Exact Inference in a Tetranomial Distribution

Abstract

Sequential sampling plans for unbiased estimation of the Bernoulli parameter ‘p’ and its functions have been studied almost 70 years back. An extension of the idea to parametric function estimation in a tetranomial distribution has been considered in this paper. The cell probabilities are taken to be p², q², r² and 2(pq+pr+qr), satisfying p, q, r > 0, p +q +r = 1. Some illustrative examples have been studied to demonstrate the underlying concepts and the computational procedure. The emphasis is on unbiased estimation in the exact sense which makes it difficult and challenging.

Keywords:

• Repeated Bernoulli trials
• Tetranomial multi-parameter distribution
• Simultaneous unbiased estimation
• Generalized waiting time distribution

ACKNOWLEDGEMENT

The authors thank the reviewers and the Associate Editor for carefully going through the manuscript. Their comments have helped to improve the presentation of the paper. The second author was attached to the Department of Statistics, University of Calcutta, India during preparation of the paper.