Assuming that the population response follows a multivariate normal distribution , the conditional dependencies between pairs of neurons are expressed by the partial correlations between them.

We evaluated the covariance matriX estimators using a loss function derived from the normal distribution .

However, this does not limit the applicability of its conclusions to normal distributions .

Here, in the role of the loss function we adopted the Kullback-Leibler divergence between multivariate normal distributions with equal means, scaled by; to make its values comparable across different population sizes:

For simulation, ground truth covariance matrices were produced by taking 150 independent samples from an artificial population of 50 independent, identically normally distributed units.

Samples were then drawn from multivariate normal distributions models with the respective true covariance matrices to be estimated by each of the estimators.

Based on the probability theory and statistics, if the random variable X is log-normally distributed, then Y = log(X) has a normal distribution .

Likewise, if Y has a normal distribution , then X = exp(Y) has a log-normal distribution.

Therefore, there is a physical explanation of the difference in distributions of binding kinetics: Above the characteristic transition temperature Tc, there are multiple parallel kinetic paths, each experiencing certain barriers (barrier has a normal distribution ), resulting in log-normal kinetics (seen also in protein conformational dynamics simulations [31]).

We see that the logarithm of equilibrium constant can be fitted well with a normal distribution near the mean while near the tail can be fitted well with a exponential distribution.

We also see that the distribution of the intrinsic specificity can be fitted well with the normal distribution near the mean and also well fitted with the exponential distribution at the tail.

A random phenotype is first generated for the reference data, drawing from the standard normal distribution .

This yields a roughly normally distributed variable Z with elements zg that reflects the strength of the association each gene has with the phenotype, with higher values corresponding to stronger associations.

Evaluating fig 2 0 against the alternative fig > 0 yields a self-contained test, since under the self-contained null hypothesis that none of the genes is associated with the phenotype zg has a standard normal distribution for every gene g. Competitive gene-set analysis tests whether the genes in a gene-set are more strongly associated with the phenotype of interest than other genes.

One complication that arises in this gene-level regression framework is that the standard linear regression model assumes that the error terms have independent normal distributions , i.e.

As discussed in Methods, we attributed tomographic density to each of the 25 long edges of the polyhedral cage representing the icosahedrally-averaged density considered in this analysis and fitted it to a normal distribution .

A ranking of the level of density associated with these edges was achieved using the mean of the fitted normal distribution .

We computed fitted normal distributions using the normfit function from the scipy.stats python library, since for a sparse dataset the mean of a fitted normal distribution is less affected by outliers than the raw data.

The normal fitting function automatically calculated the best positioning of a unimodal normal distribution for the dataset.

7 (top picture) shows the normalized distribution of windows flexibility values for all 16 chromosomes of yeast genome.

A: Flexibility values normalized distribution for all the yeast chromosomes.

It can be used to determine if two sets of data are significantly different from each other, and is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known.

The relationship between projections and ensemble parameters is eXpressed as with Normal([,t,7t,-'1) denoting the normal distribution with mean [,4 and variance M1.

Here MVN indicates the multivariate normal distribution and ET the covariance matriX.

To demonstrate the effect that a priori trust in different modeling assumptions can have on the posterior estimates, we consider the case where the best, most likely and worst case scenarios for each of the two varied parameters corresponds to percentile 2.5, 50 and 97.5, respectively, of a normal distribution .

Others use the von Mises circular distribution [9, 10], which is a wrapped normal distribution .

Assuming OOPp and OOPQ are normally distributed with the standard deviation UOOPP and O'OOPQ, respectively, and OOPP and OOPQ are independent, then the variance: and the standard deviation:

3) contained 108 random numbers (MATLAB function normrnd) that were normally distributed With the specified mean and standard deviation.

However, Kendall's tau is not appropriate for this type of data because Kendall's tau typically requires the underlying population to be bivariate normal; the frequencies we observe are not normally distributed .

From these quantities, a Z-score and p-Value can be computed assuming a normal distribution using Z = (PfPs)/SE.

While the distribution of PS and Pf are not necessarily normal, the distribution of (PfPS) is normally distributed .

Then, § (given 5) is normally distributed , and eq.

We obtain them as the best (MSE) fit to the following formula: where (I) is the standard cumulative normal distribution .

(Actually, we postulate that E[PlK] is exactly diagonal when the random vectors x.- follow a normal distribution .