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...

We give formulas for the conditional expectations of a product of multivariate Hermite polynomials with multivariate normal arguments. These results are extended to include conditional expectations of a product of linear combination of multivariate normals. A unified approach is given that...