The Overlooked Polynomial Coefficient in Zero-Inflated Distribution Likelihood

• Activity Number: 33
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Peng Liu*+
• Companies: SAS Institute Inc.
• Keywords: Zero-inflated Distribution ; Likelihood Approximation ; Polynomial Coefficient

Abstract

The probability function of a zero-inflated distribution is usually expressed as two conditional probability or density, given whether the value of the random variable is zero or not. And the likelihood function is constructed by multiplying such probabilities or densities. There were no concerns until the maximized likelihood or related quantities are listed with those quantities obtained by maximizing other distribution models, which do not belong to zero-inflated distribution family. We notice that a polynomial coefficient constant in the likelihood has been overlooked. We have not seen this constant mentioned in the literature. In this paper, we enumerate some forms of zero-inflated distribution in the literature. We describe the situation where concerns arise. And we construct a simulation study to illustrate situations with or without taking the constant into account.