Approximating the Probability Density Function of a Transformation of Random Variables

Denys Pommeret () and Laurence Reboul
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Denys Pommeret: Institut de Mathématiques de Marseille - CNRS - Ecole Centrale - Case 907
Laurence Reboul: Institut de Mathématiques de Marseille - CNRS - Ecole Centrale - Case 907

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 2, 633-645

Abstract: Abstract We propose a general formula for the probability density function of transformations of continuous or discrete random variables. Approximations and estimations are derived. Particular cases are treated when transformations are sum or products of random variables. The formula has a simple form when probability density functions are expressed with respect to a reference measure which belongs to the class of natural exponential families with quadratic variance functions. Some numerical results are provided to illustrate the method.

Keywords: Approximations; Natural exponential families; Orthogonal polynomials; Probability density function; Product of random variables; Ratio; Reference measure; Sum of random variables; 62E17 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11009-018-9629-0

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