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In probability and statistics, the term cross-correlations refers to the correlations between the entries of two random vectors and , while the correlations of a random vector are the correlations between the entries of itself, those forming the correlation matrix of . If each of and is a scalar random variable which is realized repeatedly in a ...
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 ...
Two dimensional correlation analysis is a mathematical technique that is used to study changes in measured signals. As mostly spectroscopic signals are discussed, sometime also two dimensional correlation spectroscopy is used and refers to the same technique. In 2D correlation analysis, a sample is subjected to an external perturbation while ...
Not to be confused with Tau distribution. In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic used to measure the ordinal association between two measured quantities. A τ test is a non-parametric hypothesis test for statistical dependence ...
The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship (anti-correlation), [5] and some value in the open interval (,) in all other cases, indicating the degree of linear dependence between the variables. As it ...
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
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 ...
The Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance of the variables divided by the product of their standard deviations. [4] This is the best-known and most commonly used type of ...