Recently, the maximum product spacing method has become one of the most efficient parameters estimation methods because of its estimates efficiency which retains most of the maximum likelihood estimation method properties including the invariance property. In this paper, relative efficiency measures will be used to compare the efficiency of the maximum product spacing method with the maximum likelihood estimation method using classical and Bayesian approaches for the power Topp-Leone distribution. The relative efficiency of the maximum product spacing method will be investigated using progressive Type-II censoring scheme. A simulation study and a real data set are performed to compare the efficiency between estimation methods. The relative efficiency of the MPS method will be investigated using a complete sample and progressive Type-II censoring scheme. A simulation study and a real data set are performed to compare the efficiency between estimation methods.
In this study, one can see that the transformation of completing the square gives the PTL distribution more flexibility in mathematical properties and generating random numbers which helps easily to use MLE and MPS methods in generating random numbers in a simulation study with accurate results.