\name{la}

\alias{la}

\title{Analytical first derivative with respect to alpha of the GBSD}

\description{
  This function computes the first analytical derivative of the loglikelihood 
  with respect to \eqn{\alpha} of the GBSD.
}

\usage{
la(theta, x, nu = 1.0, kernel = "normal")
}

\arguments{
  \item{theta}{Vector of parameters {alpha} and {beta}.}
  \item{x}{Vector of observations.}
  \item{nu}{Shape parameter corresponding to the degrees of freedom of the t 
            distribution. In the case of the Laplace, logistic, normal kernels,
            nu can be fixed at the value 1.0 since this parameter is not 
            involved in these kernels.}
  \item{kernel}{Kernel of the pdf of the associated symmetrical distribution 
                by means of which the GBSD is obtained. The kernels: 
                {laplace}, {logistic}, {normal} and 
                {t} are available.}
}

\value{
  \code{la()} return the first analytical derivative of the loglikelihood 
  with respect to \eqn{\alpha} of the GBSD.
}

\references{Diaz-Garcia, J.A., Leiva, V. (2005)  A new family of life
distributions based on elliptically contoured distributions. J. Stat. Plan. Infer.
128:445-457 (Erratum: J. Stat. Plan. Infer. 137:1512-1513).

Leiva, V., Barros, M., Paula, G.A., Sanhueza, A. (2008) Generalized 
Birnbaum-Saunders distributions applied to air pollutant concentration.
Environmetrics 19:235-249.

Sanhueza, A., Leiva, V., Balakrishnan, N. (2008) The generalized Birnbaum-Saunders
distribution and its theory, methodology and application. Comm. Stat. Theory and
Meth. 37:645-670.}


\author{
Barros, Michelli <michelli.karinne@gmail.com> \cr 
Leiva, Victor <victor.leiva@uv.cl, victor.leiva@yahoo.com> \cr
Paula, Gilberto A. <giapaula@ime.usp.br> 
}

\keyword{math}