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## ##
## Copyright Yoann Robin, 2020 ##
## ##
## yoann.robin.k@gmail.com ##
## ##
## This software is a computer program that is part of the ROOPSD (R Object ##
## Oriented Programming for Statistical Distribution). This library makes it ##
## possible to draw, fit and access to CDF and SF function ##
## for classic statistical distribution. ##
## ##
## This software is governed by the CeCILL-C license under French law and ##
## abiding by the rules of distribution of free software. You can use, ##
## modify and/ or redistribute the software under the terms of the CeCILL-C ##
## license as circulated by CEA, CNRS and INRIA at the following URL ##
## "http://www.cecill.info". ##
## ##
## As a counterpart to the access to the source code and rights to copy, ##
## modify and redistribute granted by the license, users are provided only ##
## with a limited warranty and the software's author, the holder of the ##
## economic rights, and the successive licensors have only limited ##
## liability. ##
## ##
## In this respect, the user's attention is drawn to the risks associated ##
## with loading, using, modifying and/or developing or reproducing the ##
## software by the user in light of its specific status of free software, ##
## that may mean that it is complicated to manipulate, and that also ##
## therefore means that it is reserved for developers and experienced ##
## professionals having in-depth computer knowledge. Users are therefore ##
## encouraged to load and test the software's suitability as regards their ##
## requirements in conditions enabling the security of their systems and/or ##
## data to be ensured and, more generally, to use and operate it in the ##
## same conditions as regards security. ##
## ##
## The fact that you are presently reading this means that you have had ##
## knowledge of the CeCILL-C license and that you accept its terms. ##
## ##
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## ##
## Copyright Yoann Robin, 2020 ##
## ##
## yoann.robin.k@gmail.com ##
## ##
## Ce logiciel est un programme informatique faisant partie de la librairie ##
## ROOPSD (R Object Oriented Programming for Statistical Distribution). Cette ##
## librarie permet de tirer aléatoirement, inférer et acceder aux fonctions ##
## CDF et SF des distributions statistisques classiques. ##
## ##
## Ce logiciel est régi par la licence CeCILL-C soumise au droit français et ##
## respectant les principes de diffusion des logiciels libres. Vous pouvez ##
## utiliser, modifier et/ou redistribuer ce programme sous les conditions ##
## de la licence CeCILL-C telle que diffusée par le CEA, le CNRS et l'INRIA ##
## sur le site "http://www.cecill.info". ##
## ##
## En contrepartie de l'accessibilité au code source et des droits de copie, ##
## de modification et de redistribution accordés par cette licence, il n'est ##
## offert aux utilisateurs qu'une garantie limitée. Pour les mêmes raisons, ##
## seule une responsabilité restreinte pèse sur l'auteur du programme, le ##
## titulaire des droits patrimoniaux et les concédants successifs. ##
## ##
## A cet égard l'attention de l'utilisateur est attirée sur les risques ##
## associés au chargement, à l'utilisation, à la modification et/ou au ##
## développement et à la reproduction du logiciel par l'utilisateur étant ##
## donné sa spécificité de logiciel libre, qui peut le rendre complexe à ##
## manipuler et qui le réserve donc à des développeurs et des professionnels ##
## avertis possédant des connaissances informatiques approfondies. Les ##
## utilisateurs sont donc invités à charger et tester l'adéquation du ##
## logiciel à leurs besoins dans des conditions permettant d'assurer la ##
## sécurité de leurs systèmes et ou de leurs données et, plus généralement, ##
## à l'utiliser et l'exploiter dans les mêmes conditions de sécurité. ##
## ##
## Le fait que vous puissiez accéder à cet en-tête signifie que vous avez ##
## pris connaissance de la licence CeCILL-C, et que vous en avez accepté les ##
## termes. ##
## ##
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## dgpd {{{
#' dgpd
#'
#' Density function of Generalized Pareto Distribution
#'
#' @param x [vector] Vector of values
#' @param loc [vector] Location parameter
#' @param scale [vector] Scale parameter
#' @param shape [vector] Shape parameter
#' @param log [bool] Return log of density if TRUE, default is FALSE
#'
#' @return [vector] Density of GPD at x
#'
#' @examples
#' ## Data
#' loc = 1
#' scale = 0.5
#' shape = -0.2
#' x = base::seq( -5 , 5 , length = 1000 )
