# negative binomial distribution

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## negative binomial distribution

A distribution parameterised by a mean and an aggregation parameter that is large when aggregation is small; as it becomes larger, the negative binomial distribution approximates a Poisson distribution. Aggregated distributions are often well described empirically by the negative binomial distribution. For instance, macroparasites are typically aggregated in their host populations, such that most hosts harbour few or no parasites while a few have large parasite burdens.
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Estimated incidence rate ratios of the seasonal component from the negative binomial regression models before and after the 2011 upsurge of scarlet fever, Hong Kong.
Table 1 presents baseline negative binomial regression results using homicide data respectively calculated from the SHR and CDC and controls for the effects of state and time using two different fixed-effects specifications.
Of the 3 data sets that used 4 classes and were not satisfactorily fit, one (Premeaux tier 2) approached statistical significance with the negative binomial distribution, but the other two (Premeaux tier 1 and McCabe) did not come close to a satisfactory fit.
To determine the final multivariate model, at first a univariate negative binomial regression analysis was conducted to measure unadjusted effect of factors influencing unhealthy snacking behavior.
The negative binomial multivariable models assessing the effects of distance provided evidence of a statistically significant inverse association with distance for the CFPP models (i.
In a negative binomial regression model, pleasant image rating at baseline predicted less drinks per week at 12-month follow-up (B = -.
First, we identified the environmental triggers that might have an impact on rescue inhaler use through an unadjusted zero-truncated negative binomial model.
2) to find the best model in each of four model classes (Poisson, P; negative binomial, NB; zero-inflated Poisson, ZIP; zero-inflated negative binomial, ZINB), by eliminating vegetation parameters from the full model until we arrived at a subset of vegetation components with the lowest corrected Akaike Information Criterion (AICc) (Burnham et al.
Notice that all the estimated coefficients (Table 3) need to be interpreted, considering that the model is in the log scale (the negative binomial part) and in the logit scale (the zero-inflated part).
The k parameter of the negative binomial distribution estimated by the maximum likelihood method is calculated iteratively and is the value that equates the two members of the following (Bliss and Fisher, 1953):
After adjusting for gender, age, and chronic health conditions (other than asthma), the results for the negative binomial regressions (Table 6) show that the mean percentage difference in physician visits for the control group (compared to the uncontrolled group) was -92.
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