# Affine transformations and marginals of a skew-elliptical distribution

### Description

Compute the distribution of a (multivariate) marginal or the distribution
of an affine transformation *a + A'Y* of a multivariate
variable *Y* with skew-elliptical (SEC) distribution.

### Usage

1 2 | ```
affineTransSECdistr(object, a, A, name, compNames, drop=TRUE)
marginalSECdistr(object, comp, name, drop=TRUE)
``` |

### Arguments

`object` |
an object of class |

`a` |
a numeric vector with the length |

`A` |
a full-rank matrix with |

`name` |
an optional character string representing the name of the outcome distribution; if missing, one such string is constructed. |

`compNames` |
an optional vector of length |

`drop` |
a logical flag (default value: |

`comp` |
a vector formed by a subset of |

### Value

If `object`

defines the distribution of a SEC random
variable *Y*, `affineTransSECdistr`

computes the
distribution of *a+A'Y* and `marginalSECdistr`

computes the marginal
distribution of the `comp`

components. In both cases the returned
object is of class `SECdistrMv`

, except when `drop=TRUE`

operates, leading to an object of class `SECdistrUv`

.

### Background

These functions implement formulae given in Sections 5.1.4, 5.1.6 and 6.2.2 of the reference below.

### References

Azzalini, A. with the collaboration of Capitanio, A. (2014).
*The Skew-Normal and Related Families*.
Cambridge University Press, IMS Monographs series.

### See Also

`makeSECdistr`

, `SECdistrMv-class`

### Examples

1 2 3 4 5 6 | ```
dp3 <- list(xi=1:3, Omega=toeplitz(1/(1:3)), alpha=c(3,-1,2), nu=5)
st3 <- makeSECdistr(dp3, family="ST", name="ST3", compNames=c("U", "V", "W"))
A <- matrix(c(1,-1,1, 3,0,-2), 3, 2)
new.st <- affineTransSECdistr(st3, a=c(-3,0), A=A)
#
st2 <- marginalSECdistr(st3, comp=c(3,1), name="2D marginal of ST3")
``` |