# Simulate Joint Binary Probabilities

### 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 |

`n1` |
number of normal variates if method is |

`n2` |
number of repetitions if method is |

### 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))`

.

### Author(s)

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

### See Also

`rmvbin`

### Examples

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