Sinha, Pankaj and Jayaraman, Prabha (2009): Bayes reliability measures of Lognormal and inverse Gaussian distributions under MLII εcontaminated class of prior distributions.

PDF
MPRA_paper_16528.pdf Download (258kB)  Preview 
Abstract
In this paper we employ MLII εcontaminated class of priors to study the sensitivity of Bayes Reliability measures for an Inverse Gaussian (IG) distribution and Lognormal (LN) distribution to misspecification in the prior. The numerical illustrations suggest that reliability measures of both the distributions are not sensitive to moderate amount of misspecification in prior distributions belonging to the class of MLII εcontaminated.
Item Type:  MPRA Paper 

Original Title:  Bayes reliability measures of Lognormal and inverse Gaussian distributions under MLII εcontaminated class of prior distributions 
English Title:  Bayes reliability measures of Lognormal and inverse Gaussian distributions under MLII εcontaminated class of prior distributions 
Language:  English 
Keywords:  Bayes reliability, MLII εcontaminated prior 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C44  Operations Research ; Statistical Decision Theory C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions ; Specific Statistics C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  16528 
Depositing User:  Pankaj Sinha 
Date Deposited:  02. Aug 2009 02:12 
Last Modified:  11. Feb 2013 10:45 
References:  Aase, K.K. (2000). An equilibrium asset pricing model based on Levy processes : relations to stochastic volatility and the survival hypothesis. Insurance Mathematics and Economics, 27, 345363. Aitchison, J. and Brown, J. (1957). The Lognormal Distribution.Cambridge University Press. Banerjee, A.K. and Bhattacharyya, G.K. (1976). A purchase incidence model with inverse Gaussian interpurchase times. J. Amer. Statist. Assoc., 71, 823829. Banerjee, A.K. and Bhattacharyya, G.K. (1979). Bayesian results for the inverse Gaussian distribution with an application. Techonometrics, 21, 247251. Bansal, A.K. and Sinha, P. (2008). Bayesian optimization analysis with MLII ε contaminated prior. Journal of Applied Statistics, 35, 203211. Barlow, R.E., Toland, R.H., and Freeman, T. (1979).Stress rupture life of Kevlar/Epoxy spherical pressure vessels, UCID1755 Part 3, Lawrence Livermore Laboratory, Livermore, CA. Berger, J.O. (1984). The robust Bayesian viewpoint (with discussion). In Robustness of Bayesian Analysis, J. Kadane (Ed.), North Holland, Amsterdam, 63124. Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. SpringerVerlag, New York. Berger, J.O. (1990). Robust Bayesian analysis: sensitivity to the prior. Journal of Statistical Planning and Inference, 25, 303323. Berger, J.O. (1994). An overview of robust Bayesian analysis. Test, 559. Berger, J.O. and Berlinear, M. (1986). Robust Bayes and empirical Bayes analysis with ε contaminated priors. Annals of Statistics, 14, 461486. Berger, J.O. and Sellke, T. (1987). Testing a point null hypothesis: The irreconcilability of p values and evidence. J. Amer. Statist. Assoc., 82,112139. Blishke,W. and Murthy D. (2000). Reliability : Modeling, Prediction, and Optimization, Wiley. Chhikara, R.S. and Folks, J.L. (1989). The Inverse Gaussian distribution. Marcel Decker, Inc., New York. Chhikara, R.S. and Folks, J.L. (1977). The Inverse Gaussian distribution as a lifetime model. Technometrics, 19, 461–468. Devroye, L. (1986). NonUniform Random Variate Generation. SpringerVerlag, New York. Good, I.J. (1965). The Estimation of Probabilities. MIT Press, Cambridge, MA. Linhardt, H. and Zucchini, W. (1986). Model Selection. New York : Wiley. Martín, J. and Pérez, C.J. (2009). Bayesian analysis of a generalized lognormal distribution. Computational Statistics and Data Analysis, 53, 13771387. Martz, F.H. and Waller, A.R. (1982). Bayesian Reliability Analysis. New York : Wiley. Nadarajha, S. and Kotz, S. (2007). Inverse Gaussian random variables with application to price indices. Applied Economics Letters, 14, 673677. Nadas, A. (1973). Best tests for zero drift based first passage times in Brownian motion. Techonometrics, 15, 125132. Seshadri, V. (1999). The Inverse Gaussian Distribution, Statistical Theory and application. SpringerVerlag, New York. Whitemore, G.A. (1976). Management applications of the inverse Gaussian distributions. Int. J. Manage. Sci., 4, 215223. Whitemore, G.A. (1986). Inverse Gaussian ratio estimation. Applied Statistics, 35, 815. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/16528 