# 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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The simulated envelopes of the negative binomial distribution (Figure 2) showed that the residuals are distributed around the mean and inside the confidence limits; and therefore, the results confirm the good fit of the model.
The negative binomial distribution was used to build a sequential sampling plan using Wald's (1945) SPRT, on the basis of the number of fruits with at least one mite data.
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.e., when infected persons disproportionately transmit the virus to others) (25).
Besides, the P value of negative binomial distribution is the largest, which means that negative binomial distribution is able to fit the frequency best.
where NB refers to the negative binomial distribution with fitted dispersion parameter k and mean [[mu].sub.i] is the expected number of seals in a given block, modeled as the exponential of a linear combination f(.) of the covariates.
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).
Exponent k of the negative binomial distribution: the exponent k is a suitable dispersion index when the size and numbers of sample units are the same in each sample, since this is frequently influenced by the size of the sampling units.
For this reason, the negative binomial distribution (nbd) was deemed more appropriate than Poisson.
A random variable X has negative binomial distribution with parameters r>0 and p [member of] (0,1), if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where the binomial coefficient is defined by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The univariate negative binomial distribution is uniquely defined in many statistical textbooks.
Thus, when the variance is substantially larger than the mean, overdispersion is suggested and the negative binomial distribution is considered more appropriate.
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