# simul.commonprob: Simulate Joint Binary Probabilities In orddata: Generation of Artificial Ordinal and Binary Data

## Description

Compute common probabilities of binary random variates generated by thresholding normal variates at 0.

## Usage

 `1` ```simul.commonprob(margprob, corr=0, method="integrate", n1=10^5, n2=10) ```

## Arguments

 `margprob` vector of marginal probabilities. `corr` vector of correlation values for normal distribution. `method` either `"integrate"` or `"monte carlo"`. `n1` number of normal variates if method is `"monte carlo"`. `n2` number of repetitions if method is `"monte carlo"`.

## Details

The output of this function is used by `rmvbin`. For all combinations of `marginprob[i]`, `marginprob[j]` and `corr[k]`, the probability that both components of a normal random variable with mean `qnorm(marginprob[c(i,j)])` and correlation `corr[k]` are larger than zero is computed.

The probabilities are either computed by numerical integration of the multivariate normal density, or by Monte Carlo simulation.

For normal usage of `rmvbin` it is not necessary to use this function, one simulation result is provided as variable `SimulVals` in this package and loaded by default.

## Value

`simul.commonprob` returns an array of dimension `c(length(margprob), length(margprob), length(corr))`.

Friedrich Leisch

## References

Friedrich Leisch, Andreas Weingessel and Kurt Hornik (1998). On the generation of correlated artificial binary data. Working Paper Series, SFB “Adaptive Information Systems and Modelling in Economics and Management Science”, Vienna University of Economics, http://www.wu-wien.ac.at/am

`rmvbin`
 ```1 2 3``` ```simul.commonprob(seq(0,1,0.5), seq(-1,1,0.5), meth="mo", n1=10^4) data(SimulVals) ```