# negative binomial distribution

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## negative binomial distribution

[¦neg·əd·iv bī¦nō·mē·əl ‚di·strə′byü·shən]
(statistics)
The distribution of a negative binomial random variable. Also known as Pascal distribution.
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the inflated negative binomial distribution has three parameters).
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):
The use of the negative binomial distribution for the outcome variable ensures that overdispersion (where the variance of the outcome variable is greater than the mean) is also accounted for, something which the Poisson distribution does not do.
The researchers used generalized linear model (GLM) for modelling the frequency of women's visits for ANC, where response followed the negative binomial distribution.
We fit the transmission data from patients within subgroups to the negative binomial distribution with mean R and dispersion parameter k, which characterizes individual variation in transmission, including the likelihood of superspreading events (i.
As the negative binomial distribution model has exponential conditional mean, its coefficient estimate can be interpreted as a semi-elasticity (Cameron and Trivedi 2009).
When fitting a negative binomial distribution to the entire pond using a Chi-Square test, the distribution was not statistically different from a negative binomial distribution at P = 0.
1978; Perry and Taylor 1985) we used the finite version of negative binomial distribution (Zillio and He 2010; Chen 2013a) to measure distributional aggregation of species.
The parameters a and b of the beta-binomial model can be chosen to provide flexibility to handle many possible situations in health services research that have this "probability" nature of constraining between 0 and 1, and are more diffuse than the over-dispersion capabilities of the negative binomial distribution (Morris and Lock 2009).
Moreover, of all the 15 sampling events performed, ten samples adjusted to the negative binomial distribution model with non-significant chi-square value.
For this reason, the negative binomial distribution (nbd) was deemed more appropriate than Poisson.

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