Goodness-of-fit tests for multinomial models with inverse sampling

Abstract

This article proposes goodness-of-fit tests for multinomial models using an inverse sampling scheme. From the multiple decision-theoretic perspective, we devise a test statistic and stopping rule that satisfy a prespecified probability level P* and obtain corresponding optimal sample sizes. Incomplete Dirichlet type II distribution functions are used to develop the procedure and to express the probability of correct decisions for various cell configurations for multinomial models. For empirical studies, Monte Carlo experiments are conducted, and for illustrations, various cell configurations of a wheel of fortune are demonstrated.

Keywords:

• Dirichlet type II distribution
• goodness-of-fit test
• inverse sampling
• multiple decision-theoretic framework
• optimal sample size

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62L15
• 62F03
• 62F07

ACKNOWLEDGMENTS

The author is grateful to three anonymous referees for their detailed editorial comments and suggestions on the initial manuscript and to the Editor for providing an extension to revise. I would like to express my deep gratitude to Professor S. Ethier for his editorial suggestions, comments, and discussion during the revision of this article.

DISCLOSURE

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by the University of Nevada, Las Vegas under Faculty Opportunity Award (FOA) Research Grant No. GF06713.