Bayesian inference for the Pareto lifetime model in the presence of outliers under progressive censoring with binomial removals

Here we have used Type II progressive censoring with random removal for the Pareto lifetime model in the presence of outliers. The number of units removed at each failure time follows a Binomial distribution. The analysis is based on Bayesian approach. In the last, we have given examples with real data.

Keywords:

Pareto distribution, Bayesian estimation, Prior, Progressive censoring, Type II censoring Linex loss function, Outliers,

PDF

___

M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover, NewYork, 1965.
Zeinab H. Amin, Bayesian inference for the Pareto lifetime model under progressive cen- soring with binomial removals, Journal of Applied Statistics 35(11) (2008), pp. 12031217.
B.C. Arnold and S.J. Press, Bayesian inference for Pareto populations, J. Econ. 21 (1983), pp. 287306.
B.C. Arnold and S.J. Press, Bayesian estimation and prediction for Pareto data, J. Amer. Statist. Assoc. 84 (1989), pp. 10791084.
N. Balakrishnan and R. Aggarwalla, Progressive Censoring: Theory, Methods and Applica- tions, Birkhauser, Boston, 2000.
J.M. Berger and B. Mandelbrot, A new model for error clustering in telephone circuits, IBM J. Res. Develop. 7 (1963), pp. 224236.
A.C. Cohen, Progressively censored samples in lifetesting, Technometrics 5 (1963), pp. 327 339.
H.T. Davis and M.L. Feldstein, The generalized Pareto law as a model for progressively censored survival data, Biometrika 66 (1979), pp. 299306.
U.J. Dixit, Estimation of parameters of the Gamma Distribution in the presence of Outliers, Commun. Statist. Theory and Meth. 18 (1989), pp. 30713085.
U.J. Dixit, M.M. Ali and Jungsoo Woo, Ecient Estimation of parameters of a uniform distribution in the presence of outliers, Soochow Journal of Mathematics, 29(4) (2003), pp. 363369.
U.J. Dixit and M. Jabbari Nooghabi, Ecient estimation in the Pareto distribution with the presence of outliers, Statistical Methodology, 8(4) (2011), 340355.
U.J. Dixit and M. Jabbari Nooghabi, Ecient Estimation of the parameters of the Pareto Distribution in the Presence of Outliers, Communications of the Korean Statistical Society, 18(6) (2011), 817835.
U.J. Dixit, K.L. Moore and V. Barnett, On the estimation of the scale parameter of the exponential distribution in the presence of outliers generated from uniform distribution, Metron, LIV(3-4) (1996), pp. 201211.
U.J. Dixit and F.P. Nasiri, Estimation of parameters of the exponential distribution in the presence of outliers generated from uniform distribution, Metron, LIX(3-4) (2001), pp. 187 198.
I.R. Dunsmore and Z.H. Amin, Bayesian prediction and tolerance regions in Pareto popu- lations, Proceedings of the ninth annual conference on Statistics and Computer modeling in Human and Social Sciences, Cairo University, Cairo, Egypt, 1997.
I.R. Dunsmore and Z.H. Amin, Some prediction problems concerning samples from the Pareto distribution, Comm. Statist. 27 (1998), pp. 12211238.
E.C. Freiling, A comparison of the fallout mass-size distributions calculated by lognormal and power-law models, Report No. USNRDLTR-1105 for the US Naval Radiological Defence Laboratory, San Francisco, 1966.
C.M. Harris, The Pareto distribution as a queue service discipline, Oper. Res. 16 (1968), pp. 307313.
D.W. Hosmer and S. Lemeshow, Applied Survival Analysis, Regression Modeling of Time to Event Data, Wiley, NewYork, 1999.
T. Lwin, Estimation of the tail of the Paretian law, Skand. Aktuarietidskr. 55 (1972), pp. 170178.
A.M. Nigm and H.I. Hamdy, Bayesian prediction bounds for the Pareto life time model, Comm. Statist. 16(6) (1987), pp. 17611772.
S.K. Tse, C.Yang, and H.K.Yuen, Statistical analysis ofWeibull distributed lifetime data under Type II progressive censoring with binomial removals, J. Appl. Statist. 27 (2000), pp. 10331043.

Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

Arşiv