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One by Chakraborty and Ong (2014) known as the COM-Negative binomial distribution and the other by Imoto (2014) referred to as the generalized COM-Poisson Distribution.
Commonly used statistical distributions, namely the Normal distribution, various types of the Poisson distribution, the Lognormal distribution, the Gamma distribution, the Negative Binomial distribution, and the Poisson-Lognormal distribution are examined and their strengths and weaknesses evaluated.
This probability is calculated using the binomial distribution and the expectation of the motif occurring at each site in the UPC, which is a simple calculation based on the frequency of each amino acid (fa), and the total number of positions that a motif can occur (Nm).
Fortunately, our model represented risk as a simple dichotomy (win vs. lose) which enables the state of the population to be described by a single binomial distribution, and the stochasticity of individual reproduction was represented by a Poisson distribution, which has the convenient property that the sum of multiple Poisson variates is again Poisson.
The 95% confidence intervals (CI) for proportions were estimated by approximation to the binomial distribution and the use of exact methods.
Indeed, the probability that we would observe no mutations if the sample size had a binomial distribution and the mutation rate were high as 0.28 is approximately 1%.
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The sample-size method in a single-stage Fleming design uses a normal approximation to the binomial distribution, and this helped facilitate the calculations for multiple stage testing.
This is achieved by projecting the spatial distribution of habitat complexity scores derived from the videography, backward in time using a combination of simple Boolean logic, estimated binomial distributions, and the use of random fluctuations to mimic natural forest dynamics that are likely to have occurred over the modeling period.
In addition, the covariates included in the model were then fitted using GEE with both Poisson and negative binomial distributions and the following correlation structures: exchangeable, first order autoregressive structure, second order autoregressive structure, non-stationary, and stationary.
The model for infection presence assumes a binomial distribution and models the logit of the probability of infection.
For the nodes in the first cluster, ai, ksubjects to binomial distribution, and therefore the probability of receiving k packets successfully for each node in the first cluster is obtained with Equation (4.11).
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