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HandWiki. Product Distribution. Encyclopedia. Available online: https://encyclopedia.pub/entry/34012 (accessed on 22 September 2026).
HandWiki. Product Distribution. Encyclopedia. Available at: https://encyclopedia.pub/entry/34012. Accessed September 22, 2026.
HandWiki. "Product Distribution" Encyclopedia, https://encyclopedia.pub/entry/34012 (accessed September 22, 2026).
HandWiki. (2022, November 11). Product Distribution. In Encyclopedia. https://encyclopedia.pub/entry/34012
HandWiki. "Product Distribution." Encyclopedia. Web. 11 November, 2022.
Product Distribution
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A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable Z that is formed as the product is a product distribution.

product distribution probability distribution random variable

References

  1. Springer, Melvin Dale (1979). The Algebra of Random Variables. John Wiley & Sons. ISBN 978-0-471-01406-5. https://archive.org/details/algebraofrandomv0000spri. Retrieved 24 September 2012. 
  2. Rohatgi, V. K. (1976). An Introduction to Probability Theory and Mathematical Statistics. Wiley Series in Probability and Statistics. New York: Wiley. doi:10.1002/9781118165676. ISBN 978-0-19-853185-2.  https://dx.doi.org/10.1002%2F9781118165676
  3. Grimmett, G. R.; Stirzaker, D.R. (2001). Probability and Random Processes. Oxford: Oxford University Press. ISBN 978-0-19-857222-0. http://ukcatalogue.oup.com/product/9780198572220.do?keyword=grimmett+stirzaker&sortby=bestMatches. Retrieved 4 October 2015. 
  4. Sarwate, Dilip (March 9, 2013). "Variance of product of multiple random variables". Stack Exchange. https://stats.stackexchange.com/q/52699. 
  5. "How to find characteristic function of product of random variables". Stack Exchange. January 3, 2013. https://math.stackexchange.com/q/269579. 
  6. heropup (1 February 2014). "product distribution of two uniform distribution, what about 3 or more". Stack Exchange. https://math.stackexchange.com/q/659278. 
  7. Gradsheyn, I S; Ryzhik, I M (1980). Tables of Integrals, Series and Products. Academic Press. pp. section 6.561. 
  8. Nadarajah, Saralees; Pogány, Tibor (2015). "On the distribution of the product of correlated normal random variables". Comptes Rendus de l'Académie des Sciences, Série I 354 (2): 201–204. doi:10.1016/j.crma.2015.10.019.  https://dx.doi.org/10.1016%2Fj.crma.2015.10.019
  9. Equ(13.18.9). "Digital Library of Mathematical Functions". https://dlmf.nist.gov. 
  10. Cui, Guolong (2016). "Exact Distribution for the Product of Two Correlated Gaussian Random Variables". IEEE Signal Processing Letters 23 (11): 1662–1666. doi:10.1109/LSP.2016.2614539. Bibcode: 2016ISPL...23.1662C.  https://dx.doi.org/10.1109%2FLSP.2016.2614539
  11. Kan, Raymond (2008). "From moments of sum to moments of product". Journal of Multivariate Analysis 99 (3): 542–554. doi:10.1016/j.jmva.2007.01.013.  https://dx.doi.org/10.1016%2Fj.jmva.2007.01.013
  12. Wells, R T; Anderson, R L; Cell, J W (1962). "The Distribution of the Product of Two Central or Non-Central Chi-Square Variates". The Annals of Mathematical Statistics 33 (3): 1016–1020. doi:10.1214/aoms/1177704469.  https://dx.doi.org/10.1214%2Faoms%2F1177704469
  13. O’Donoughue, N; Moura, J M F (March 2012). "On the Product of Independent Complex Gaussians". IEEE Transactions on Signal Processing 60 (3): 1050–1063. doi:10.1109/TSP.2011.2177264. Bibcode: 2012ITSP...60.1050O.  https://dx.doi.org/10.1109%2FTSP.2011.2177264
  14. Wolfies (August 2017). "PDF of the product of two independent Gamma random variables". https://math.stackexchange.com/q/2396324. 
  15. Nagar, D K; Orozco-Castañeda, J M; Gupta, A K (2009). "Product and quotient of correlated beta variables". Applied Mathematics Letters 22: 105–109. doi:10.1016/j.aml.2008.02.014.  https://dx.doi.org/10.1016%2Fj.aml.2008.02.014
  16. Johnson, Norman L.; Kotz, Samuel; Balakrishnan, N. (1995). Continuous Univariate Distributions Volume 2, Second edition. Wiley. p. 306. ISBN 978-0-471-58494-0. http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471584940.html. Retrieved 24 September 2012. 
  17. Nadarajah, Saralees (June 2011). "Exact distribution of the product of n gamma and m Pareto random variables". Journal of Computational and Applied Mathematics 235 (15): 4496–4512. doi:10.1016/j.cam.2011.04.018.  https://dx.doi.org/10.1016%2Fj.cam.2011.04.018
  18. Servedio, Rocco A. (2004), "On learning monotone DNF under product distributions", Information and Computation 193 (1): 57–74, doi:10.1016/j.ic.2004.04.003  https://dx.doi.org/10.1016%2Fj.ic.2004.04.003
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