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Estimation methods for the probability density function and the cumulative distribution function of the Pareto-Rayleigh distribution

ABSTRACT The purpose of the present paper is to investigate the estimation of the probability density function and the cumulative distribution function of the Pareto-Rayleigh distribution for known scale parameter. In this regard, the following estimators are considered: uniformly minimum variance unbiased estimator, maximum likelihood estimator, percentile estimator, least squares estimator and weighted least squares estimator. To do so, the analytical expressions are derived for the mean integrated squared error. As the result of simulation studies and real data applications indicate, the maximum likelihood estimator outperforms the others.