Bayes Estimator for inverse Gaussian Distribution with Jeffrey’s Prior

Volume 6, Issue 4, August 2021     |     PP. 44-50      |     PDF (245 K)    |     Pub. Date: October 24, 2021
DOI: 10.54647/mathematics11287    98 Downloads     2900 Views  

Author(s)

Zul Amry, Department of Mathematics, State University of Medan, Indonesia

Abstract
This paper presents a Bayesian analysis of the parameters for the inverse Gaussian distribution under the Jeffrey’s prior assuming a quadratic loss function. Analysis begins with the parameterization to the parameters in the distribution, then construct the posterior distribution based the likelihood function and prior, while the Bayes estimator is concluded based the posterior mean.

Keywords
inverse Gaussian distribution, bayes theorem, Jeffrey’s prior

Cite this paper
Zul Amry, Bayes Estimator for inverse Gaussian Distribution with Jeffrey’s Prior , SCIREA Journal of Mathematics. Volume 6, Issue 4, August 2021 | PP. 44-50. 10.54647/mathematics11287

References

[ 1 ] Bain, L. J. and Engelhardt, M., Introduction to Probability and Mathematical Statistics, 2nd, Duxbury Press, Belmont, California, 2006.
[ 2 ] Berger, J. O., Statistical Decision Theory and Bayesian Analysis, second edition, Springer-Verlag, New York, 1985.
[ 3 ] Bolstad, W. M., Introduction to Bayesian Statistics, John Willey and Sons, 2004.
[ 4 ] DeGroot, Optimal Statistical decision, John Willey and Sons, New Yersey, 2004.
[ 5 ] Jia, J., Yan, Z., and Peng, X., Estimation for Inverse Gaussian Distribution Under First-failure Progressive Hybrid Consored Samples, Filomat 31:18 (2017),5743-5752.
[ 6 ] Mudholkar, G. S. and Natarajan, R. (2002), The Inverse Gaussian Models: Analogues of Symmetry, Skewness and Kurtosis, Ann. Inst. Statist. Math., Vol. 54, No.1,138-154
[ 7 ] Ramachandran, K. M. and Tsokos, C. P., Mathematical Statistics with Applications. Elsevier Academic Press, San Diego, California, 2009.
[ 8 ] Vladimirescu, I. and Tunaru, R., Estimation Functions and Uniformly Most Powerful Test for Inverse Gaussian Distribution, Comment.Math.Univ.Caroline 44,1 (2003) 153-164.
[ 9 ] Zul Amry, Bayesian Estimate of Parameters for ARMA Model Forecasting. Tatra Mountains Mathematical Publication, Vol.75, (2020), 23-32.