.

http://rec2012.fce.vutbr.cz/documents/papers/zhang.pdf

and other publications by Hao Zhang tackle this problem and give useful referneces

(also a proposal of importance sampling by the same author

http://www.sciencedirect.com/science/article/pii/S0167473012000124

but behind a paywall)

.

Hello Konstantin! I agree with Lenny that more information is needed so we can understand better what you need. I have been working on simulation studies for which we have generated different type of data but I do not know it is what you are asking for. Thus, in you can provide more information, it will help us understand your research question/problem better. In the meantime, I hope that the following reference is of help. This SAS macro generates response data from provided parameters. This macro generates data for several logistic models, one of which follows a CDF (which you mention in your message). This macro might not be what you need but the documentation is very helpful because it explain how the data are generated based on probabilities distributions. it might help you understand what you would need to do to create your sample data. This is the reference: Whittaker, T. A., Fitzpatrick, S. J., Williams, N. J., and Dodd, B.G. (2003). IRTGEN: A SAS Macro Program to Generate Known Trait Scores and Item Responses from Commonly Used Item Response Theory Models. Applied Psychological Measurement, 27, 299-300. You could request the SAS code and documentation from Dr. Whittaker (her contact information is in the attached document). If it happens that you cannot contact her, I will share the documents with you. I hope this helps. Cheers!

Dear friends,

thank you very much for your reasonable comments and listed papers.

I think that Zhang's papers are what I need.

My problem to be studied is similar to risk assessment: I need to estimate if uncertainty propagation tool for metrological software is reliable or not. The traditional approach is to use Monte-Carlo technique to model initial data uncertainty, propagate samples through data processing program and estimate uncertainty characteristics for final results of computations. All uncertainties are traditionally supposed to be uniformly or normally distributed (such assumptions are often placed in guides and recommendations) inside known bounds. This is not acceptable, I think. That's why I want to apply probability boxes as uncertainty models to validate tested software.

I have asked for methods to sample real-valued quantities from p-boxes, not intervals (as it is proposed in Zhang's papers), because the software to be validated cannot process intervals, only real numbers as initial data and bounds on its uncertainty absolute values (maybe separately for systematic component of uncertainty and for its random component).

I think, the better formulation of my question may be the following one: how to propagate efficiently p-box through the data processing software (that has been already compiled) if it can deal with only real numbers. It seems to me, that two-step Monte-Carlo simulations can be applied: firstly, interval Monte-Carlo technique can be used (from Zhang's papers) and after that traditional Monte-Carlo approach can be used to propagate each sampled interval. The only thing is how to organize this scheme efficiently.

With best regards, Konstantin.