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A compter du 1er avril, attention à vos pipelines :
Nouvelles limitations de Docker Hub
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ImHorPhen
mstudentd
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1d72c35f
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1d72c35f
authored
8 months ago
by
SANTAGOSTINI Pierre
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Small corrections (math formulae)
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e2485152
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man/kldstudent.Rd
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@@ -27,9 +27,9 @@ Computes the Kullback-Leibler divergence between two random vectors distributed
according to multivariate \eqn{t} distributions (MTD) with zero location vector.
}
\details{
Given \eqn{X_1}, a random vector of \eqn{
R
^p} distributed according to the centered MTD
Given \eqn{X_1}, a random vector of \eqn{
\mathbb{R}
^p} distributed according to the centered MTD
with parameters \eqn{(\nu_1, 0, \Sigma_1)}
and \eqn{X_2}, a random vector of \eqn{
R
^p} distributed according to the MCD
and \eqn{X_2}, a random vector of \eqn{
\mathbb{R}
^p} distributed according to the MCD
with parameters \eqn{(\nu_2, 0, \Sigma_2)}.
Let \eqn{\lambda_1, \dots, \lambda_p} the eigenvalues of the square matrix \eqn{\Sigma_1 \Sigma_2^{-1}}
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@@ -59,9 +59,9 @@ and \eqn{D} is given by:
}
\eqn{F_D^{(p)}} is the Lauricella \eqn{D}-hypergeometric function defined for \eqn{p} variables:
\deqn{ \displaystyle{ F_D^{(p)}\left(a; b_1, ..., b_p; g; x_1, ..., x_p\right) = \sum\limits_{m_1 \geq 0} ... \sum\limits_{m_p \geq 0}{ \frac{ (a)_{m_1+...+m_p}(b_1)_{m_1} ... (b_p)_{m_p} }{ (g)_{m_1+...+m_p} } \frac{x_1^{m_1}}{m_1!} ... \frac{x_p^{m_p}}{m_p!} } } }
The computation of the partial derivative uses the \code{\link{pochhammer}} function.
\deqn{ \displaystyle{ F_D^{(p)}\left(a; b_1, ..., b_p; g; x_1, ..., x_p\right) = \sum\limits_{m_1 \geq 0} ... \sum\limits_{m_p \geq 0}{ \frac{ (a)_{m_1+...+m_p}(b_1)_{m_1} ... (b_p)_{m_p} }{ (g)_{m_1+...+m_p} } \frac{x_1^{m_1}}{m_1!} ... \frac{x_p^{m_p}}{m_p!} } } }
\if{html}{\out{
<!-- The computation of the partial derivative uses the \code{\link{pochhammer}} function. -->
}}
}
\examples{
nu1 <- 2
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