A compound probability distribution is the distribution of some combination of independent and identically distributed variables whose parameters themselves follow some probability distribution.

**Compound Poisson Distribution:**

Suppose X_{1},…, X_{N} are independent and identically distributed Poisson variables with N itself being a random variable following Poisson distribution then,

**Y = X _{1}+….+X_{N}** is said to follow compound Poisson distribution.

Then mean of this distribution is given as E(Y) =E(N)*E(X_{i})

The compound Poisson distribution finds applications in the theory of stochastic processes and queuing theory.

**Other examples of compound distributions are:**

- A normal distribution whose mean follows normal distribution is once again normally distributed.
- A Poisson distribution whose parameter is distributed according to a gamma distribution gives a negative binomial distribution.

**Mixture Distribution:**

If we are given a collection (possibly uncountable) of random variables and we choose one of them randomly according to some probabilistic method then the resulting distribution so obtained is called a mixture distribution.