A generalisation of geometric distribution

Abstract

We consider a sequence of independent and identical trinomial experiments and a typical stopping rule. The distribution of the stopping time is obtained by using a recurrence relation. Moments, generating functions and characteristic functions of stopping time are obtained. The parameters are estimated by three different methods and their performance is evaluated using extensive simulation. As applications, it is shown that the model gives a better fit than some of the recently proposed models for a count data set and can be used to develop process control charts. Scope for generalization is indicated.

Keywords:

• Multinomial distribution
• stopping rule and time
• recurrence relation

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 62F10

Acknowledgement

We are grateful to an Associate Editor and a Reviewer for their comments which helped to improve the manuscript.