The distribution of linear combinations of random variables arises explicitly in many areas of engineering. This has increased the need to have available the widest possible range of statistical results on linear combinations of random variables. In this note, the exact distribution of the...

This paper concerns a family of univariate distributions suggested by Topp & Leone in 1955. Topp & Leone provided no motivation for this new family and by way of properties they derived only the first four integer-order moments, i.e. E(Xn) for n=1, r 2, r 3, r 4 . In this paper we provide a...

Inverse Gaussian distributions have proved to fit economic indices remarkably well in empirical investigations (Aase, 2000). In this note, the exact distribution of the ratio W = X/(X + Y) is derived when X and Y are independent inverse Gaussian random variables. This distribution arises when...

About twenty expansions applicable for a wide range of bivariate copulas are given. These expansions being mostly elementary enable easy computation of measures and properties of copulas.

Consider a sequence of n observations from an autoregressive process of order 1 with maximum Mn and minimum mn. We give their joint cumulative distribution function first in terms of n repeated integrals and then, for the case, where the marginal distribution of the observations is absolutely...

<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

It is shown that the total amount of income earned during a reference period can be expressed as the products of components of bivariate Pareto distributions. The exact distribution of the total amount of income P = XY and the corresponding moment properties are derived when (X, Y ) follows...

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...