Abstract: We consider maximum likelihood estimation of the parameters of a finite mixture model for independent order statistics data arising from ranked set sampling, as well as classification of the observed data. We propose two ranked-based sampling designs from a finite mixture density and explain how to estimate the unknown parameters of the model for each design. To exploit the special structure of the ranked set sampling, we develop a new expectation-maximization algorithm that turns out to be different from its counterpart with simple random sample data. Our findings are that estimators based on ranked set sampling are more efficient than their counterparts based on the commonly used simple random sampling technique. Theoretical results are augmented with simulation studies.

key words and phrases: Classification, complete-data likelihood, expectation maximization algorithm, finite mixture models, order statistics, ranked set samples.