Full Bayesian Significance Test for Zero-Inflated Distributions

ABSTRACT

In this article, we discuss an application of the Full Bayesian Significance Test (FBST) introduced by Pereira and Stern (1999) to compute the evidence of the Poisson distribution against the Zero-Inflated Poisson distribution (ZIP). The FBST is intuitive and easy to implement via Winbugs as an alternative to the classical tests formulated by Xie et al. (2001) in statistical process context. This evidence measure is based on the augmented data and used to test the fitting of the ZIP model for count data with excess of zeros in two illustrative examples in the statistical process control and the horticultural research.

Keywords:

• Augmented data
• Evidence
• Gibbs sampling
• Poisson distributions
• Horticultural research
• Mixture distributions
• Statistical control process

Mathematics Subject Classification:

• 62F15

Acknowledgment

The author is very grateful to the anonymous referee for his helpful comments and valuable suggestions on previous version of this article.

Notes

Fitted frequency: O = Total observed frequency; E _P  = Fitted Poisson frequency; E _ZIP = Fitted ZIP frequency