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The Negative Binomial distribution can model the over-dispersed Poisson gene count where ϕ > 0 and reduces to the Poisson distribution as ϕ → 0.
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We show that the negative binomial distribution can be used to model such datasets on the condition that the overdispersion parameter is known and have proposed an estimator of this parameter that performs well in our segmentation framework.
A negative binomial distribution can be used to model various forms of data and allows us to account for clustering, which is an expected clinical phenomena confirmed by our results.
Especially in cases with the occurrence and abundance of a species resulting from distinct processes, the zero-inflated modification of the negative binomial distribution can result in considerable model improvements (Wenger and Freeman [2008]).
The negative binomial distribution can be derived from a two-stage model for the distribution of a discrete variable Y (Venables and Ripley [2002]).
It is known that for a fixed dispersion, a negative binomial distribution can be placed in a generalized linear model framework.
A generalized linear model using a negative binomial distribution can be readily adapted to multi-factor comparisons using DESeq or edgeR software as we demonstrated here.
For example, if there are biological replicates, the count data may have over-dispersed variances, other models such as over-dispersed Poisson distribution or negative binomial distribution can be used [ 8, 9].
Since the negative binomial distribution can be regarded as the discrete equivalent to the gamma distribution, a number of alternative statistical models could be constructed to explain the PG distribution [ 19].
In a fixed-effects model, the beta-binomial distribution can be used when there is overdispersion with respect to the binomial distribution.
The results proved that the beta-binomial distribution can be very useful for analyzing vegetation landscapes.
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