Estimation of Reliability in the Two-Parameter Geometric Distribution

In this article, the reliabilities $R(t)=P(X\geq t)$, when $X$ follows two-parameter geometric distribution and $R=P(X\leq Y)$, arises under stress-strength setup, when X and Y assumed to follow two-parameter geometric independently have been found out. Maximum Likelihood Estimator (MLE) and an Unbiased Estimator (UE) of these have been derived. MLE and UE of the reliability of k-out-of-m system have also been derived. The estimators have been compared through simulation study.