Sinha, Pankaj and Jayaraman, Prabha (2009): Robustness of Bayesian results for Inverse Gaussian distribution under MLII epsiloncontaminated and Edgeworth Series class of prior distributions.

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Abstract
This paper aims to study the sensitivity of Bayes estimate of location parameter of an Inverse Gaussian (IG) distribution to misspecification in the prior distribution. It also studies the effect of misspecification of the prior distribution on twosided predictive limits for a future observation from IG population. Two prior distributions, a class MLII εcontaminated and Edgeworth Series (ESD), are employed for the location parameter of an IG distribution, to investigate the effect of misspecification in the priors. The numerical illustrations suggest that moderate amount of misspecification in prior distributions belonging to the class of MLII εcontaminated and ESD does not affect the Bayesian results.
Item Type:  MPRA Paper 

Original Title:  Robustness of Bayesian results for Inverse Gaussian distribution under MLII epsiloncontaminated and Edgeworth Series class of prior distributions 
Language:  English 
Keywords:  Bayesian results,Inverse Gaussian distribution,MLII εcontaminated prior,Edgeworth Series Distributions 
Subjects:  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 A  General Economics and Teaching > A1  General Economics > A10  General C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General 
Item ID:  15396 
Depositing User:  Pankaj Sinha 
Date Deposited:  26 May 2009 00:04 
Last Modified:  28 Sep 2019 16:07 
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. 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.(1978). Robustness of Bayes estimator for the mean of a normal population with nonnormal prior. Commun. Statist.Theor.Meth., A7(5), 453460. Bansal, A.K. and Sinha, P. (1992). Sensitivity of Bayesian sampling inspection schemes to a nonnormal prior distribution. Journal of Applied Statistics, 19, 103109. Bansal, A.K. and Sinha, P. (2008). Bayesian optimization analysis with MLII ε contaminated prior. Journal of Applied Statistics, 35, 203211. Barton, D.E. and Dennis, K.E. (1952). The condition under which GramCharlier and Edgeworth curves are positive definite and unimodal. Biometrica, 39, 425427. 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. Chakravarti, S. and Bansal, A.K. (1988). Effect of nonnormal prior for regression parameter on Bayes decisions and forecasts. Journal of Quantitative Economics, 4, 247259. 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. Chhikara, R.S, and Guttman, I. (1982). Prediction limits for the Inverse Gaussian distribution. Techonometrics, 24, 319–314. Devroye, L. (1986). NonUniform Random Variate Generation. SpringerVerlag, New York. Draper, N.R. and Tierney, D.E. (1972). Regions of positive and unimodal series expansion of the Edgeworth and GramCharlier approximations. Biometrika, 59, 463465. Good, I.J. (1965). The Estimation of Probabilities. MIT Press, Cambridge, MA. Nadarajha, S. and Kotz, S. (2007). Inverse Gaussian random variables with application to price indices. Applied Economics Letters, 14, 673677. 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/15396 