naginterfaces.library.stat.prob_bivariate_normal¶
- naginterfaces.library.stat.prob_bivariate_normal(x, y, rho)[source]¶
prob_bivariate_normal
returns the lower tail probability for the bivariate Normal distribution.For full information please refer to the NAG Library document for g01ha
https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g01/g01haf.html
- Parameters
- xfloat
, the first argument for which the bivariate Normal distribution function is to be evaluated.
- yfloat
, the second argument for which the bivariate Normal distribution function is to be evaluated.
- rhofloat
, the correlation coefficient.
- Returns
- pfloat
The lower tail probability for the bivariate Normal distribution.
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- Notes
For the two random variables following a bivariate Normal distribution with
the lower tail probability is defined by:
For a more detailed description of the bivariate Normal distribution and its properties see Abramowitz and Stegun (1972) and Kendall and Stuart (1969). The method used is described by Genz (2004).
- References
Abramowitz, M and Stegun, I A, 1972, Handbook of Mathematical Functions, (3rd Edition), Dover Publications
Genz, A, 2004, Numerical computation of rectangular bivariate and trivariate Normal and probabilities, Statistics and Computing (14), 151–160
Kendall, M G and Stuart, A, 1969, The Advanced Theory of Statistics (Volume 1), (3rd Edition), Griffin