Definition:Parameter of Probability Distribution

This page is about parameter of probability distribution. For other uses, see parameter.

Definition

Let $\PP$ be a probability distribution of a particular type.

A parameter of $\PP$ is a constant that determines the specific properties of $\PP$.

Examples

Normal Distribution

Let $X$ be a continuous random variable with a normal distribution:

$X \sim \Gaussian \mu {\sigma^2}$

The expectation $\mu$ and the variance $\sigma^2$ are the parameters of $\Gaussian \mu {\sigma^2}$.

Poisson Distribution

Let $X$ be a discrete random variable with a Poisson distribution:

$X \sim \Poisson \lambda$

Then $\lambda$ is the parameter of $\Poisson \lambda$.

Binomial Distribution

Let $X$ be a discrete random variable with a binomial distribution:

$X \sim \Binomial n p$

Then $n$ and $p$ are the parameters of $\Binomial n p$.

Also see

• Results about parameters of probability distributions can be found here.

Sources

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