Semiparametric inference based on a class of zero-altered distributions

Abstract

In modeling count data collected from manufacturing processes, economic series, disease outbreaks and ecological surveys, there are usually a relatively large or small number of zeros compared to positive counts. Such low or high frequencies of zero counts often require the use of underdispersed or overdispersed probability models for the underlying data generating mechanism. The commonly used models such as generalized or zero-inflated Poisson distributions are parametric and can usually account for only the overdispersion, but such distributions are often found to be inadequate in modeling underdispersion because of the need for awkward parameter or support restrictions. This article introduces a flexible class of semiparametric zero-altered models which account for both underdispersion and overdispersion and includes other familiar models such as those mentioned above as special cases. Consistency and asymptotic normality of the estimator of the dispersion parameter are derived under general conditions. Numerical support for the performance of the proposed method of inference is presented for the case of common discrete distributions.

Estimation of SCRAM Rate Trends in Nuclear Power Plants Using Hierarchical Bayes Models

“…However, when modeling the underdispersion, the support of the generalized Poisson distribution depends on the parameter making it unsuitable for real applications. For an extension of such models that account for both over and under dispersion, see Ghosh and Kim (2007). In the present case, empirical analysis…”

“…One possibility could be to use generalized Poisson distribution to allow for overdispersion or underdispersion. Another possibility would be to relax the Poisson assumption within the Zero-Inflated Distribution (ZID) framework by considering models similar to those proposed by Ghosh and Kim (2007). Also, an extension to the higher order autoregressive processes (or even a random walk process) for the log ij 's instead of the simple AR(1) process that we have explored in this article could be implemented.…”

Derivation and verification of influence function on parameter δ proposed by Ghosh and Kim

“…본 논문에서는 비음정수값을 갖는 변수에 적용되는 Ghosh와 Kim (2007)의 영 변환(zero-altered) 모형 모수 δ에 대한 영향함수를 유도하고 통계청 인구주택총조사(표본)의 '연령 및 출생자녀수별 기혼여성인 구(15세 이상)' 자료를 적용하여 유도한 영향함수의 타당성을 평가하였다.…”

“…. }에서 값을 가지는 이산확률변수 U 의 확률질량함수를 f0(u)라 하고, 모든 u에서 f0(u) < 1이라 가정하고, 이 확률분포의 u = 0에서의 확률 f0(0)를 임의로 변경했을 때 Ghosh와 Kim (2007)의 산포형태모수(dispersion type parameter) δ ∈ (−1, 1)가 정의되면 다음과 같은 확률질량함수 f δ (x)를 구할 수 있다. Kim, 2007).…”

Type I multivariate zero-inflated Poisson distribution with applications

“…For univariate ZIP distribution, considerable work has been done in Cohen (1960Cohen ( , 1963, Singh (1963), Martin and Katti (1965), Johnson and Kotz (1969), Goraski (1977), Kemp (1986) and Böhning et al (1999). Examples of the ZIP distribution have studied in Ghosh and Kim (2007). When effects were incorporated into the extra zero Poisson components, the ZIP regression models with covariates were considered by Lambert (1992), Cheung (2002), Famoye and Singh (2006), and also Cui and Yang (2009).…”