For a simulation, I need to compute the distribution of the product of two discrete random variables. Although I could implement it from scratch, I thought that the distr package already provides this functionality.
The operatorsIimplemented in the package do not seem to be documented, but, by trying, I have figured out that + stands for the convolution operation (sum of independent random variables):
> X <- DiscreteDistribution(supp=c(-1,0,1), prob=c(0.25,0.5,0.25))
> Y <- X + X
> attr(Y, "support")
[1] -2 -1 0 1 2
> d(Y)(attr(Y, "support"))
[1] 0.0625 0.2500 0.3750 0.2500 0.0625
Although there seems to be a multiplication operator (at least methods(class="DiscreteDistribution") reports one), it does not work as expected (actually, it does not work at all):
> Y <- X * X
Error in apply(mixDistr.dfs, 1, all) : dim(X) must have a positive length
Does someone know how to compute the distribution of the product of two discrete independent random variables with distr? Or does the package lack this functionality?
It turned out that this was a bug in distr.
As @allan-cameron points out, the operators for distributions are documented with ?'operators-methods'. There is a multiplication operator listed for arbitrary distributions (class AcDcLcDistribution), and this indeed works for most cases:
> X <- DiscreteDistribution(1:2)
> Y <- DiscreteDistribution(1:2)
> Z <- X*Y
> support(Z)
[1] 1 2 4
> prob(Z)
1 2 4
0.25 0.50 0.25
My example did not work due to a bug in distr. I have reported it to the maintainers of distr, and the bug will be fixed in the upcoming release 2.9.3.