Multivariate normal cumulative distribution function
returns the cumulative distribution function (cdf) of the multivariate normal
distribution with zero mean and identity covariance matrix, evaluated at each
row of p
= mvncdf(X
)X
. For more information, see Multivariate Normal Distribution.
specifies control parameters for the numerical integration used to compute
p
= mvncdf(___,options
)p
, using any of the input argument combinations in the
previous syntaxes. Create the options
argument using the
statset
function with any
combination of the parameters 'TolFun'
,
'MaxFunEvals'
, and 'Display'
.
[
additionally returns an estimate of the error in p
,err
] = mvncdf(___)p
. For
more information, see Algorithms.
In the one-dimensional case, Sigma
is the variance, not
the standard deviation. For example, mvncdf(1,0,4)
is the
same as normcdf(1,0,2)
, where 4
is the
variance and 2
is the standard deviation.
For bivariate and trivariate distributions, mvncdf
uses adaptive
quadrature on a transformation of the t density, based on methods
developed by Drezner and Wesolowsky [1]
[2]
and by Genz [3]. For four or more dimensions,
mvncdf
uses a quasi-Monte Carlo integration algorithm based on
methods developed by Genz and Bretz [4]
[5].
[1] Drezner, Z. “Computation of the Trivariate Normal Integral.” Mathematics of Computation. Vol. 63, 1994, pp. 289–294.
[2] Drezner, Z., and G. O. Wesolowsky. “On the Computation of the Bivariate Normal Integral.” Journal of Statistical Computation and Simulation. Vol. 35, 1989, pp. 101–107.
[3] Genz, A. “Numerical Computation of Rectangular Bivariate and Trivariate Normal and t Probabilities.” Statistics and Computing. Vol. 14, No. 3, 2004, pp. 251–260.
[4] Genz, A., and F. Bretz. “Numerical Computation of Multivariate t Probabilities with Application to Power Calculation of Multiple Contrasts.” Journal of Statistical Computation and Simulation. Vol. 63, 1999, pp. 361–378.
[5] Genz, A., and F. Bretz. “Comparison of Methods for the Computation of Multivariate t Probabilities.” Journal of Computational and Graphical Statistics. Vol. 11, No. 4, 2002, pp. 950–971.
[6] Kotz, S., N. Balakrishnan, and N. L. Johnson. Continuous Multivariate Distributions: Volume 1: Models and Applications. 2nd ed. New York: John Wiley & Sons, Inc., 2000.