Definition:Parameter

Definition

A parameter is a constant or a variable that distinguishes special cases of a general mathematical expression.

Parameter of an Integral Equation

Consider the integral equation:

of the first kind:

$\map f x = \lambda \ds \int_{\map a x}^{\map b x} \map K {x, y} \map g y \rd x$

of the second kind:

$\map g x = \map f x \lambda \ds \int_{\map a x}^{\map b x} \map K {x, y} \map g y \rd x$

of the third kind:

$\map u x \map g x = \map f x \lambda \ds \int_{\map a x}^{\map b x} \map K {x, y} \map g y \rd x$

The number $\lambda$ is known as the parameter of the integral equation.

Parameter of Probability Distribution

In the context of probability distributions:

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

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

Parameter of Stochastic Model

In the context of mathematical models:

Let $\MM$ be a stochastic model of a particular type.

A parameter of $\MM$ is a constant that determines the precise form of $\MM$.

Population Parameter

In the context of descriptive statistics and inductive statistics:

Let $P$ be a population.

A population parameter is a parameter of the probability distribution which underlies $P$.

Parameter of Differential Equation

In the context of differential equations:

Let $f$ be a differential equation with general solution $F$.

A parameter of $F$ is an arbitrary constant arising from the solving of a primitive during the course of obtaining the solution of $f$.

Examples

Equation of Straight Line

Consider the slope-intercept form of equation of the straight line in the plane:

Let $\LL$ be the straight line in the Cartesian plane such that:

the slope of $\LL$ is $m$

the $y$-intercept of $\LL$ is $c$

Then $\LL$ can be described by the equation:

$y = m x c$

such that $m$ is the slope of $\LL$ and $c$ is the $y$-intercept.

The constants $m$ and $c$ are the parameters of this equation.

Also defined as

In the context of predicate logic, a parameter is another term for proper name, or constant symbol.

Also see

• Definition:Parametric Equation

• Definition:Parameter of One-Parameter Family of Curves

• Results about parameters can be found here.

Historical Note

The term parameter was introduced by Gottfried Wilhelm von Leibniz.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): parameter: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): parameter: 1.