Symbols:Abbreviations/P/PGF

Abbreviation: PGF or p.g.f.

Probability generating function:

Let $X$ be a discrete random variable whose codomain, $\Omega_X$, is a subset of the natural numbers $\N$.

Let $p_X$ be the probability mass function for $X$.

The probability generating function for $X$, denoted $\map {\Pi_X} s$, is the formal power series defined by:

$\ds \map {\Pi_X} s := \sum_{n \mathop = 0}^\infty \map {p_X} n s^n \in \R \sqbrk {\sqbrk s}$

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): p.g.f.