We characterize all stationary time-reversible Markov processes whose finite-dimensional marginal distributions (of all orders) are infinitely divisible. Aside from two trivial cases (iid and constant), every such process with full support in both discrete and continuous time is a branching process with Poisson or Negative Binomial marginal distributions and a specific bivariate distribution at...

Background: The number of failed courses and semesters in students are indicatorsof their performance. These amounts have zero inflated (ZI) distributions. Using ZI Poisson and negative binomial distributions we can model these count data to find the associated factors and estimate the parameters. This study aims at to investigate the important factors related to the educational performance of ...

Counting outcomes such as days of physical activity or servings of fruits and vegetables often have distributions that are highly skewed toward the right with a preponderance of zeros, posing analytical challenges. This paper demonstrates how such outcomes may be analyzed with several modifications to Poisson regression. Five regression models 1) Poisson, 2) overdispersed Poisson, 3) negative b...

The importation model is a venerable theoretical explanation for inmate misconduct but it has not been extended in nearly 50 years. The current study advances a life course importation model of inmate behavior where life events in childhood cascade to predict antisocial behavior during adolescence and misconduct occurring during periods of confinement. Based on data from 2,520 institutionalized...

Copy number variations (CNVs) are a significant source of genetic variation and have been found frequently associated with diseases such as cancers and autism. High-throughput sequencing data are increasingly being used to detect and quantify CNVs; however, the distributional properties of the data are not fully understood. A hidden Markov model (HMM) is proposed using inhomogeneous emission di...