Explicit closed form expressions are derived for moments of order statistics from the normal, log normal, gamma and beta distributions. The usefulness of the results is illustrated through two data sets on quality control testing.

<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

Simple transformations are given for reducing/stabilizing bias, skewness and kurtosis, including the first such transformations for kurtosis. The transformations are based on cumulant expansions and the effect of transformations on their main coefficients. The proposed transformations are...

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Over reported income is commonly expressed as Z = X/Y, where X denotes the true income and Y a multiplicative error taking values in (0, 1). If Y has the power function distribution then it is well known that X is Pareto distributed if and only if Z is also. Often, the gamma distribution is...

The first known bivariate distribution with gamma and beta marginals is introduced. Various representations are derived for its joint probability density function (pdf), joint cumulative distribution function (cdf), product moments, conditional pdfs, conditional cdfs, conditional moments, joint...