Cumulative distributions and quantiles of t
In this exercise, you will calculate the probability integrals and quantiles or inverse CDFs of multivariate t-distribution.
Cet exercice fait partie du cours
Multivariate Probability Distributions in R
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.simand variance-covariance matrixsigma.simand 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 \(P[-x ≤ X ≤ x] = p.\)
Exercice interactif pratique
Essayez cet exercice en complétant cet exemple de 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))