Statistical Analysis of Location Parameter of Inverse Gaussian Distribution Under Noninformative Priors
Abstract
Bayesian estimation for location parameter of the inverse Gaussian distribution is presented in this paper. Noninformative priors (Uniform and Jeffreys) are assumed to be the prior distributions for the location parameter as the shape parameter of the distribution is considered to be known. Four loss functions: Squared error, Trigonometric, Squared logarithmic and Linex are used for estimation. Bayes risks are obtained to find the best Bayes estimator through simulation study and real life data
Downloads
References
Chhikara, R. S., & Folks, J. L. (1974). Estimation of the inverse Gaussian distribution function, Journal of the American Statistical Association, 69(345), 250-254.
Feroze, N. (2012). Estimation of scale parameter of inverse Gausian distribution under a Bayesian framework using different loss functions. Scientific Journal of Review, 1(3), 39-52.
Ismail, S. A., & Auda, H. A. (2006). Bayesian and fiducial inference for the inverse Gaussian distribution via Gibbs sampler. Journal of Applied Statistics, 33(8), 787-805. https://doi.org/10.1080/02664760600742268.
Khan, N. (2014), Statistical Analysis of Inverse Gaussian Distribution in Bayesian Framework (Unpublished MPhil Thesis), Quaid-i-Azam University, Islamabad, Pakistan.
Lemeshko, B. Y., Lemeshko, S. B., Akushkina, K. A., Nikulin, M. S., Saaidia, N., Saaidia N. (2010). Inverse Gaussian model and its applications in reliability and survival analysis. In Mathematical and statistical models and methods in reliability (pp. 433-453). Birkhäuser, Boston, MA: United States. https://doi.org/10.1007/978-0-8176-4971-5 33,
Lindley, D. V. (1980). Approximate Bayesian methods. Trabajos De Estadística Y De Investigación Operativa, 31(1), 223-245. https://doi.org/10.1007/BF02888353.
Ma, T., Liu, S., & Ahmed, S. E. (2014). Shrinkage estimation for the mean of the inverse Gaussian population. Metrika, 77(6), 733-752. https://doi.org/10.1007/s00184-013-0462-8.
Meintanis, S. G. (2008). Tests of fit for normal variance inverse Gaussian distributions. In Proceedings of the World Congress on Engineering (Vol. 2) London, U.K.
Pandey, H., & Rao, A. K. (2010). Bayesian estimation of scale parameter of inverse Gaussian distribution using linex loss function. Journal of Computer and Mathematical Sciences, 1(2), 103-273.
Stogiannis, D., & Caroni, C. (2012). Tests for outliers in the inverse Gaussian distribution, with application to first hitting time models. Journal of Statistical Computation and Simulation, 82(1), 73-80. https://doi.org/10.1080/00949655.2010.527843.
Sinha, S. K. (1986). Bayesian estimation of the reliability function of the Inverse Gaussian distribution. Statistics & Probability Letters, 4(6), 319-323. https://doi.org/10.1016/0167-7152(86)90052-0.
Copyright (c) 2019 Nida Khan, Muhammad Aslam
This work is licensed under a Creative Commons Attribution 4.0 International License.
JQM follows an open-access publishing policy and full text of all published articles is available free, immediately upon publication of an issue. The journal’s contents are published and distributed under the terms of the Creative Commons Attribution 4.0 International (CC-BY 4.0) license. Thus, the work submitted to the journal implies that it is original, unpublished work of the authors (neither published previously nor accepted/under consideration for publication elsewhere). On acceptance of a manuscript for publication, a corresponding author on the behalf of all co-authors of the manuscript will sign and submit a completed Copyright and Author Consent Form.