Utilizing various statistical techniques to estimate the scale parameter for the Rayleigh distribution
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Keywords:
Robust Bayes, Bayes, Rank set, Rayleigh distribution, Frechet distributionAbstract
The purpose of this paper is to use statistical estimating techniques to estimate the scale parameter of the Rayleigh distribution (maximum likelihood, rank set sampling, Bayes, and robust Bayes estimators) under complete data. A non-Bayes estimator is obtained by rank set sampling and maximum likelihood. The inverted gamma distribution and the inverted exponential distribution based on symmetric unbalanced (squared error) and balanced (squared) loss functions were used as Bayesian estimators. Robust Bayes analysis for the Rayleigh distribution depends on (unbalanced and balanced) loss functions based on (ML-II-ϵ-contaminated class and derived under the prior contaminant distribution of the Frechet distribution. The estimators' performances were contrasted according to simulation experiments for different cases and sample sizes depending on the value for the mean squared error.
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