A negative binomial mixture integer-valued GARCH model

A mixture integer-valued GARCH model

Abstract. In this paper, we generalize the mixture integer-valued ARCH model (MINARCH) introduced by Zhu et al. (2010) to a mixture integer-valued GARCH (MINGARCH) for modeling time series of counts. This model include the ability to take into account the moving average (MA) components of the series. We give the necessary and sufficient first and second order stationarity conditions. The estima...

Negative Binomial Mixture Conditioning

Fisher's logarithmic series model (Fisher et al. (1943)) is a classical model in statistical ecology. In this paper we show that this model is a key model linking three models discussed in Takemura (1997), i.e., Poisson-gamma model (Bethlehem et al. (1990)), Dirichlet-multinomial model (Takemura (1997)), and Ewens model (Ewens (1990)). This connection opens up the possibility of applying existi...

On Some Negative Integer Moments of Quasi-Negative-Binomial Distribution

Negative Binomial as a hierarchical mixture for read counts

In this supplementary material we go over some of the statistical details pertaining to the use of hierarchical mixture models such as the Negative Binomial and the Beta Binomial, which are appropriate for addressing additional sources of variability inherent to microbiome experimental data, while still retaining statistical power. We have concentrated our comparison efforts on the Gamma-Poisso...

The Negative Binomial Distribution Efficiency in Finite Mixture of Semi-parametric Generalized Linear Models

Introduction Selection the appropriate statistical model for the response variable is one of the most important problem in the finite mixture of generalized linear models. One of the distributions which it has a problem in a finite mixture of semi-parametric generalized statistical models, is the Poisson distribution. In this paper, to overcome over dispersion and computational burden, finite ...