The IMSL_BINORMALCDF function evaluates the bivariate normal distribution function.
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The IMSL_BINORMALCDF function evaluates the distribution function F of a bivariate normal distribution with means of zero, variances of 1, and correlation of rho; that is, ρ = rho and |ρ| < 1.
To determine the probability that U ≤ u0 and V ≤ v0, where (U, V) is a bivariate normal random variable with mean µ = (µU, µV) and the following variance-covariance matrix:
transform (U, V)T to a vector with zero means and unit variances. The input to IMSL_BINORMALCDF would be as follows:
and
The IMSL_BINORMALCDF function uses the method of Owen (1962, 1965). For |ρ| = 1, the distribution function is computed based on the univariate statistic Z = min(x, y) and on the normal distribution IMSL_NORMALCDF.
Examples
Suppose (x, y) is a bivariate normal random variable with mean (0, 0) and the following variance-covariance matrix:
This example finds the probability that x is less than –2.0 and y is less than 0.0.
x = -2
y = 0
rho = .9
p = IMSL_BINORMALCDF(x, y, rho)
PM, 'P((x < -2.0) and (y < 0.0)) = ', p, FORMAT = '(a29, f8.4)'
IDL prints:
P((x < -2.0) and (y < 0.0)) = 0.0228
Syntax
Result = IMSL_BINORMALCDF(X, Y, Rho [, /DOUBLE])
Return Value
The probability that a bivariate normal random variable with correlation Rho takes a value less than or equal to x and less than or equal to y.
Arguments
Rho
Correlation coefficient.
X
The x-coordinate of the point for which the bivariate normal distribution function is to be evaluated.
Y
The y-coordinate of the point for which the bivariate normal distribution function is to be evaluated.
Keywords
DOUBLE (optional)
If present and nonzero, double precision is used.
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