On Interval Estimation of the Geometric Parameter in a Zero–inflated Geometric Distribution

Abstract

Many real-life situations contain count data with an excessive number of zeros. Such situations can be explained by a zero-inflated geometric distribution (ZIG). The score confidence intervals using observed and expected Fisher information based on profile likelihood and the Wald confidence interval using profile likelihood (WCP) are all derived for the geometric parameter of the ZIG in this paper. These proposed intervals are compared with the Wald confidence interval using full likelihood (WC), the most commonly used interval. Then, Monte-Carlo simulations are used to compare all the intervals, and the results show that the score intervals outperform the Wald-type intervals in terms of coverage probability. Also, proposed score intervals and the WCP have closed forms and can be computed without the use of a computer, whereas the WC does not. As a result, the proposed formulas are beneficial in practice.