R/gen.GPD.R

Defines functions rgpd qgpd pgpd dgpd

Documented in dgpd pgpd qgpd rgpd

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## Copyright Yoann Robin, 2020                                                ##
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## yoann.robin.k@gmail.com                                                    ##
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## 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.                                      ##
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## This software is governed by the CeCILL-C license under French law and     ##
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## "http://www.cecill.info".                                                  ##
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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".                                      ##
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## En contrepartie de l'accessibilité au code source et des droits de copie,  ##
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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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ROOPSD documentation built on Aug. 26, 2020, 5:15 p.m.