dmultinorm | R Documentation |

Density for the multivariate Normal distribution

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

`vec.x` |
For the |

`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 |

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 \times (R + 1) / 2`

,
where the first `R`

entries are the variances
`\sigma^2{i}`

, `i = 1, \ldots, R`

, and
then the covariances arranged as per rows, that is,
`cov_{ij}`

```
i = 1, \ldots, R,
j = i + 1, \ldots, R
```

.

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

The density of the multivariate Normal distribution.

For observations whose covariance matrix is not positive definite,
`NaN`

will be returned.

Victor Miranda

`binormal`

.

```
###
### 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)
```

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