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Approximating the Probability Density Function of a Transformation of Random Variables

Author

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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)

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.

Suggested Citation

  • Denys Pommeret & Laurence Reboul, 2019. "Approximating the Probability Density Function of a Transformation of Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 633-645, June.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:2:d:10.1007_s11009-018-9629-0
    DOI: 10.1007/s11009-018-9629-0
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    References listed on IDEAS

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