Estimation of parameters and the mean life of a mixed failure time distribution

This paper deals with estimation of parameters and the mean life of a mixed failure time distribution that has a discrete probability mass at zero and an exponential distribution with mean theta for positive values. A new sampling scheme similar to Jayade and Prasad (1990) is proposed for estimation of parameters. We derive expressions for biases and mean square errors (MSEs) of the maximum likelihood estimators (MLEs). We also obtain the uniformly minimum variance unbiased estimators (UMVUEs) of the parameters. We compare the estimator of theta and mean life mu based on the proposed sampling scheme with the estimators obtained by using the sampling scheme of Jayade and Prasad (1990).