Skip to content

IAI Actuarial Core Principles · Economic Modelling · Valuing benefit guarantees using simulation

When generating a standard normal variate from a uniform random number U on (0,1) by the inverse transform method, which is the correct procedure?

Apply the inverse of the standard normal distribution function to the uniform number, giving Z equal to Phi inverse of U. This works because F of X is uniform on (0,1) for any continuous X.

  1. AZ = U, because uniform and normal variates are the same after scaling
  2. BZ = Phi^{-1}(U), where Phi is the standard normal distribution functionCorrect
  3. CZ = Phi(U), applying the normal distribution function to U
  4. DZ = ln(U), the log of the uniform variate
  5. Z = 1 - U squared

Explanation

The inverse transform method sets X = F^{-1}(U). For the standard normal, F is Phi, so Z = Phi^{-1}(U). Applying Phi to U would give a value in (0,1), not a normal variate.

Did you get it right without looking?

One question tells you little. A timed set on Valuing benefit guarantees using simulation shows your real accuracy, how long you take and where you lose marks.

Practise Valuing benefit guarantees using simulationFree diagnostic mock

More Valuing benefit guarantees using simulation questions