LAUSR

In this work, some characterizations of the geometric distribution based on two kinds of residual lifetime are presented. Firstly we characterize geometric distribution by using certain relationships of moments of the truncated life from below, that is $$\max \{X-t,0\}$$max{X-t,0}, where X is a positive integer-valued random variable. Secondly using certain relationships of moments of residual life $$\gamma _{t}$$γt at t of a renewal process, we characterize the common distribution of the inter-arrival times $$ \{X_{i},i\ge 1\}$${Xi,i≥1} to be geometrically distributed when $$X_{1}$$X1 is also a positive integer-valued random variable.