Using the pmvnorm function
Along with the density of multivariate normals, you often need to calculate the cumulative distributions of multivariate normals to obtain the volume of the density between two specified values. In this exercise, you will use the pmvnorm() function to calculate the cumulative distribution for specified bivariate normals.
Este exercício faz parte do curso
Multivariate Probability Distributions in R
Instruções do exercício
- Compute the volume under a standard bivariate normal distribution between \(\begin{pmatrix} -1\\ -1 \end{pmatrix}\) and \(\begin{pmatrix} 1 \\ 1 \end{pmatrix}\).
- Calculate the volume between \(\begin{pmatrix} -5 \\ -5\end{pmatrix}\) and \(\begin{pmatrix} 5 \\ 5 \end{pmatrix}\) for a bivariate normal with mean
mu.simand variancesigma.sim.
Exercício interativo prático
Experimente este exercício completando este código de exemplo.
# Volume under a bivariate standard normal
pmvnorm(lower = ___, upper = ___)
# Volume under specified mean and variance-covariance matrix
pmvnorm(___, mean = ___, sigma = ___)