Approximating the Probability Density Function of a Transformation of Random Variables

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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 

Mathematic Subject Classification (2010)

62E17 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut de Mathématiques de Marseille - CNRS - Ecole Centrale - Case 907Marseille cedex 9France

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