EZ.SGB {SGB}

Expectations of Z under the SGB distribution

Description

Expectations under Lebesgue and Aitchison measures for the transformed composition $Z= C((U/scale)^{shape1})$ and $C(Z^{1/shape1})$, where $C(.)$ is the closure operation.

Usage

EZ.SGB(D, x)

Arguments

x

vector of parameters (shape1,coefi,shape2) where shape1 is the overall shape, coefi is the vector of regression coefficients (see initpar.SGB) and shape2 the vector of $D$ Dirichlet shape parameters

D

number of parts

Value

A matrix with 4 rows and D columns giving on each row the expectation of parts

EZ

$E(Z)$, expectation under the (ordinary) Lebesgue measure,

EAZ

$E_A(Z)$, expectation under the Aitchison measure,

EZa

$E(Z^{1/shape1})$, expectation under the (ordinary) Lebesgue measure,

EAZa

$E_A(Z^{1/shape1})$, expectation under the Aitchison measure.

See Also

zval

Examples

set.seed(1234)
x <- c(2,rnorm(4,0,1),1.8,3.1,4.0) 
D <- 3
EZ.SGB(D,x)