A parameter is an independent variable; one of the inputs for a function. Parametric equations are equations in which the variables of interest in are given in terms of another variable. For example, f (x) = ax ² + b is the general equation of a set of points corresponding to a parabola, expressed in terms of the parameters a and b. Substitutions of specific values of these defines a particular set. In statistics, the parameters of a distribution are those elements of it which can be used to loosely define it. They may be location parameters, such as the mean, median, and mode, or parameters of dispersion, such as the standard deviation.

 

Parametric representation of a curve

The representation of the points P (x, y, z) of a curve by three functions x = u(t ), y = v(t ), z = w(t ) dependent on a parameter t is described as a parametric representation of a curve.

 

Parametric representation of a surface

The points P (x, y, z) of a surface can be represented by three functions

x = u (s, t ), y = v (s, t ), z = w (s, t )

dependent upon two parameters, s and t. This is referred to as a parametric representation of the surface.