# dMVNcov: Density for the multivariate Normal distribution In VGAMextra: Additions and Extensions of the 'VGAM' Package

## Description

Density for the multivariate Normal distribution

## Usage

 ```1 2 3``` ``` dmultinorm(vec.x, vec.mean = c(0, 0), mat.cov = c(1, 1, 0), log = FALSE) ```

## Arguments

 `vec.x` For the R–multivariate Normal, an R–vector of quantiles. `vec.mean` The vector of means. `mat.cov` The vector of variances and covariances, arranged in that order. See below for further details. `log` Logical. If `TRUE`, the logged values are returned.

## Details

This implementation of the multivariate (say R–dimensional) Normal density handles the variances and covariances, instead of correlation parameters.

For more than one observation, arrange all entries in matrices accordingly.

For each observation, `mat.cov` is a vector of length R * (R + 1) / 2, where the first R entries are the variances σ^2[i], i = 1, …, R, and then the covariances arranged as per rows, that is, cov[ij] i = 1, …, R, j = i + 1, …, R.

By default, it returns the density of two independent standard Normal distributions.

## Value

The density of the multivariate Normal distribution.

## Warning

For observations whose covariance matrix is not positive definite, `NaN` will be returned.

## Author(s)

Victor Miranda

`binormal`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```### ### Two - dimensional Normal density. ### set.seed(180228) nn <- 25 mean1 <- 1; mean2 <- 1.5; mean3 = 2 var1 <- exp(1.5); var2 <- exp(-1.5); var3 <- exp(1); cov12 = 0.75 dmvndata <- rbinorm(nn, mean1 = 1, mean2 = 1.5, var1 = var1, var2 = var2, cov12 = cov12) ## Using dbinorm() from VGAM. d2norm.data <- dbinorm(x1 = dmvndata[, 1], x2 = dmvndata[, 2], mean1 = mean1, mean2 = mean2, var1 = var1, var2 = var2, cov12 = cov12) ## Using dmultinorm(). d2norm.data2 <- dmultinorm(vec.x = dmvndata, vec.mean = c(mean1, mean2), mat.cov = c(var1, var2, cov12)) summary(d2norm.data) summary(d2norm.data2) ## ## 3--dimensional Normal. ## dmvndata <- cbind(dmvndata, rnorm(nn, mean3, sqrt(var3))) d2norm.data3 <- dmultinorm(dmvndata, vec.mean = c(mean1, mean2, mean3), mat.cov = c(var1, var2, var3, cov12, 0, 0)) hist(d2norm.data3) summary(d2norm.data3) ```