On a Class of Affine Invariant Dependent Random Variables Related to Characterization Results by Lukacs, Letac and Dufresne
نویسنده
چکیده
Conditions under which a naive algebraic solution to a random affine stochastic equation yields a genuine stochastic solution with a given independence property are derived. The well-known example by Letac is characterized and generalized to a non-trivial dependence structure. As by-products, a series representation of the exact probability density of a sum of independent gamma random variables is recovered, and a new elementary proof of Lukacs’ characterization of the gamma distribution is added. Mathematics Subject Classification: 60E05, 62E10, 62P05
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تاریخ انتشار 2015