In this article we employ certain techniques in divided differences to relate the generalized Stieltjes transform of the distribution of a randomly weighted average of independent random variables X1, . . . , Xm to the generalized Stieltjes transforms of the distribution functions F1, . . . , Fm; Xi ∼ Fi, i = 1, . . . ,m. The random weights are assumed to be cuts of [0, 1] by m − 1 ordered statistics of independent and identically uniformly distributed random variables U1, . . . , Un on [0, 1]; m ≤ n. Soltani and Homei (2009) treated the case m = n using the Schwartz distribution theory. We identified fairly large classes of randomly weighted average distributions by their generalized Stieltjes transforms; in particular including the uniform, Wigner and certain power semicircle distributions.
کلید واژگان :Randomly weighted average, Generalized Stieltjes transform, Stieltjes transform, divided difference
ارزش ریالی : 600000 ریال
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