Generalized additive models for position, scale and shape parameters

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In the statistics  are generalized additive models for positional , economies of scale and shape parameters , and generalized additive models for Lokations-, scale and shape parameters ( english Generalized Additive Model for Location, Scale and Shape ( GAMLSS ) ) modern distribution based approaches semi-parametric regression proposed by Rigby and Stasinopoulos in 2005. GAMLSS models are based on generalized linear models . In general, generalized regression models are models in which the normal distribution assumption for y has been relaxed and then other distributions (mainly from the exponential family ) can also be assumed. The GAMLSS statistical framework enables flexible regression and smoothing models to be fitted to the data. The GAMLSS model assumes that the response variable has any parameter distribution that can be strong or weak, and positive or negative, skewed. In addition, all parameters of the distribution [ location parameters (e.g. mean value ), scale parameters (e.g. variance ) and shape parameters ( skewness and curvature )] can be modeled as linear , nonlinear or smoothing functions of explanatory variables.

Web links

Individual evidence

  1. ^ Ludwig Fahrmeir , Thomas Kneib , Stefan Lang, Brian Marx: Regression: models, methods and applications. Springer Science & Business Media, 2013, ISBN 978-3-642-34332-2 , p. 65.