We propose a log-linear Poisson regression model driven by stationary latent gamma autoregression. This process has negative binomial (NB) marginals to analyze overdispersed count time series data. Estimation and statistical inference are performed using composite (CL) likelihood function. establish theoretical properties of the proposed model, in particular, strong consistency asymptotic norma...

In this paper, we are concerned with the situations, where sometimes value two is reported erroneously as one in relation to size biased generalized negative binomial distribution (SBGNBD) with probability αα. We have obtained the Maximum likelihood estimator and Bayes estimator under general entropy loss function. A simulated study is carried out to access the performance of the maximum likeli...

The number of new gadolinium-enhancing lesions discovered via magnetic resonance imaging is a well-established outcome for multiple sclerosis studies, especially Phase II Studies. Due to the high cost of magnetic resonance imaging scans, many investigators select participants for the presence of lesions. While this selection procedure is thought to improve the power of inferences, the effect of...

A b s t r a c t . In this paper, we investigate the exact distribution of the waiting time for the r-th t-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of order k and an extended Poisson distr...

This note develops an encompassing model for two well known variants of the negative binomial model (the NB1 and NB2 forms). We conclude with an application of the proposed model using the data employed in a recent health care study. © 2007 Elsevier B.V. All rights reserved.

Accurate statistical model of PET measurements is a prerequisite for a correct image reconstruction when using statistical image reconstruction algorithms, or when pre-filtering operations must be performed. Although radioactive decay follows a Poisson distribution, deviation from Poisson statistics occurs on projection data prior to reconstruction due to physical effects, measurement errors, c...