Safety analysts usually use post-modeling methods, such as the Goodness-of-Fit statistics or the Likelihood Ratio Test, to decide between two or more competitive distributions or models. Such metrics require all competitive distributions to be fitted to the data before any comparisons can be accomplished. Given the continuous growth in introducing new statistical distributions, choosing the bes...

In cohort studies binary outcomes are very often analyzed by logistic regression. However, it is well-known that when the goal is to estimate a risk ratio, the logistic regression is inappropriate if the outcome is common. In these cases, a log-binomial regression model is preferable. On the other hand, the estimation of the regression coefficients of the log-binomial model is difficult due to ...

This study describes four statistical models—Poisson; Negative Binomial; Zero-Inflated Poisson; and Zero-Inflated Negative Binomial—which were devised in order to examine traffic accidents and estimate the best probability estimating model in terms of future risk assessment at interurban road sections. The study was conducted on four sets of fixed-length sections of the road network: 500, 750, ...

The Poisson regression model is widely used for count data. This assumes equidispersion. In practice, equidispersion seldom reflected in However, real-life data, the variance usually exceeds mean. situation known as overdispersion. Negative binomial distribution and other mix models are often to overdispersion Another extension of negative another data univariate generalized Waring. addition, d...

In this article, we present a general procedure to analyze exchangeable binary data that may also be viewed as realizations of binomial mixtures. Our approach unifies existing models and is practical and computationally easy. Resulting from completely monotonic functions, we introduce a rich family of parametric parsimonious binomial mixtures, including the incomplete Beta-, Gamma-, Normal-, an...

*Correspondence: [email protected] 1Department of Mathematics and Statistics, Georgetown University, 306 St. Mary’s Hall, Washington, DC, 20057, USA Full list of author information is available at the end of the article Abstract The Poisson, geometric and Bernoulli distributions are special cases of a flexible count distribution, namely the Conway-Maxwell-Poisson (CMP) distribution – a two-pa...

Hall (2000) has described zero-inflated Poisson and binomial regression models that include random effects to account for excess zeros and additional sources of heterogeneity in the data. The authors of the present paper propose a general score test for the null hypothesis that variance components associated with these random effects are zero. For a zero-inflated Poisson model with random inter...

I consider the problem of evaluating the effect of a health care reform on the demand for doctor visits when the effect is potentially different in different parts of the outcome distribution. Quantile regression is a useful technique for studying such heterogeneous treatment effects. Recent progree has been made to extend such methods to applications with a count dependent variable. An analysi...

We discuss the identification of features that are associated with an outcome in RNA-Sequencing (RNA-Seq) and other sequencing-based comparative genomic experiments. RNA-Seq data takes the form of counts, so models based on the normal distribution are generally unsuitable. The problem is especially challenging because different sequencing experiments may generate quite different total numbers o...