PROBBNRM Function

Returns a probability from a bivariate normal distribution.

Category:	Probability
Returned data type:	DOUBLE

Syntax

Arguments

Details

Example

Syntax

PROBBNRM(x, y, r)

Arguments

x

specifies a numeric constant, variable, or expression.

Data type

DOUBLE

y

specifies a numeric constant, variable, or expression.

Data type

DOUBLE

r

is a numeric correlation coefficient.

Range	-1 ≤ r ≤ 1
Data type	DOUBLE

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:

$table with 1 row and 1 column , row1 column 1 , p r o b b n r m . open x comma y comma r close . equals . fraction 1 , over 2 pi . square root of 1 minus , r squared end root end fraction . integral , from , negative infinity , to , x , of . modified integral with minus infinity below and with y above . e x p . left bracket negative . fraction u squared , minus . 2 . r u v plus , v squared , over 2 . open 1 minus , r squared , close end fraction . right bracket . d v d u , end table$

Example

The following statement illustrates the PROBBNRM function:

Statements	Results
select probbnrm(.4, -.3, .2);	0.27831833451902