Estimating the Negative Binomial Dispersion Parameter

Estimating the Dispersion Parameter of the Negative Binomial Distribution for Analyzing Crash Data Using a Bootstrapped Maximum Likelihood Method

The objective of this study is to improve the estimation of the dispersion parameter of the negative binomial distribution for modeling motor vehicle collisions. The negative binomial distribution is widely used to model count data such as traffic crash data, which often exhibit low sample mean values and small sample sizes. Under such situations, the most commonly used methods for estimating t...

Adjustment for the Maximum Likelihood Estimate of the Negative Binomial Dispersion Parameter

Negative Binomial (or Poisson-gamma) model has been used extensively by highway safety analysts because it can accommodate the over-dispersion, often exhibited in crash data. However, it has been reported in the literature that the maximum likelihood estimate of the dispersion parameter of NB models can be significantly affected when the data are characterized by small sample size and low sampl...

Confidence intervals for negative binomial random variables of high dispersion.

We consider the problem of constructing confidence intervals for the mean of a Negative Binomial random variable based upon sampled data. When the sample size is large, it is a common practice to rely upon a Normal distribution approximation to construct these intervals. However, we demonstrate that the sample mean of highly dispersed Negative Binomials exhibits a slow convergence in distributi...

Modeling over-dispersed crash data with a long tail: Examining the accuracy of the dispersion parameter in negative binomial models

Maximum Likelihood Estimation of the Negative Binomial Dispersion Parameter for Highly Overdispersed Data, with Applications to Infectious Diseases

BACKGROUND The negative binomial distribution is used commonly throughout biology as a model for overdispersed count data, with attention focused on the negative binomial dispersion parameter, k. A substantial literature exists on the estimation of k, but most attention has focused on datasets that are not highly overdispersed (i.e., those with k>or=1), and the accuracy of confidence intervals ...