Xi'an's Og

An interesting (if vaguely formulated) question on X validated: given two Gaussian variates that are maximally coupled, what is the correlation between these variates? The answer depends on the parameters of both Gaussian, with a correlation of one when both Gaussians are identical. Answering the question by simulation (as I could not figure out the analytical formula on Boxing Day…) led me back to Pierre Jacob’s entry on the topic on Statisfaction, where simulating the maximal coupling stems from the decompositions

p(x)=p(x)∧q(x)+{p(x)-p(x)∧q(x)}  and  q(x)=p(x)∧q(x)+{q(x)-p(x)∧q(x)}

and incidentally to the R function image.plot (from the R library fields) for including the side legend.

This entry was posted on January 3, 2018 at 12:18 am and is filed under Books, Kids, pictures, R, Statistics, University life with tags Boxing Day, cross validated, fields, maximal coupling, Pierre Jacob, R, Statisfaction. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.