View source for Correlate With

[[category:Multivariate Distribution Functions]]

= Correlate_With( S, ReferenceS, rankCorr ) =

Used to specify a distribution having a specified rank correlation with a reference distribution.  S is the marginal distribution of the result.  ReferenceS is the reference distribution.

Reorders the samples of S so that the result is correlated with the reference sample with a rank correlation close to rankcorr.  

= Library =

Multivariate Distributions.ana 

= Example =

To generate a [[LogNormal]] distribution that is highly correlation with Ch1 (which may be any distribution), use e.g.:
 Correlate_With( LogNormal(2,3), Ch1, 0.8)

= Notes =

Most commonly, when the term "correlation" is used, it is implied to mean Pearson [[Correlation]], which is essentially a measure of linearity.  Creating a distribution with this measure of correlation makes most sense when the joint distribution is [[Gaussian]], i.e., each marginal distribution is [[Normal]].  In this case, you can specify the mean and variance of each variable, and the covariance for each pair of variables, and use the [[Gaussian]] function (found in the Multivariate Distribution library) to define the joint distribution.  The covariance of two random variables is the [[Correlation|correlation]] of the two variables times the product of their standard deviations, so the [[Gaussian]] can be defined directly in terms of Pearson Correlations.  The [[BiNormal]] function may also be used when defining a 2-D Gaussian.

For non-Gaussian distributions, it is not necessarily possible for two distributions to have a desired Pearson correlation.  However, we can ensure a given [[RankCorrel|Rank Correlation]], also called Spearman correlation.  This is what Correlate_With and [[Correlate_Dists]] use.

Correlate_With is the most convenient way for specifying two univariate distributions with a given rank correlation.  If you have three or more distributions that are mutually correlated, then you will need a symmetrix matrix of rank correlations, and will need to use the [[Correlate_Dists]] function.

= See Also =

* [[Correlate_Dists]]
* [[Gaussian]]
* [[Correlation]]