Is the Selected Multinomial Cell the Best?

Abstract

Suppose observations are taken sequentially from a multinomial distribution with k cells until the count in one of the cells reaches a predetermined number M. With a view to select the cell with the largest probability, we select the cell that has the largest count M. The problem of testing if the selected multinomial cell is the best is being considered in this paper. We propose the test procedure and show that the supremum of the probability of error for our procedure can be written as a single integral involving the gamma distribution. Exact values of the supremum of the probability of error are tabulated and its approximation formula for large values of M is provided.

Keywords:

• Inverse sampling
• Multinomial distribution
• Normal approximation
• Optimality property
• Probability of error

Subject Classifications:

• 62L10
• 62C99
• 62F99

ACKNOWLEDGMENTS

Our sincere thanks go to the Editor, the Associate Editor, and two anonymous referees for their criticisms and constructive comments, which led to a considerable improvement of this paper.