Cumulative distributions and quantiles of t

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

本练习是课程的一部分

Multivariate Probability Distributions in R

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练习说明

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 \(P[-x ≤ X ≤ x] = p.\)

交互式实操练习

通过完成这段示例代码来试试这个练习。

# 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))

编辑并运行代码