On integration, substitution and the probability integral transform

Thomas H. Savits

Statistics & Probability Letters, 1994, vol. 21, issue 3, 173-179

Abstract: It is well known that if X is a random variable with distribution function G, then G-1 (U) has the same distribution as X, where U is uniform on (0, 1); moreover, if G is a continuous function, then G(X) has a uniform distribution on (0, 1). In this paper we consider some related results.

Keywords: Distribution; function; Inverse; function; Probability; integral; transformation (search for similar items in EconPapers)
Date: 1994
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