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Computing the distribution of the product of two continuous random variables. (English) Zbl 1429.62059

Summary: We present an algorithm for computing the probability density function of the product of two independent random variables, along with an implementation of the algorithm in a computer algebra system. We combine this algorithm with the earlier work on transformations of random variables to create an automated algorithm for convolutions of random variables. Some examples demonstrate the algorithm’s application.

MSC:

62E10 Characterization and structure theory of statistical distributions
62-08 Computational methods for problems pertaining to statistics

Software:

Maple; APPL
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Full Text: DOI

References:

[1] Devroye, L., 1996. Random variate generation in one line of code. In: Charnes, J., Morrice, D., Brunner, D., Swain, J. (Eds.), Proceedings of the 1996 Winter Simulation Conference. Institute of Electrical and Electronics Engineers, Coronado, CA, Institute of Electrical and Electronics Engineers, Piscataway, NJ, pp. 265-272.; Devroye, L., 1996. Random variate generation in one line of code. In: Charnes, J., Morrice, D., Brunner, D., Swain, J. (Eds.), Proceedings of the 1996 Winter Simulation Conference. Institute of Electrical and Electronics Engineers, Coronado, CA, Institute of Electrical and Electronics Engineers, Piscataway, NJ, pp. 265-272.
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