Approximating the Probability Density Function of a Transformation of Random Variables
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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.
KeywordsApproximations 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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- Barndorff-Nielsen O (1978) Information and exponential families: in statistical theory. Wiley Series in Probability and Mathematical Statistics Series J. WileyGoogle Scholar
- Lefevre C, Picard P (2014a) Appell pseudopolynomials and Erlang type risk models. Stochastics 86:676–695Google Scholar
- Lefevre C, Picard P (2014b) Ruin probabilities for risk models with ordered claim arrivals. Methodol Comput Appl Probab 16:885–905Google Scholar
- Letac G (1992) Lectures on natural exponential families and their variance functions. Instituto de matemática pura e aplicada: Monografias de matemática, 50, Río de Janeiro, BrésilGoogle Scholar