Abstract
In this paper, we consider inference about the shape parameters of several inverse Gaussian distributions. At first, an approach is given to test the equality of these parameters based on modified likelihood ratio test. Then, five approaches are presented to construct confidence intervals for the common shape parameter. The performance of these approaches is studied using Monte Carlo simulation, and illustrated using a real data set.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barndorff-Nielsen OE (1991) Modified signed log likelihood ratio. Biometrika 78(3):557–563
Chaubey YP, Sen D, Saha KK (2014) On testing the coefficient of variation in an inverse Gaussian population. Stat Probab Lett 90:121–128
Chhikara RS, Folks JL (1989) The inverse Gaussian distribution. Marcel Dekker, New York
Cox DR, Hinkley DV (1979) Theoretical statistics. Chapman and Hall, London
DiCiccio TJ, Martin MA, Stern SE (2001) Simple and accurate one-sided inference from signed roots of likelihood ratios. Can J Stat 29(1):67–76
Fraser DAS, Reid N, Wu J (1999) A simple general formula for tail probabilities for frequentist and Bayesian inference. Biometrika 86(2):249–264
Hsieh HK (1990) Inferences on the coefficient of variation of an inverse Gaussian distribution. Commun Stat Theory Methods 19(5):1589–1605
Krishnamoorthy K, Lee M (2014) Improved tests for the equality of normal coefficients of variation. Comput Stat 29(1–2):215–232
Lin S-H (2013) The higher order likelihood method for the common mean of several log-normal distributions. Metrika 76(3):381–392
Liu X, Xu X (2015) A note on combined inference on the common coefficient of variation using confidence distributions. Electron J Stat 9(1):219–233
Liu X, Li N, Hu Y (2015) Combining inferences on the common mean of several inverse Gaussian distributions based on confidence distribution. Stat Probab Lett 105:136–142
Niu C, Guo X, Xu W, Zhu L (2014) Testing equality of shape parameters in several inverse Gaussian populations. Metrika 77(6):795–809
Schweder T, Hjort NL (2002) Confidence and likelihood. Scand J Stat 29(2):309–332
Seshadri V (1988) A U-statistic and estimation for the inverse Gaussian distribution. Stat Probab Lett 7(1):47–49
Seshadri V (1999) The inverse Gaussian distribution: statistical theory and applications. Springer, New York
Singh K, Xie M, Strawderman WE (2005) Combining information from independent sources through confidence distributions. Ann Stat 33(1):159–183
Skovgaard IM (2001) Likelihood asymptotics. Scand J Stat 28(1):3–32
Tian L (2006) Testing equality of inverse Gaussian means under heterogeneity, based on generalized test variable. Comput Stat Data Anal 51(2):1156–1162
Acknowledgements
The authors are grateful to the Editor in Chief and anonymous referees for their helpful comments and suggestions to improve this manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kazemi, M.R., Jafari, A.A. Inference about the shape parameters of several inverse Gaussian distributions: testing equality and confidence interval for a common value. Metrika 82, 529–545 (2019). https://doi.org/10.1007/s00184-018-0693-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-018-0693-9