell...

Expressions for moment properties have not been known even for the simplest of the bivariate extreme value distributions. Here, simple expansions are derived for various properties of any given bivariate extreme value distribution. Each expansion is a single infinite sum. The properties...