Estimation under Progressive Type-II censoring for Reciprocal Exponential Distribution

Abstract

Estimation related to the parameters of reciprocal exponential distribution is discussed for progressively type-II censored samples. A maximum likelihood estimator for the parameters is developed. A simulation study is considered for different pattern of censoring. Here we have used the simulation algorithm given by Aggarwala (2001) to generate samples. Here we have specified the proportion of surviving units to be removed at five monitoring and censoring point. The percentages of removing units from the surviving units at five stages are increasing in pattern R1 while decreasing in pattern R2. In pattern R3, a conventional type- II censoring scheme is employed. Using the likelihood level r, the likelihood inequality can be solved in order to construct a likelihood interval for θ. From a graph of likelihood ratio= ˆ L L ( ) / ( )   plotted against various values of θ, the likelihood interval for θ can be obtained for given level r, by drawing a horizontal line at ˆ L L ( ) / ( )   =r and the corresponding likelihood interval will contain all values of θ below this line. For bootstrapping, we again have simulated 1000 samples using the value of ˆ as a true value of θ and calculated ˆ ( ) boot  p for p = 0.025 and p = 0.975 to obtain the 95% confidence interval.