PROBBNRM Function

Returns a probability from a bivariate normal distribution.

Category:

Probability

Syntax

PROBBNRM(x,y,r)

Required Arguments

x

specifies a numeric constant, variable, or expression.

y

specifies a numeric constant, variable, or expression.

r

is a numeric correlation coefficient.

Range

-1 ≤ r ≤ 1

Details

The PROBBNRM function returns the probability that an observation (X, Y) from a standardized bivariate normal distribution with mean 0, variance 1, and a correlation coefficient r, is less than or equal to (x, y). That is, it returns the probability that X≤x and Y≤y. The following equation describes the PROBBNRM function, where u and v represent the random variables x and y, respectively:

\begin{matrix} P R O B B N R M (x, y, r) = \frac{1}{2 π \sqrt[]{1 - r^{2}}} \int_{- \infty}^{x} \int_{- \infty}^{y} e x p [- \frac{u^{2} - 2 r u v + v^{2}}{2 (1 - r^{2})}] d v d u \end{matrix}

Example

The following SAS statements produce this result.

SAS Statement	Result
p=probbnrm(.4, -.3, .2); put p;	0.2783183345

PROBBNRM Function

Syntax

Required Arguments

x

y

r

Details

Example

See Also