Function File: p = mvncdf (x, mu, sigma)

Function File: mvncdf (a, x, mu, sigma)

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

Compute the cumulative distribution function of the multivariate normal distribution.

Arguments

• x is the upper limit for integration where each row corresponds to an observation.
• mu is the mean.
• sigma is the correlation matrix.
• 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];
          mu = [0.5 1.5];
          sigma = [1.0 0.5; 0.5 1.0];
          p = mvncdf (x, mu, sigma)
          
          a = [-inf 0];
          p = mvncdf (a, x, mu, sigma)

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.