Bayesian inference for the Pareto lifetime model in the presence of outliers under progressive censoring with binomial removals
Year 2017,
Volume: 46 Issue: 5, 887 - 906, 01.10.2017
U. J. Dixit
M. Jabbari Nooghabi
Abstract
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.
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Laboratory, San Francisco, 1966.
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pp. 307313.
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to Event Data, Wiley, NewYork, 1999.
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170178.
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Comm. Statist. 16(6) (1987), pp. 17611772.
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under Type II progressive censoring with binomial removals, J. Appl. Statist. 27 (2000), pp.
10331043.
Year 2017,
Volume: 46 Issue: 5, 887 - 906, 01.10.2017
U. J. Dixit
M. Jabbari Nooghabi
References
- 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.