Search results
Results from the WOW.Com Content Network
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure
In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be in. It is also called the theory of irregularities of distribution . This refers to the theme of classical discrepancy theory, namely distributing points in some space such that they are evenly distributed with respect to some ...
The total variation distance (or half the norm) arises as the optimal transportation cost, when the cost function is (,) =, that is, ‖ ‖ = (,) = {(): =, =} = [], where the expectation is taken with respect to the probability measure on the space where (,) lives, and the infimum is taken over all such with marginals and , respectively.
Squared deviations from the mean (SDM) result from squaring deviations.In probability theory and statistics, the definition of variance is either the expected value of the SDM (when considering a theoretical distribution) or its average value (for actual experimental data).
Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered.
The mean absolute difference is twice the L-scale (the second L-moment), while the standard deviation is the square root of the variance about the mean (the second conventional central moment). The differences between L-moments and conventional moments are first seen in comparing the mean absolute difference and the standard deviation (the ...
Then, under the null hypothesis that M 2 is the true model, the difference between the deviances for the two models follows, based on Wilks' theorem, an approximate chi-squared distribution with k-degrees of freedom. [5] This can be used for hypothesis testing on the deviance. Some usage of the term "deviance" can be confusing. According to ...
With any number of random variables in excess of 1, the variables can be stacked into a random vector whose i th element is the i th random variable. Then the variances and covariances can be placed in a covariance matrix, in which the (i, j) element is the covariance between the i th random variable and the j th one.