Bayesian estimation of the parameter and reliability of a Rayleigh distribution using records

Article type: Research Article

Authors: Dey, Sanku^{a; *} | Dey, Tanujit^b

Affiliations: [a] Department of Statistics, St. Anthony's College, Shillong, Meghalaya, India | [b] Department of Mathematics, The College of William & Mary, Williamsburg, Virginia, USA

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper we obtain Bayes estimators for the unknown parameter of a Rayleigh distribution based on upper record values. Bayes estimators are obtained under symmetric and asymmetric loss functions using a conjugate family of priors. The performance of the estimators is assessed on the basis of their relative risk under the two loss functions. A numerical study illustrates the results. We also estimate the reliability function using an asymmetric loss function and compare its performance to the symmetric loss function based on a Monte Carlo simulation study. A real life data set is used for illustrative purposes.

Keywords: Bayes estimator, LINEX loss function, record values, reliability function, risk function, squared error loss function

DOI: 10.3233/MAS-2011-0214

Journal: Model Assisted Statistics and Applications, vol. 7, no. 2, pp. 81-90, 2012