# Density for the multivariate Normal distribution ```r 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 $\sigma^2[i]$, $i = 1, \ldots, R$, and then the covariances arranged as per rows, that is, $cov[ij]$ c("$i = 1, \\ldots, R,\n$", "$ j = i + 1, \\ldots, R$"). By default, it returns the density of two independent standard Normal distributions. ## Returns 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 ## See Also `binormal`. ## Examples ```r ### ### 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) ```

dMVNcov function