Two-stage and sequential estimation of parameter N of binomial distribution when p is known

ABSTRACT

In this article, we propose two-stage and purely sequential procedures to construct bounded width and prescribed proportional closeness confidence intervals for the unknown parameter N of B(N,p) distribution where the parameter p is assumed to be known. The exact distributions of the stopping variables and the estimators of N at stopping are derived for all cases. The coverage probabilities of the proposed interval estimator are computed exactly and are shown to be nearly the same as the prescribed level.

KEYWORDS:

• Bounded width
• exact computations
• proportional closeness interval
• sequential sampling
• stopping variable
• two-stage sampling

MATHEMATICS SUBJECT CLASSIFICATION:

• 60G51
• 60K15
• 60K40

Acknowledgments

The authors gratefully acknowledge Professor Rasul A. Khan for suggesting this problem and for his assistance and encouragement. We also thank the Editor, Professor Nitis Mukhopadhyay, for providing his valuable feedback that helped improve this article.