UMVUE and MLE in a family of lifetimes distributions. (English) Zbl 1462.62614
Summary: A family of lifetime distributions is proposed. Problems of estimating the reliability function \(R(t) = P(X > t)\) and \(P = P(X > Y)\) have been considered. Uniformly minimum variance unbiased and maximum likelihood estimators are derived for \(R(t)\) and \(P\). Performance of the estimators has been judged with the help of a simulation study.
MSC:
62N05 | Reliability and life testing |
62E15 | Exact distribution theory in statistics |
62F10 | Point estimation |