Products Of Independent Random Variables Research Articles

Gamma-distributed products of independent random variables

Gamma-distributed products of independent random variables Get access ALAN STUART ALAN STUART London School of Economics Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 49, Issue 3-4, 1962, Pages 564–565, https://doi.org/10.1093/biomet/49.3-4.564 Published: 01 December 1962

A theorem on the cumulative product of independent random variables

1. Introductory discussion and summary. Consider a sequence {ui} of independent real or complex-valued random variables such that E(ui) = 1, and a sequence of mutually exclusive events S1, S2,…, such that Si depends only on u1, u2, …,ui, with ΣP(Sj) = 1. Define the random variable n = n(u1, u2,…) = m when Sm occurs. We shall obtain the necessary and sufficient conditions under whichreferred to as the product theorem.