#' y = dgpd( x , loc = loc , scale = scale , shape = shape )
#' @export
dgpd = function( x , loc = 0 , scale = 1 , shape = 0 , log = FALSE )
{
size_x = length(x)
loc = if( length(loc) == size_x ) loc else base::rep( loc[1] , size_x )
scale = if( length(scale) == size_x ) scale else base::rep( scale[1] , size_x )
shape = if( length(shape) == size_x ) shape else base::rep( shape[1] , size_x )
Z = ( x - loc ) / scale
shape_zero = ( shape == 0 )
cshape_zero = !shape_zero
valid = (Z > 0) & (1 + shape * Z > 0)
out = numeric(length(x)) + NA
if( base::any(shape_zero) )
{
idx = shape_zero & valid
if( base::any(idx) )
{
out[idx] = -base::log(scale[idx]) - Z[idx]
}
}
if( base::any(cshape_zero) )
{
idx = cshape_zero & valid
if( base::any(idx) )
{
out[idx] = -base::log(scale[idx]) - base::log(1. + shape[idx] * Z[idx]) * ( 1 + 1 / shape[idx] )
}
}
if( base::any(!valid) )
{
out[!valid] = -Inf
}
if( log )
return(out)
else
return(base::exp(out))
}
##}}}
## pgpd {{{
#' pgpd
#'
#' Cumulative distribution function (or survival function) of Generalized Pareto distribution
#'
#' @param q [vector] Vector of quantiles
#' @param loc [vector] Location parameter
#' @param scale [vector] Scale parameter
#' @param shape [vector] Shape parameter
#' @param lower.tail [bool] Return CDF if TRUE, else return survival function
#'
#' @return [vector] CDF (or SF) of GPD at x
#'
#' @examples
#' ## Data
#' loc = 1
#' scale = 0.5
#' shape = -0.2
#' x = base::seq( -5 , 5 , length = 1000 )
#' cdfx = pgpd( x , loc = loc , scale = scale , shape = shape )
#' @export
pgpd = function( q , loc = 0 , scale = 1 , shape = 0 , lower.tail = TRUE )
{
if( !lower.tail )
{
return( 1 - pgpd( q , loc , scale , shape , lower.tail = TRUE ) )
}
size_q = length(q)
loc = if( length(loc) == size_q ) loc else base::rep( loc[1] , size_q )
scale = if( length(scale) == size_q ) scale else base::rep( scale[1] , size_q )
shape = if( length(shape) == size_q ) shape else base::rep( shape[1] , size_q )
shape_zero = ( shape == 0 )
cshape_zero = !shape_zero
Z = ( q - loc ) / scale
valid = (Z > 0) & (1 + shape * Z > 0)
out = numeric(size_q) + NA
if( base::any(shape_zero) )
{
idx = shape_zero & valid
if( base::any(idx) )
{
out[idx] = 1. - base::exp( - Z[idx] )
}
}
if( base::any(cshape_zero) )
{
idx = cshape_zero & valid
if( base::any(idx) )
{
out[idx] = 1. - ( 1. + shape[idx] * Z[idx] )^( -1. / shape[idx] )
}
}
if( base::any(!valid) )
{
idx0 = (Z > 1) & !valid
idx1 = !(Z > 1) & !valid
if( base::any(idx0) )
out[idx0] = 1
if( base::any(idx1) )
out[idx1] = 0
}
return(out)
}
##}}}
## qgpd {{{
#' qgpd
#'
#' Inverse of CDF (or SF) function of Generalized Pareto distribution
#'
#' @param p [vector] Vector of probabilities
#' @param loc [vector] Location parameter
#' @param scale [vector] Scale parameter
#' @param shape [vector] Shape parameter
#' @param lower.tail [bool] Return inverse of CDF if TRUE, else return inverse of survival function
#'
#' @return [vector] Inverse of CDF or SF of GPD for probabilities p
#'
#' @examples
#' ## Data
#' loc = 1
#' scale = 0.5
#' shape = -0.2
#' p = base::seq( 0.01 , 0.99 , length = 100 )
#' q = qgpd( p , loc = loc , scale = scale , shape = shape )
#' @export
qgpd = function( p , loc = 0 , scale = 1 , shape = 0 , lower.tail = TRUE )
{
if( !lower.tail )
return( qgpd( 1 - p , loc , scale , shape , TRUE ) )
## Test size
size_p = length(p)
loc = if( length(loc) == size_p ) loc else base::rep( loc[1] , size_p )
scale = if( length(scale) == size_p ) scale else base::rep( scale[1] , size_p )
shape = if( length(shape) == size_p ) shape else base::rep( shape[1] , size_p )
## Difference shape == 0 and non zero
shape_zero = ( shape == 0 )
cshape_zero = !shape_zero
out = numeric(length(p)) + NA
if( base::any(shape_zero) )
{
out[shape_zero] = loc - scale * base::log(1. - p)
}
if( base::any(cshape_zero) )
{
out[cshape_zero] = loc + scale * ( (1. - p)^(-shape) - 1 ) / shape
}
return(out)
}
##}}}
## rgpd {{{
#' rgpd
#'
#' Random value generator of Generalized Pareto distribution
#'
#' @param n [int] Numbers of values generated
#' @param loc [vector] Location parameter
#' @param scale [vector] Scale parameter
#' @param shape [vector] Shape parameter
#'
#' @return [vector] Random value following a loc + GPD(scale,shape)
#'
#' @examples
#' ## Data
#' loc = 1
#' scale = 0.5
#' shape = -0.2
#' gev = rgpd( 100 , loc = loc , scale = scale , shape = shape )
#' @export
rgpd = function( n = 1 , loc = 0 , scale = 1 , shape = 0 )
{
p = stats::runif( n = n )
return( qgpd( p , loc , scale , shape ) )
}
##}}}
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