sandbox.distributions.extras.mvstdnormcdf()

statsmodels.sandbox.distributions.extras.mvstdnormcdf

statsmodels.sandbox.distributions.extras.mvstdnormcdf(lower, upper, corrcoef, **kwds) [source]

standardized multivariate normal cumulative distribution function

This is a wrapper for scipy.stats.kde.mvn.mvndst which calculates a rectangular integral over a standardized multivariate normal distribution.

This function assumes standardized scale, that is the variance in each dimension is one, but correlation can be arbitrary, covariance = correlation matrix

Parameters:

lower, upper : array_like, 1d lower and upper integration limits with length equal to the number of dimensions of the multivariate normal distribution. It can contain -np.inf or np.inf for open integration intervals corrcoef : float or array_like specifies correlation matrix in one of three ways, see notes optional keyword parameters to influence integration : maxpts : int, maximum number of function values allowed. This parameter can be used to limit the time. A sensible strategy is to start with maxpts = 1000*N, and then increase maxpts if ERROR is too large. abseps : float absolute error tolerance. releps : float relative error tolerance.

Returns:

cdfvalue : float value of the integral

See also

mvnormcdf

cdf of multivariate normal distribution without standardization

Notes

The correlation matrix corrcoef can be given in 3 different ways If the multivariate normal is two-dimensional than only the correlation coefficient needs to be provided. For general dimension the correlation matrix can be provided either as a one-dimensional array of the upper triangular correlation coefficients stacked by rows, or as full square correlation matrix

Examples

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>>> print mvstdnormcdf([-np.inf,-np.inf], [0.0,np.inf], 0.5) 0.5 >>> corr = [[1.0, 0, 0.5],[0,1,0],[0.5,0,1]] >>> print mvstdnormcdf([-np.inf,-np.inf,-100.0], [0.0,0.0,0.0], corr, abseps=1e-6) 0.166666399198 >>> print mvstdnormcdf([-np.inf,-np.inf,-100.0],[0.0,0.0,0.0],corr, abseps=1e-8) something wrong completion with ERROR > EPS and MAXPTS function values used;                     increase MAXPTS to decrease ERROR; 1.048330348e-006 0.166666546218 >>> print mvstdnormcdf([-np.inf,-np.inf,-100.0],[0.0,0.0,0.0], corr,                         maxpts=100000, abseps=1e-8) 0.166666588293