Generalized transformations of random variables

James Weber

Statistics & Probability Letters, 1991, vol. 12, issue 2, 161-166

Abstract: We present a formula for all the densities that a random variable may have so that a given transform of it has a given density. The collection of densities which are changed by a prescribed transform to have a prescribed density may be called the generalized transformations of a random variable. This terminology is analogous to 'generalized inverse' for reasons given in the paper. Special cases include theorems of Roberts and Geisser: (i) the densities that a random variable may have if its mth absolute power is gamma (Roberts, 1971), (ii) the densities that a random variable may have if its square is gamma (Roberts and Geisser, 1966).

Keywords: Chi-squared; density; generalized; inverse; function; normal; random; variable; transformation (search for similar items in EconPapers)
Date: 1991
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