About precision of cdfMvn and multi-thread

Here are some working examples from the GAUSS 17 command reference page for cdfmvne
Example 1

//Upper limits of integration for K dimensional multivariate distribution
x = { 0  0 };
 
//Identity matrix, indicates
//zero correlation between variables
R = { 1 0,
      0 1 };
				
//Define non-centrality vector 
m  = { 0, 0 };	
						
//Define control structure				
struct cdfmControl ctl;
ctl = cdfmControlCreate();
 
//Calculate cumulative probability of
//both variables being ≤ 0
{p, err, retcode} = cdfMvne(ctl, x, R, m );
 
//Calculate joint probablity of two
//variables with zero correlation,
//both, being ≤ 0
p2 = cdfn(0) .* cdfn(0);

Both p and p2 should equal 0.25.

Example 2: Compute the multivariate normal cdf at 3 separate pairs of upper limits

//Upper limits of integration
//x1 ≤ -1 and x2 ≤ -1.1
//x1 ≤ 0 and x2 ≤ 0.1
//x1 ≤ 1 and x2 ≤ 1.1
x = {  -1   -1.1,
        0    0.1,
        1    1.1 };
 
//Correlation matrix
R = {   1  0.31,
     0.31     1 };
				
//Define non-centrality vector 
m  = { 0, 0 };
        				
//Define control structure
struct cdfmControl ctl;
ctl = cdfmControlCreate();
				
//Calculate cumulative probability of
//each pair of upper limits
{ p, err, retcode }  = cdfMvne(ctl, x, R, m);

Hi,

Thank you for your answer. However, those are the examples I already had and they are not helping. My question is how I can modify the attributes of cdfmControlCreate() to be able to set the error tolerance myself. If I understand correctly, those examples you shared are using the default error tolerance.

And also, are cdfMvn or cdfMvne using multi-threading?

What is the default tolerance for cdfMvn and cdfMvne?

Thank you very much,

Sebastian

The default values for the cdfmControl structure are:

• Maximum evaluations: 5e5
• Absolute error tolerance: 1e-6
• Relative error tolerance: 1e-12

You can set the members of the cdfmControl structure using the '.' operator. Here is a modified version of the earlier examples, which modifies the control structure:

//Upper limits of integration for K dimensional multivariate distribution
x = { 0  0 };
 
//Identity matrix, indicates
//zero correlation between variables
R = { 1 0,
      0 1 };
				
//Define non-centrality vector 
m  = { 0, 0 };	
						
//Define control structure				
struct cdfmControl ctl;
 
//Fill control structure with default values
ctl = cdfmControlCreate();
 
//Adjust tolerance
ctl.absErrorTolerance = 1e-4;
ctl.relErrorTolerance = 1e-4;
 
//Calculate cumulative probability of
//both variables being ≤ 0
{p, err, retcode} = cdfMvne(ctl, x, R, m );

With any structure that is in a loaded library (cdfmControl is loaded by default), after you declare a variable to be an instance of the structure, for example:

//Declare 'ctl' to be a cdfmControl structure
struct cdfmControl ctl;

when you enter the name of the structure instance, followed by the 'dot operator':

ctl.

you will get an autocomplete list, containing the names of all members of the structure.

If you right-click on cdfmControlCreate() in the GAUSS Editor and select 'Open function definition', it will show you the code for the procedure. In this case it is just a few lines, applying the default settings.