A pivot function and its limiting distribution: applications in goodness of fit and testing hypothesis

ABSTRACT

In this paper, a pivot function which is in terms of the sample and the underlying population distribution is introduced. It is assumed that the population distribution is continuous and strictly increasing on its support. Then, the martingale central limit theorem is applied to prove that limiting distribution of the pivot function is the standard normal. Interestingly, this result provides a unified procedure that can be applied for the goodness of fit, and for the purpose of parametric and nonparametric inferences, for the populations having distribution functions that are continuous and strictly increasing on their supports. The method is fairly simple and can be easily applied.

KEYWORDS:

• Pivot function
• testing hypothesis
• confidence intervals
• confidence regions
• goodness of fit

AMS subject classifications:

• 60F05
• 60E99

Acknowledgments

The author would like to thank the Kuwait University Research Administration for funding this research project, under SS01/17. The author is indeed indebted to the referees for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This Research is supported and funded by the Kuwait University Research Administration under the Research Project SS01/17.