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This method of forming a negative binomial approximation for the coverage spectrum is robust when bins have few reads, but is more sensitive to fluctuations in the number of bins with very many reads.
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Therefore, we propose a fast bi-binomial approximation for calculation of P-values and show that this statistic is superior to other measures of association such as the Jaccard coefficient and the uncertainty coefficient.
Having determined p2 (12) and p1 (13) as well a N1 and N2 (16, 16, 6), we can now calculate the bi-binomial approximation of the Poisson-binomial distribution in a fashion that is very similar to calculate the binomial P-value.
We first present in details how the delta-method can be used to get a Gaussian approximation for the distribution of S N (using a binomial approximation to compute the pattern statistics).
A binomial approximation to the normal distribution was used to calculate the Z-score where: A Z-score > 1.64 (P < 0.05, one-sided test) was considered significant when testing for overrepresentation of a given HT.
Some approximate statistical inference procedures which are based on the binomial approximation are available in the literature.
The variances for the year of autopsy interval black and white standardized proportions were calculated using the binomial approximation method without corrections for finite populations (Cochran 1977).
As Fig. 1 (the dotted line) shows, for a wide range of λ the binomial approximation is valid.
By taking this extreme example, qmin is calculated with the additive assumption but without the binomial approximation.
Then, the probability of neutral replication is obtained (by using the binomial approximation) as where d = v + δ.
The convergence (21) is the standard Gaussian approximation for the binomial distribution.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com