Skip to content

IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to copulas

If X has a continuous distribution function F_X, which statement is used to obtain the uniform inputs for a copula from observed losses?

For a continuous random variable X, applying its own distribution function gives F_X(X), which is uniformly distributed on (0,1). This probability integral transform produces the uniform margins needed by a copula, whatever the form of the original distribution.

  1. AF_X(X) has a uniform(0,1) distributionCorrect
  2. BF_X(X) has a standard normal distribution
  3. CF_X(X) has the same distribution as X
  4. DF_X(X) has an exponential distribution with mean 1
  5. F_X(X) has a uniform distribution only if X is normal

Explanation

The probability integral transform states that for continuous X, U=F_X(X) is uniform on (0,1). This is why a copula, with uniform marginals, captures dependence separately from the marginals. It holds for any continuous distribution, not only the normal.

Did you get it right without looking?

One question tells you little. A timed set on Introduction to copulas shows your real accuracy, how long you take and where you lose marks.

Practise Introduction to copulasFree diagnostic mock

More Introduction to copulas questions