omxMnor {OpenMx} | R Documentation |

## Multivariate Normal Integration

### Description

Given a covariance matrix, a means vector, and vectors of lower and upper bounds, returns the multivariate normal integral across the space between bounds.

### Usage

```
omxMnor(covariance, means, lbound, ubound)
```

### Arguments

`covariance` |
the covariance matrix describing the multivariate normal distribution. |

`means` |
a row vector containing means of the variables of the underlying distribution. |

`lbound` |
a row vector containing the lower bounds of the integration in each variable. |

`ubound` |
a row vector containing the upper bounds of the integration in each variable. |

### Details

The order of columns in the ‘means’, ‘lbound’, and ‘ubound’ vectors are assumed to be the same as that of the covariance matrix. That is, means[i] is considered to be the mean of the variable whose variance is in covariance[i,i]. That variable will be integrated from lbound[i] to ubound[i] as part of the integration.

The value of ubound[i] or lbound[i] may be set to Inf or -Inf if a boundary at positive or negative infinity is desired.

For all i, ubound[i] must be strictly greater than lbound[i].

The algorithm for multivariate normal integration we use is Alan Genz's FORTRAN implementation of the SADMVN routine described by Genz (1992).

### References

Genz, A. (1992). Numerical Computation of Multivariate Normal Probabilities. *Journal of Computational Graphical Statistics, 1,* 141-149.

### Examples

```
data(myFADataRaw)
covariance <- cov(myFADataRaw[,1:3])
means <- colMeans(myFADataRaw[,1:3])
lbound <- c(-Inf, 0, 1) # Integrate from -Infinity to 0 on first variable
ubound <- c(0, Inf, 2.5) # From 0 to +Infinity on second, and from 1 to 2.5 on third
omxMnor(covariance, means, lbound, ubound)
# 0.0005995
# An alternative specification of the bounds follows
# Integrate from -Infinity to 0 on first variable
v1bound = c(-Inf, 0)
# From 0 to +Infinity on second
v2bound = c(0, Inf)
# and from 1 to 2.5 on third
v3bound = c(1, 2.5)
bounds <- cbind(v1bound, v2bound, v3bound)
lbound <- bounds[1,]
ubound <- bounds[2,]
omxMnor(covariance, means, lbound, ubound)
```

*OpenMx*version 2.21.11 Index]