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  5. Multivariate Probability Distributions in R

Exercise

Comparing normal and t probabilities

Here, you will calculate the volume under multivariate t-distributions for two different degrees of freedom compared to a multivariate normal distribution. Fix the location parameter, the mean in case of normal and non-centrality in case of t-distribution, to mu.sim and variance-covariance matrix to sigma.sim for all distributions. Calculate the volumes between \(\begin{pmatrix} -5 \\ -5\end{pmatrix}\) and \(\begin{pmatrix} 5 \\ 5 \end{pmatrix}\) for

  • (a) A multivariate t, \(df = 5\).
  • (b) A multivariate t, \(df = 1\).
  • (c) A multivariate normal.

What is the order of the volumes?

Instructions

50 XP

Possible answers