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= Package GrzLinModel =

Max-likelihood and bayesian estimation of 
[http://en.wikipedia.org/wiki/Generalized_linear_model generalized linear models].

== Weighted Generalized Regresions ==

Abstract class 
[source:/tolp/OfficialTolArchiveNetwork/GrzLinModel/WgtReg.tol @WgtReg] 
is the base to inherit weighted generalized linear regressions as poisson, 
binomial, logit, probit or any other, given just the scalar distribution 
function [[LatexEquation( F )]] and the corresponding density function 
[[LatexEquation( f )]]. In a weighted regression each row of input data 
has a distinct weight in the likelihood function. For example, it can be 
very usefull to handle with data extrated from an stratified sample.

Let be 
 * [[LatexEquation( X\in\mathbb{R}^{m\times n} )]] the regression input matrix 
 * [[LatexEquation( w\in\mathbb{R}^{m} )]] the vector of weights of each register
 * [[LatexEquation( y\in\mathbb{R}^{m} )]] the regression output matrix 
 * [[LatexEquation( \beta\in\mathbb{R}^{n} )]] the regression coefficients 
 * [[LatexEquation( \eta=X\beta\in\mathbb{R}^{n} )]] the linear prediction
 * [[LatexEquation( \eta=X\beta\in\mathbb{R}^{n} )]] the linear prediction
 * [[LatexEquation( g )]] the link function
 * [[LatexEquation( f )]] the density fuciton of a distribution of the 
[http://en.wikipedia.org/wiki/Exponential_family exponential family]

Then we purpose that the average of the output is the inverse of the link function 
applyied to the linear predictor

  [[LatexEquation( E\left[y\right]=\mu=g^{-1}\left(X\beta\right) )]]