Get startedGet started for free

Calculating probability contours using qmvnorm

The inverse problem to the calculation of cumulative probability is as follows: for a given a probability \(p\) calculate the contour that contains \(p\) proportion of the total volume of the density. This contour is the same as the \(p^{th}\) quantile of the distribution. The qmvnorm() function provides the tools to perform the above calculations.

This exercise is part of the course

Multivariate Probability Distributions in R

View Course

Exercise instructions

  • Compute the contour for a standard bivariate normal which contains probability \(p=0.9\).
  • Calculate the contour for a bivariate normal with mean mu.sim and variance-covariance matrix sigma.sim which contains probability \(p=0.95\).

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Probability contours for a standard bivariate normal
qmvnorm(___, tail = "both", sigma = diag(2))

# Probability contours for a bivariate normal 
Edit and Run Code