International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 9, Pages 587-592
doi:10.1155/S0161171203207237

A regression characterization of inverse Gaussian distributions and application to EDF goodness-of-fit tests

Khoan T. Dinh,1 Nhu T. Nguyen,2 and Truc T. Nguyen3

 1US Environmental Protection Agency (EPA), Washington 20460, DC, USA
2Department of Mathematical Sciences, New Mexico State University, Las Cruces 88003-8001, NM, USA
3Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403-0221, OH, USA
Received 15 July 2002

Abstract

We give a new characterization of inverse Gaussian distributions using the regression of a suitable statistic based on a given random sample. A corollary of this result is a characterization of inverse Gaussian distribution based on a conditional joint density function of the sample. Application of this corollary as a transformation in the procedure to construct EDF (empirical distribution function) goodness-of-fit tests for inverse Gaussian distributions is also studied.