rchemo (version 0.1-3)

dmnorm: Multivariate normal probability density

Description

Prediction of the normal probability density of multivariate observations.

Usage

dmnorm(X = NULL, mu = NULL, sigma = NULL)
# S3 method for Dmnorm
predict(object, X, ...)

Value

For dmnorm:

mu

means of the X variables

Uinv

inverse of the Cholesky decomposition of the covariance matrix

det

squared determinant of the Cholesky decomposition of the covariance matrix

For predict:

pred

Prediction of the normal probability density of new multivariate observations

Arguments

X

For the main function: Training data (\(n, p\)) used for estimating the mean and the covariance matrix population (if mu or/and sigma are not provided). --- For the auxiliary functions: New data (\(m, p\)) for which the density has to be predicted.

mu

The mean (\(p, 1\)) of the normal distribution. If NULL (default), \(mu\) is estimated by the column-wise mean of the training data.

sigma

The covariance matrix (\(p x p\)) of the normal distribution. If NULL (default), \(sigma\) is estimated by the empirical covariance matrix (denominator \(n - 1\)) of the training data.

object

For the auxiliary functions: A result of a call to dmnorm.

...

For the auxiliary functions: Optional arguments.

Examples

data(iris)

X <- iris[, 1:2]

Xtrain <- X[1:40, ]
Xtest <- X[40:50, ]

fm <- dmnorm(Xtrain)
fm

k <- 50
x1 <- seq(min(Xtrain[, 1]), max(Xtrain[, 1]), length.out = k)
x2 <- seq(min(Xtrain[, 2]), max(Xtrain[, 2]), length.out = k)
zX <- expand.grid(x1, x2)
pred <- predict(fm, zX)$pred
contour(x1, x2, matrix(pred, nrow = 50))

points(Xtest, col = "red", pch = 16)