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The number of positions shared by chance between two species is a random variable distributed, approximately, according to a binomial distribution with the probability of success p = N i N j / N, and N experiments.
Upper control limits were then calculated as the 68th, 95th, and 99th‰ of the corresponding binomial distribution, with the mean being equal to n times the estimated proportion.
R i follows a binomial distribution with the mean and variance indicated below: mu(R_{i}) = N * bp * n * p_{i} - (e_{i} + m_{i} r_{i})*n.
The higher ROC curve originates from the binomial distribution with the same sampling plan; nevertheless, due to the mathematics of the binomial, consumer and supplier risks result in much larger values, greater than 10%.
In this approximation of independent events, the probability to have energy ζ localized in a group of a oscillators out of a total of s is given by a binomial distribution with the probability of each event p = a/s v (14).
De Moivre's most notable achievement in probability was the discovery of the first instance of central limit theorem, by which he was able to approximate the binomial distribution with the normal distribution.
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We specify a sample size of n = 110, so that under the binomial distribution with FPR=.01, the upper 2.5% bound equals.03 × 110.
p-values for individual mice were computed using the probability density function of the binomial distribution, with N = the number of trials of a given type and p = baseline accuracy.
This proportion is the maximum likelihood estimate of p. The probability of a set of observations, conditioned on an underlying sex ratio, is calculated according to the binomial distribution with parameter p. The likelihood of the observations is proportional to this probability.
The sampling was performed with random generation for the binomial distribution with probability given by the frequency of each codon in the lowly expressed genes (supplementary table S6, Supplementary Material online).
This requires the adaptation of the algorithm to the negative binomial distribution with which we model the data.
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