Cumulative distributions and quantiles of t

In this exercise, you will calculate the probability integrals and quantiles or inverse CDFs of multivariate t-distribution.

This exercise is part of the course

Multivariate Probability Distributions in R

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Exercise instructions

Calculate the volume between \(\begin{pmatrix} -5 \\ -5\end{pmatrix}\) and \(\begin{pmatrix} 5 \\ 5 \end{pmatrix}\) for a bivariate t-distribution with location parameter mu.sim and variance-covariance matrix sigma.sim and 5 degrees of freedom.
Calculate the equal probability contour for a standard bivariate t-distribution for \(p=.9\). Don't forget to specify tail = "both" to get a two sided contour of the form \(P[-x ≤ X ≤ x] = p.\)

Hands-on interactive exercise

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

# Calculate the volume under the specified t-distribution
pmvt(lower = ___, upper = ___, delta = mu.sim, df = 5, sigma = sigma.sim)


# Calculate the equal probability contour
qmvt(p = ___, tail = "both", sigma = diag(2))

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