In the previous
tutorial we used variables and methods to find properties and traits
of the Normal distribution. Before that we looked at statistical methods
and construction of the Normal distribution. In this tutorial we look at
multivariate distributions, which should feel similar to univariate
distributions.

## Constructing a Multivariate Distribution

Construction of a multivariate distribution is identical to a
univariate distribution, except that a vector input is likely to be
required for one of the parameters. In keeping with our running Normal
example, we will now use the Multivariate Normal distribution.

```
MN <- MultivariateNormal$new(mean = c(0,0), cov = c(1,0,0,1))
MultivariateNormal$new() # This is in fact the default
#> MultiNorm(cov = c(1, 0, 0, 1), mean = c(0, 0))
```

Notice how this is almost identical to constructing a univariate
Normal distribution. We even allow multiple parameterisations

```
MultivariateNormal$new(mean = c(0,0), prec = c(1,0,0,1))
#> MultiNorm(mean = c(0, 0), prec = c(1, 0, 0, 1))
```

## d/p/q/r

The biggest difference between univariate and multivariate
distributions is in how arguments are passed to the d/p/q/r methods.
This differs slightly from R stats. For example to evaluate the pdf of
the multinomial distribution at (1,2) in R stats we would run

```
dmultinom(c(1,2), size = 3, prob = c(0.2,0.8))
#> [1] 0.384
```

Whereas in distr6, each point is its own argument

```
Multinomial$new(size = 3, probs = c(0.2,0.8))$pdf(1,2)
#> [1] 0.384
```

There is a very important reason for this: vectorisation. In R stats
there is no way to generate multiple points from a multivariate
distribution, whereas in distr6…

```
MN$pdf(c(1,2), c(2,3))
#> [1] 0.0130642333 0.0002392798
MN$rand(5)
#> V1 V2
#> 1: 1.3709584 -0.56469817
#> 2: 0.3631284 0.63286260
#> 3: 0.4042683 -0.10612452
#> 4: 1.5115220 -0.09465904
#> 5: 2.0184237 -0.06271410
```

Note: `cdf()`

and `quantile()`

are often
omitted from multivariate distributions n distr6 as no closed form
analytic expression exists.

## Summary

In this tutorial we looked at multivariate distributions and
discussed the difference between distr6 and R stats in using the d/p/q/r
functions. The next
tutorial concludes the ‘Basic’ set of tutorials with a look at
listing in distr6 to help you navigate the package more easily.