Sinha, Pankaj and Jayaraman, Prabha (2009): Robustness of Bayesian results for Inverse Gaussian distribution under ML-II epsilon-contaminated and Edgeworth Series class of prior distributions.
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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 two-sided predictive limits for a future observation from IG population. Two prior distributions, a class ML-II ε-contaminated 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 ML-II ε-contaminated and ESD does not affect the Bayesian results.
|Item Type:||MPRA Paper|
|Original Title:||Robustness of Bayesian results for Inverse Gaussian distribution under ML-II epsilon-contaminated and Edgeworth Series class of prior distributions|
|Keywords:||Bayesian results,Inverse Gaussian distribution,ML-II ε-contaminated 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
|Depositing User:||Pankaj Sinha|
|Date Deposited:||26. May 2009 00:04|
|Last Modified:||19. Feb 2013 14:05|
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, 345-363.
Banerjee, A.K. and Bhattacharyya, G.K. (1976). A purchase incidence model with inverse Gaussian interpurchase times. J. Amer. Statist. Assoc., 71, 823-829.
Banerjee, A.K. and Bhattacharyya, G.K. (1979). Bayesian results for the inverse Gaussian distribution with an application. Techonometrics, 21, 247-251.
Bansal, A.K.(1978). Robustness of Bayes estimator for the mean of a normal population with non-normal prior. Commun. Statist.-Theor.Meth., A7(5), 453-460.
Bansal, A.K. and Sinha, P. (1992). Sensitivity of Bayesian sampling inspection schemes to a non-normal prior distribution. Journal of Applied Statistics, 19, 103-109.
Bansal, A.K. and Sinha, P. (2008). Bayesian optimization analysis with ML-II ε contaminated prior. Journal of Applied Statistics, 35, 203-211.
Barton, D.E. and Dennis, K.E. (1952). The condition under which Gram-Charlier and Edgeworth curves are positive definite and unimodal. Biometrica, 39, 425-427.
Berger, J.O. (1984). The robust Bayesian viewpoint (with discussion). In Robustness of Bayesian Analysis, J. Kadane (Ed.), North Holland, Amsterdam, 63-124.
Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, New York.
Berger, J.O. (1990). Robust Bayesian analysis: sensitivity to the prior. Journal of Statistical Planning and Inference, 25, 303-323.
Berger, J.O. (1994). An overview of robust Bayesian analysis. Test, 5-59.
Berger, J.O. and Berlinear, M. (1986). Robust Bayes and empirical Bayes analysis with ε contaminated priors. Annals of Statistics, 14, 461-486.
Berger, J.O. and Sellke, T. (1987). Testing a point null hypothesis: The irreconcilability of p values and evidence. J. Amer. Statist. Assoc., 82,112-139.
Chakravarti, S. and Bansal, A.K. (1988). Effect of non-normal prior for regression parameter on Bayes decisions and forecasts. Journal of Quantitative Economics, 4, 247-259.
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 life-time 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). Non-Uniform Random Variate Generation. Springer-Verlag, New York.
Draper, N.R. and Tierney, D.E. (1972). Regions of positive and unimodal series expansion of the Edgeworth and Gram-Charlier approximations. Biometrika, 59, 463-465.
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, 673-677.
Seshadri, V. (1999). The Inverse Gaussian Distribution, Statistical Theory and application. Springer-Verlag, New York.
Whitemore, G.A. (1976). Management applications of the inverse Gaussian distributions. Int. J. Manage. Sci., 4, 215-223.
Whitemore, G.A. (1986). Inverse Gaussian ratio estimation. Applied Statistics, 35, 8-15.