โ Scribed by Peter C.C. Wang
No coin nor oath required. For personal study only.
be a discrete random vwiable with parameter h :E EJXj < OQ and denote BCWJ) = (7 ;4q i a?" _ I. Let the distribution of X be compounded with B(ur,qa), If the resulting diwibution is governed by the same law as X, then a characterization elf the Pc)isson distribution is obtained. An altexnarive proof of the Rao --Rukmin chara::tcriza tion is provided.
๐ SIMILAR VOLUMES
Recently attempts have been made to characterize probability distributions via truncated expectations in both univariate and multivariate cases. In this paper we will use a well known theorem of Lau and Rao (1982) to obtain some characterization results, based on the truncated expectations of a func
## I. fntFoduction Let {X,,, n 2 1) be a sequence of independent random variables, P, and f, the distribution function and the characteristic fundion of the X,, respectively. Let us put SN = 2 X,, where N is a pasitive integer-valued random variable independent of X,, ?t 2 1. Furthermore, let { P,
One major source of error commonly encountered in determining the fatigue life of a given element arises from the loads involved, which are usually of random nature. As a rule, resistance analyses, carried out by simulation or tests, are done by using a loading history accounting for the real loads