Simplicial Generalized Beta Regression
Inequality constraints and jacobian
Initial parameters estimates and comparison
Histograms, quantile and probability plots for the z(u)-transforms of ...
Regression for compositions following a SGB distribution
Balances to isometric log-ratio
Classical and robust asymptotic covariance matrix
Equality constraints for overall shape and/or regression parameters an...
Expectations of Z under the SGB distribution
Generalized Gamma distribution
Goodness of fit tests on the marginal distributions of each part in a ...
Imputation of missing parts in compositions from a SGB model
Package SGB
Density and random generator for the SGB distribution
SGB log-likelihood and gradient
Computation of scales and z-vectors
Stepwise backward elimination for SGB regression
Aitchison expectation and mode under the SGB distribution
Tabulation of overall SGB regression results with AIC and matrix view ...
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.