Operators and Keywords

C++ API

Function File: p = mvtcdf (x, sigma, nu)

Function File: mvtcdf (a, x, sigma, nu)

Function File: [p, err] = mvtcdf (...)

Compute the cumulative distribution function of the multivariate Student's t distribution.

#### Arguments

• x is the upper limit for integration where each row corresponds to an observation.
• sigma is the correlation matrix.
• nu is the degrees of freedom.
• a is the lower limit for integration where each row corresponds to an observation. a must have the same size as x.

#### Return values

• p is the cumulative distribution at each row of x and a.
• err is the estimated error.

#### Examples

```          x = [1 2];
sigma = [1.0 0.5; 0.5 1.0];
nu = 4;
p = mvtcdf (x, sigma, nu)

a = [-inf 0];
p = mvtcdf (a, x, sigma, nu)
```

#### References

1. Alan Genz and Frank Bretz. Numerical Computation of Multivariate t-Probabilities with Application to Power Calculation of Multiple Constrasts. Journal of Statistical Computation and Simulation, 63, pages 361-378, 1999.

Package: statistics