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Polychoric correlation. In statistics, polychoric correlation [1] is a technique for estimating the correlation between two hypothesised normally distributed continuous latent variables, from two observed ordinal variables. Tetrachoric correlation is a special case of the polychoric correlation applicable when both observed variables are ...
In statistical mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe how microscopic variables, such as spin and density, at different positions are related. More specifically, correlation functions measure quantitatively the extent to ...
Correlogram. A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation (correlogram) of the series on the bottom. In the analysis of data, a correlogram is a chart of correlation statistics. For example, in time series analysis, a plot of the sample autocorrelations versus (the time lags) is an autocorrelogram.
The Spearman correlation coefficient is defined as the Pearson correlation coefficient between the rank variables. [6] For a sample of size n, the n raw scores are converted to ranks , and is computed as. where. denotes the usual Pearson correlation coefficient, but applied to the rank variables, is the covariance of the rank variables, and are ...
where g is the total number of pairs of points which have a distance between them that is less than distance ε (a graphical representation of such close pairs is the recurrence plot). As the number of points tends to infinity, and the distance between them tends to zero, the correlation integral, for small values of ε, will take the form:
The correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case, the correlation coefficient is undefined because the variance of Y is zero.
Phi coefficient. In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or rφ) is a measure of association for two binary variables . In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by ...
Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8]. A linear congruential generator ( LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms.