EZ.SGB

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.

utilities

Main properties and regression procedures using a generalization of the Dirichlet distribution called Simplicial Generalized Beta distribution. It is a new distribution on the simplex (i.e. on the space of compositions or positive vectors with sum of components equal to 1). The Dirichlet distribution can be constructed from a random vector of independent Gamma variables divided by their sum. The SGB follows the same construction with generalized Gamma instead of Gamma variables. The Dirichlet exponents are supplemented by an overall shape parameter and a vector of scales. The scale vector is itself a composition and can be modeled with auxiliary variables through a log-ratio transformation. Graf, M. (2017, ISBN: 978-84-947240-0-8). See also the vignette enclosed in the package.

Monique Graf

Simplicial Generalized Beta Regression

EZ.SGB function

<dl> <dt>x</dt>
<dd>vector of parameters (<code>shape1</code>,<code>coefi</code>,<code>shape2</code>) where
<code>shape1</code> is the overall shape, <code>coefi</code> is the vector of regression coefficients (see <code>initpar.SGB</code>) and <code>shape2</code> the vector of \(D\) Dirichlet shape parameters</dd> <dt>D</dt>
<dd>number of parts</dd></dl>

Arguments

Expectations of Z under the SGB distribution — EZ.SGB

<dl>

 <dt>x</dt>
<dd>vector of parameters (<code>shape1</code>,<code>coefi</code>,<code>shape2</code>) where
<code>shape1</code> is the overall shape, <code>coefi</code> is the vector of regression coefficients (see <code>initpar.SGB</code>) and <code>shape2</code> the vector of \(D\) Dirichlet shape parameters</dd>

 <dt>D</dt>
<dd>number of parts</dd>

</dl>

EZ.SGB: Expectations of Z under the SGB distribution

Description

Usage

Value

Arguments

See Also

Examples