Copula

Question 1

What is the main issue with Pearson’s linear correlation coefficient?

Answer 1

It is desirable that a measure of concordance/association shows invariance, meaning if we apply monotone functions on X and Y, the correlation coefficient should remain the same

Question 2

Which correlation coefficient solves this problem?

Answer 2

Spearman’s Rho/Rank correlation coefficient

Question 3

What is the other problem with most of these correlation coefficients with regard to the tails?

Answer 3

It is a single statistic that represents the average relationship between two variables. As a result, a lot of information will be lost especially at tails. It doesn’t tell the full story

Question 4

Define a Copula

Answer 4

a function that takes the probabilities from marginal distribution function and converts them into the probabilities that would have been obtained from a joint distribution