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The parameterized power binomial mean can be immediately given by B p, t ( a, b ) = ( ( 1 − t ) a p + t b p ) 1 / p, for p ≠ 0, with B 0, t ( a, b ) = a 1 − t b t = G t ( a, b ).
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By contrast, for the negative binomial and gamma distributions, which have additional parameters which can reflect skewness, sample size calculations based on differences in means can be very conservative, giving larger numbers which substantially exceed the required power.
Sometimes, means can be very mean.
That's a practical advantage over the calculus-based Black-Scholes-Merton model, because it means binomial models can be built using standard spreadsheet software.
Unlike the binomial distribution, the beta binomial can be convex as well as concave.
Binomial data can be processed more efficiently on MapReduce.
For instance, comparisons between Zero inflated count models with ordinary Poisson, or Zero inflated negative binomial against ordinary negative binomial model can be done using Voung test.
For smaller regions, the binomial probabilities can be calculated directly.
cThe details of our negative binomial model can be found in Additional file 3, including Additional file 5: Figure S1, which shows the maximum likelihood estimates of the model's mean and dispersion parameters for 46, 446 transcript isoforms.
An HGT calculation takes O(N) time, assuming binomial coefficients can be calculated in constant time.
Again Poisson, negative binomial, zero-inflated Poisson or zero-inflated negative binomial regression can be used to model such count data depending on the extent of overdispersion.
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