A CHARACTERIZATION OF GEOMETRIC DISTRIBUTIONS THROUGH CONDITIONAL INDEPENDENCE

SummaryLet X1,…, Xn be mutually independent non‐negative integer‐valued random variables with probability mass functions fi(x) > 0 for z= 0,1,…. Let E denote the event that {X1≥X2≥…≥Xn}. This note shows that, conditional on the event E, Xi‐Xi+ 1 and Xi+ 1 are independent for all t = 1,…, k if and only if Xi (i= 1,…, k) are geometric random variables, where 1 ≤k≤n‐1. The k geometric distributions can have different parameters θi, i= 1,…, k.

A CHARACTERIZATION OF GEOMETRIC DISTRIBUTIONS THROUGH CONDITIONAL INDEPENDENCE Journal Articles