mvtcdf
Multivariate Student’s t cumulative distribution function (CDF).
p = mvtcdf (x, rho, df) returns the cumulative
probability of the multivariate student’s t distribution with correlation
parameters rho and degrees of freedom df, evaluated at each row
of x. The rows of the matrix x correspond to sample
observations and its columns correspond to variables or coordinates. The
return argument p is a column vector with the same number of rows as in
x.
rho is a symmetric, positive definite, correlation matrix. dF is a scalar or a vector with elements.
Note: mvtcdf computes the CDF for the standard multivariate Student’s
t distribution, centered at the origin, with no scale parameters. If
rho is a covariance matrix, i.e. diag(rho) is not all
ones, mvtcdf rescales rho to transform it to a correlation
matrix. mvtcdf does not rescale x, though.
The multivariate Student’s t cumulative probability at x is defined as the probability that a random vector T, distributed as multivariate normal, will fall within the semi-infinite rectangle with upper limits defined by x.
p = mvtcdf (x_lo, x_hi, rho, df) returns
the multivariate Student’s t cumulative probability evaluated over the
rectangle (hyper-rectangle for multivariate data in x) with lower and
upper limits defined by x_lo and x_hi, respectively.
[p, err] = mvtcdf (…) also returns an error estimate
err in p.
p = mvtcdf (…, options) specifies the structure,
which controls specific parameters for the numerical integration used to
compute p. The required fieds are:
"TolFun" | Maximum absolute error tolerance. Default is 1e-8 for D < 4, or 1e-4 for D >= 4. | |
"MaxFunEvals" | Maximum number of integrand evaluations when . Default is 1e7. Ignored when . | |
"Display" | Display options. Choices are "off"
(default), "iter", which shows the probability and estimated error at
each repetition, and "final", which shows the final probability and
related error after the integrand has converged successfully. Ignored when
. |
See also: bvtcdf, mvtpdf, mvtrnd, mvtcdfqmc
Source Code: mvtcdf
## Compute the cdf of a multivariate Student's t distribution with
## correlation parameters rho = [1, 0.4; 0.4, 1] and 2 degrees of freedom.
rho = [1, 0.4; 0.4, 1];
df = 2;
[X1, X2] = meshgrid (linspace (-2, 2, 25)', linspace (-2, 2, 25)');
X = [X1(:), X2(:)];
p = mvtcdf (X, rho, df);
surf (X1, X2, reshape (p, 25, 25));
title ("Bivariate Student's t cummulative distribution function");
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