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IMSL_BINORMALCDF

IMSL_BINORMALCDF

IMSL_BINORMALCDF

The IMSL_BINORMALCDF function evaluates the bivariate normal distribution function.

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.



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