Definition:Compound Distribution

Definition

Let $X_1, X_2, \ldots, X_N$ be pairwise independent random variables such that:

the $X_i$ may or may not have the same probability distribution

$N$ itself may also be a (discrete) random variable.

Let:

$S_N : X_1 + X_2 + \cdots + X_N$

Then the probability distribution of $S_N$ is known as a compound distribution.

Also see

• Results about compound distributions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): compound distribution
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): compound distribution