Noninformative Priors for the Coefficient of Variation in Two Inverse Gaussian Distributions

- Journal title : Communications for Statistical Applications and Methods
- Volume 15, Issue 3, 2008, pp.429-440
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2008.15.3.429

Title & Authors

Noninformative Priors for the Coefficient of Variation in Two Inverse Gaussian Distributions

Kang, Sang-Gil; Kim, Dal-Ho; Lee, Woo-Dong;

Kang, Sang-Gil; Kim, Dal-Ho; Lee, Woo-Dong;

Abstract

In this paper, we develop the noninformative priors when the parameter of interest is the common coefficient of variation in two inverse Gaussian distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that the one-at-a-time and two group reference priors satisfy the first order matching criterion but Jeffreys` prior does not. The Bayesian credible intervals based on the one-at-a-time reference prior meet the frequentist target coverage probabilities much better than that of Jeffreys` prior. Some simulations are given.

Keywords

Coefficient of variation;inverse Gaussian distribution;probability matching prior;reference prior;

Language

English

References

1.

Berger, J. O. and Bernardo, J. M. (1989). Estimating a product of means: Bayesian analysis with reference priors, Journal of the American Statistical Association, 84, 200-207

2.

Berger, J. O. and Bernardo, J. M. (1992). On the development of reference priors (with discussion), In Bayesian Statistics IV, 35-60, eds. J. M. Bernardo, et al., Oxford University Press, Oxford

3.

Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference, Journal of the Royal Statistical Society, Series B, 41, 113-147

4.

Chhikara, R. S. and Folks, J. L. (1989). The Inverse Gaussian Distribution; Theory, Methodology and Applications, Marcel Dekker, New York

5.

Choi, B. and Kim, K. (2004). Certain multi sample tests for inverse Gaussian populations, Communications in Statistics: Theory & Methods, 33, 1557-1576

6.

Cox, D. R. and Reid, N. (1987). Parameters orthogonality and approximate conditional inference, Journal of the Royal Statistical Society, Serise B, 49, 1-39

7.

Datta, G. S. and Ghosh, J. K. (1995a). On priors providing frequentist validity for Bayesian inference, Biometrika, 82, 37-45

8.

Datta, G. S. and Ghosh, M. (1995b). Some remarks on noninformative priors, Journal of the American Statistical Association, 90, 1357-1363

9.

Datta, G. S. and Ghosh, M. (1996). On the invariance of noninformative priors. The Annals of Statistics, 24, 141-159

10.

DiCiccio, T. J. and Steven, E. S. (1994). Frequentist and Bayesian Bartlett correction of test statistics based on adjusted profile likelihood, Journal of the Royal Statistical Society, Series B, 56, 397-408

11.

Folks, J. L. and Chhikara, R. S. (1978). The inverse Gaussian distribution and its statistical application-A review, Journal of the Royal Statistical Society, Series B, 40, 263-289

12.

Ghosh, J. K. and Mukerjee, R. (1992). Non-informative priors (with discussion), In Bayesian Statistics IV, 195-210, eds. J. M. Bernardo, et. al., Oxford University Press, Oxford

13.

Gleser, L. J. and Hwang, J. T. (1987). The non existence of 100(1-$\alpha$ )% confidence sets of finite expected diameter in error-in-variables and related models. The Annals of Statistics, 15, 1351-1362

14.

Hsieh, H. K. (1990). Inferences on the coe$\pm$ cient of variation of an inverse Gaussian distribution, Communications in Statistics-Theory and Methods, 19, 1589-1605

15.

Kang, S. G., Kim, D. H. and Lee, W. D. (2004). Noninformative priors for the ratio of parameters in inverse Gaussian distribution, The Korean Journal of Applied Statistics, 17, 49-60

16.

Mudholkar, G. and Natarajan, R. (2002). The inverse Gaussian models: Analogues of symmetry, skewness and kurtosis, Annals of the Institute Statistical thematics, 54, 138-154

17.

Mukerjee, R. and Dey, D. K. (1993). Frequentist validity of posterior quantiles in the presence of a nuisance parameter: Higher order asymptotics, Biometrika, 80, 499-505

18.

Mukerjee, R. and Ghosh, M. (1997). Second order probability matching priors, Biometrika, 84, 970-975

19.

Seshadri, V. (1999). The Inverse Gaussian Distribution: Statistical Theory and Applications, Springer, New York

20.

Stein, C. (1985). On the coverage probability of confidence sets based on a prior distribution, In Sequential Methods in Statistics, Banach Center Publications, 16, 485-514

22.

Tweedie, M. C. K. (1957a). Statistical properties of inverse Gaussian distributions I,The Annals of Mathematical Statistics, 28, 362-377

23.

Tweedie, M. C. K. (1957b). Statistical properties of inverse Gaussian distributions II, The Annals of Mathematical Statistics, 28, 696-705

24.

Welch, B. L. and Peers, H. W. (1963). On formulae for confidence points based on integrals of weighted likelihoods, Journal of the Royal Statistical Society, Serise B, 25, 318-329