Multivariate t cumulative distribution function
y = mvtcdf(X,C,DF)
y = mvtcdf(xl,xu,C,DF)
[y,err] = mvtcdf(...)
[...] = mvntdf(...,options)
y = mvtcdf(X,C,DF) returns
the cumulative probability of the multivariate t distribution
with correlation parameters
C and degrees of freedom
evaluated at each row of
X. Rows of the n-by-d matrix
to observations or points, and columns correspond to variables or
y is an
C is a symmetric, positive definite, d-by-d matrix,
typically a correlation matrix. If its diagonal elements are not 1,
mvtcdf does not rescale
a scalar, or a vector with n elements.
The multivariate t cumulative probability
X is defined as the probability that a random
T, distributed as multivariate t,
will fall within the semi-infinite rectangle with upper limits defined
y = mvtcdf(xl,xu,C,DF) returns
the multivariate t cumulative probability evaluated
over the rectangle with lower and upper limits defined by
[y,err] = mvtcdf(...) returns
an estimate of the error in
y. For bivariate and
mvtcdf uses adaptive
quadrature on a transformation of the t density,
based on methods developed by Genz, as described in the references.
The default absolute error tolerance for these cases is
For four or more dimensions,
mvtcdf uses a quasi-Monte
Carlo integration algorithm based on methods developed by Genz and
Bretz, as described in the references. The default absolute error
tolerance for these cases is
[...] = mvntdf(...,options) specifies
control parameters for the numerical integration used to compute
This argument can be created by a call to
statset parameters are:
'TolFun'— Maximum absolute error tolerance. Default is
1e-8when d < 4, or
1e-4when d ≥ 4.
'MaxFunEvals'— Maximum number of integrand evaluations allowed when d ≥ 4. Default is
'MaxFunEvals'is ignored when d < 4.
'Display'— Level of display output. Choices are
'Display'is ignored when d < 4.
Compute the Multivariate t Distribution cdf
Compute the cdf of a multivariate t distribution with correlation parameters
C = [1 .4; .4 1] and 2 degrees of freedom.
C = [1 .4; .4 1]; df = 2; [X1,X2] = meshgrid(linspace(-2,2,25)',linspace(-2,2,25)'); X = [X1(:) X2(:)]; p = mvtcdf(X,C,df);
Plot the cdf.
 Genz, A. “Numerical Computation of Rectangular Bivariate and Trivariate Normal and t Probabilities.” Statistics and Computing. Vol. 14, No. 3, 2004, pp. 251–260.
 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.
 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.