Empirical Bayes Estimation of Parameter of Burr-Type X Model under LINEX and Squared Error Loss Functions

Article Preview

Abstract:

The Empirical Bayes estimate of the parameter of Burr-type X distribution is contained .The estimate is obtained under squared error loss and Varian’s linear-exponential (LINEX) loss functions, and is compared with corresponding maximum likelihood and Bayes estimates. Finally, a Monte Carlo numerical example is given to illustrate our results.

You might also be interested in these eBooks

Info:

Periodical:

Advanced Materials Research (Volumes 403-408)

Pages:

5273-5277

Citation:

Online since:

November 2011

Authors:

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2012 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] Burr I.W. Cumulative frequency functions, Ann. Math. Statist. Vol. 13(1942), pp.215-232.

DOI: 10.1214/aoms/1177731607

Google Scholar

[2] Sartawi H.A., Abu-Salih M.S. Bayesian prediction bounds for the Burr type X model, Commun. Statist. Theory Methods, Vol. 20, No. 7(1991), pp.2307-2330.

DOI: 10.1080/03610929108830633

Google Scholar

[3] Jaheen Z.F. Bayesian approach to prediction with outliers from the Burr type model. Microelectron. Reliab. Vol. 35, No. 1(1995), pp.45-47.

DOI: 10.1016/0026-2714(94)00056-t

Google Scholar

[4] Jaheen Z.F. Empirical Bayes estimation of the reliability and failure rate functions of the Burr type X failure rate model. J. Appl. Statist. Sci. Vol. 3, No. 4(1996), pp.281-288.

Google Scholar

[5] Ahmad, K.E., Fakhry, M.E. and Jaheen, Z.F. Empirical Bayes estimation of P(Y<X) and characterizations of Burr-type X model, Journal of Statistical Planning and Inference, Vol. 64(1997), pp.297-308.

DOI: 10.1016/s0378-3758(97)00038-4

Google Scholar

[6] Raqab M.I. and Kundu,D. Comparison of different estimators of P(Y<X) for a scaled Burr type X distribution, Communications in Statistics-Simulation and Computation, Vol. 34(2005), pp.465-483.

DOI: 10.1081/sac-200055741

Google Scholar

[7] Kim,C. and Chung,Y. Bayesian estimation of P(Y<X) from Burr-type X model containing spurious observations, Statistical Papers, Vol. 47(2006), pp.643-651.

DOI: 10.1007/s00362-006-0310-2

Google Scholar

[8] Varian H.R. A Bayesian approach to real estimate assessment. In Feinberge, S. &Zellner, A. (Eds. ). Studies in Bayesian Econometrics and statistics in Honor of L.J. Savage, Amsterdam, North Holland, (1975), pp.195-208.

Google Scholar

[9] Zellner,A. Bayesian estimation and prediction using asymmetric loss function. Journal of American statistical Association, Vol. 81(1986), pp.446-451.

DOI: 10.1080/01621459.1986.10478289

Google Scholar

[10] Basu A.P., Ebrahimi,N. Bayesian approach to life testing and reliability estimation using asymmetric loss function, Journal of statistical Planning and Inferences, Vol. 29(1991), pp.21-31.

DOI: 10.1016/0378-3758(92)90118-c

Google Scholar

[11] Parkash,G. and Singh D.C. Shrinkage testimators for the inverse dispershon of the inverse Gaussian distribution under the LINEX loss function. Australian Journal of statistics, Vol. 35, No. 4(2006), pp.363-470.

DOI: 10.17713/ajs.v35i4.356

Google Scholar

[12] Singh D.C., Prakash,G. and Singh,P. Shrinkage testimators for the shape parameters of pareto distribution using the LINEX loss function. Comm. Statistist. Theory and Methods, Vol. 36, No. 4(2007) pp.741-753.

DOI: 10.1080/03610920601033694

Google Scholar

[13] Ahmad A.A., Mohammad Z.R. and Mohamed T.M. Bayesian predic- tion intervals for the future order statistics from the generalized exponential distribution, JIRSS, vol. 6, No. 1(2007), pp.17-30, (2007).

Google Scholar

[14] Prakash,G. and Singh D.C.: Shrinkage estimation in exponential Type-II censored under LINEX loss function. Journal of the Korean Statistical Society, vol. 37, No. 1(2008), pp.53-61.

DOI: 10.1016/j.jkss.2007.07.002

Google Scholar