VPC with covariance term

Phoenix Certara Forums Modelling and Simulation
1

Hi,

I tried to run a VPC with a covariance term between Volume and clearance but got an error message. It ran ok without the covariance so is this a known problem or specific to this project?

Thanks

Teresa

VPC.phxproj (1.45 MB)

2

Dear Teresa

Your variance covariance matrix is not positive definite.

A correlation between V and Cl must be between -1 and 1

We have

correlation=covariance/(product of standard deviations)

Here standard deviation=square root of 0.1=0.3162

Therefore product of stdev=0.1

OK now correlation=0.3/0.1=3 >1

Therefore the variance covariance is not positive definite.

If you use let say covariance of 0.03, it should work.

in summary, there is nothing in the program. The problem is that mathematically you cannot put any covariance value in a variance covariance matrix and expecting to simulate random value form the corresponding normal distribution.

Only variance covariance matrices that are positive definite can be used for simulations.

Best Regards

Serge

3

Hi Serge,

Thanks that is a good explanation. I had wondered if it was the value I was using. This is PK from a report so I think I got confused between correlation and covariance value.

Teresa