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Explicit expressions and statistical inference of generalized Rayleigh distribution based on lower record values. (English) Zbl 1403.62085
Summary: This article addresses the problem of frequentist and Bayesian estimation of the parameters of the generalized Rayleigh distribution using lower record values. The explicit expressions for single and product moments of lower record values from this distribution are given. The maximum likelihood and Bayes estimates based on lower records are derived for the parameters of the distribution. We consider the Bayes estimators of the parameters under the assumption of Gamma priors with respect to the shape and scale parameters. The Bayes estimators are inaccessible in explicit form. We analyze them with reference to both symmetric and asymmetric loss functions. We also derive the Bayes interval of this distribution. We carry out Monte Carlo simulations to compare the performance of the proposed methods.

62G30 Order statistics; empirical distribution functions
62N05 Reliability and life testing
62E10 Characterization and structure theory of statistical distributions
60F17 Functional limit theorems; invariance principles
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