Bayesian estimation of the Rayleigh distribution under different loss function


Abstract


In a Rayleigh distribution, we interesting of the estimation of the parameter and some feature of reliability, as, the reliability function and the failure rate function. We used the Bayesian approach under different loss function (squared loss and Linex loss) with a type II censored data. the prior law of the parameter is uninformative prior then a natural conjugated prior. The estimators of σ, S(t) and h(t) are obtained with the exact analytic expression, the posterior risks are calculated in each case. A simulation study was carried out as well as real data analysis. A comparaison between the different estimators from there posterior risks leads us to conclude that the best estimator is obtained under the Linex loss.

DOI Code: 10.1285/i20705948v10n1p50

Keywords: Rayleigh distribution, Bayesian estimation, Posterior risk, Linex loss function.

References


Balakrishnan N,,Approximate MLE of the scale parameter of the Rayleigh distribution

with censoring, IEEE transaction on reliability38 (1989), 355–357

Bakker A, ROUX J, Mostert P,A generalization of the compound Rayleigh

distribution using a Bayesian methods on cases survival times, Communications in

statistics, Theory and methods29 (2000), 1419–1433

Chansoo K, Keun L,Estimation of the scale parameter of the Rayleigh distribution

under general progressive censoring, Journal of the Korean statistical society28

(2009),239 –246

Dyer DD,Whisenand CW,Best linear unbiased of the parameter of the Rayleigh

distribution-Part I: Small sample theory for censored order statistics, IEEE transaction

on reliability22 (1973),27 –34

Fernandez AJ,Bayesian inference from type II censored data , statistics and

probability letters22 (2006),393–399

Gauss CF,Least squares method for combinations of observations, Mallet-Bacheleir-

Paris (1810),–

James RC,On a robustness property of the Rayleigh and buighan tests of uniformity,

statistics and probability letters (2016),55–59

Howlader HA, Hossain A,On Bayesian estimation and prediction from reliability

based on type II censored data, communications in statistics-Theory and

methods24 (1995),2249–2259

Kundu D, Raqab MZ,Generalized Rayleigh distribution: different methods of

estimation, Computational statistics ans data analysis49 (2005),167–200

Kundu D, Raqab MZ,Discriminating between the log-normal and generalized

distribution , Statistics46 (2007),505–515

Lalitha S, Hishra A,Modufied maximum likelihood estimation for rayleigh distribution

, Communications in statistics-Theory and Methods25 (1996),398–401

Lawless JF,Statistics and methods for lifetime data, Weiley Newyork (),–

Povoko A.M, Fundamentals of reliability theory, NewYork Academic Press (1968),–

Mohamed Z, Raqab MZ, Madi MT,Inference for the generalized rayleigh disElectronic

Journal of Applied Statistical Analysis 14

tribution based on progressively censored data, Journal of statistical planning and

inference141 (2011),3313–3322

Mousa MA, Al Sagheer SA,Statistical inference for the Rayleigh model based

on progressively type II censored data, Statistics40 (2006),149–157

Raqab MZ, Madi MT,Bayesian prediction of the total time on test using doubly

censored Rayleigh data, journal of statistical computation and simulation72

(2002),781–789

Raqab MZ,Madi MT,Bayesian analysis for the exponentiated Rayleigh distribution

, International journal of statistics (2009),269–288

Rayleigh J.W.S,On the resultats of a large number of vibrations of the some

pitch and arbitrary phase, Philosophical Magazine, 5th Series (),73–78

Sajid A,Mixture of the inverse Rayleigh distribution properties and estimation

in a Bayesian frame work, Applied mathematical modelling39 (2015),515–530

Sanku D, Tanujit D,Statistical inference for the Rayleigh distribution under

progressively type II censoring with binomial removal, Applied mathematical modeling38

(2014),974–982

Tahani AA,Estimation of the unknown parameters for the compound Rayleigh

distribution based on progressive first failure censored sampling, Open journal of

statistics (2011),161–171

Varian HR,A Bayesain approach to real estate easement , Amsterdam, North

Holland (1975),195–208

Wu SJ, Chen DH, Chen ST,Bayesian inference for the Rayleigh distribution

under progressive censored sample, applied stochastic models in business and industry22

(2006),269–279

Zeblein J,Zelen M,Statistics investigation of the fatigue life of the deep groove

ball bearing , journal of the national bureau of standards 57 (1965), 273–316.


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