Maximum likelihood estimation using probability density functions of order statistics

A variation of maximum likelihood estimation (MLE) of parameters that uses probability density functions of order statistic is presented. Results of this method are compared with traditional maximum likelihood estimation for complete and right-censored samples in a life test. Further, while the concept can be applied to most types of censored data sets, results are presented in the case of order statistic interval censoring, in which even a few order statistics estimate well, compared to estimates from complete and right-censored samples. Distributions investigated include the exponential, Rayleigh, and normal distributions. Computation methods using A Probability Programming Language running in Maple are more straightforward than existing methods using various numerical method algorithms.