  We consider a variant of the channel simulation problem with a single input
and multiple outputs, where Alice observes a probability distribution $P$ from
a set of prescribed probability distributions $\mathbb{\mathcal{P}}$, and sends
a prefix-free codeword $W$ to Bob to allow him to generate $n$ i.i.d. random
variables $X_{1},X_{2,}...,X_{n}$ which follow the distribution $P$. This can
also be regarded as a lossy compression setting for probability distributions.
This paper describes encoding schemes for three cases of $P$: $P$ is a
distribution over positive integers, $P$ is a continuous distribution over
$[0,1]$ with a non-increasing pdf, and $P$ is a continuous distribution over
$[0,\infty)$ with a non-increasing pdf. We show that the growth rate of the
expected codeword length is sub-linear in $n$ when a power law bound is
satisfied. An application of multiple-outputs channel simulation is the
compression of probability distributions.
