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In statistics, Bartlett's test, named after Maurice Stevenson Bartlett, [1] is used to test homoscedasticity, that is, if multiple samples are from populations with equal variances. [2] Some statistical tests, such as the analysis of variance , assume that variances are equal across groups or samples, which can be checked with Bartlett's test.
For most longer periods one cannot reject the null hypothesis of no autocorrelation. Note that there are two distinct formulas for generating the confidence bands: 1. If the correlogram is being used to test for randomness (i.e., there is no time dependence in the data), the following formula is recommended:
In statistics, the autocorrelation of a real or complex random process is the Pearson correlation between values of the process at different times, as a function of the two times or of the time lag.
Created Date: 8/30/2012 4:52:52 PM
One common correlation function is the radial distribution function which is seen often in statistical mechanics and fluid mechanics. The correlation function can be calculated in exactly solvable models (one-dimensional Bose gas, spin chains, Hubbard model) by means of Quantum inverse scattering method and Bethe ansatz. In an isotropic XY ...
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.
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. [1] If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an ...
For continuous time, the Wiener–Khinchin theorem says that if is a wide-sense-stationary random process whose autocorrelation function (sometimes called autocovariance) defined in terms of statistical expected value = [() ()] <,,, where the asterisk denotes complex conjugate, then there exists a monotone function in the frequency domain < <, or equivalently a non negative Radon measure on ...