.devel/R-old/p2.confint.h.R

In Rexamine/agop: Aggregation Operators and Preordered Sets

## This file is part of the 'agop' library.
##
## Copyright 2013 Marek Gagolewski, Anna Cena
##
## Parts of the code are taken from the 'CITAN' R package by Marek Gagolewski
##
## 'agop' is free software: you can redistribute it and/or modify
## it under the terms of the GNU Lesser General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## 'agop' is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU Lesser General Public License for more details.
##
## You should have received a copy of the GNU Lesser General Public License
## along with 'agop'. If not, see <http://www.gnu.org/licenses/>.


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# #' Computes the exact right-sided confidence interval for the theoretical \eqn{h}-index
# #' of a probability distribution in an \eqn{(X_1,\dots,X_n)} i.i.d. Pareto-type II
# #' model with known scale parameter \eqn{s>0}.
# #'
# #' See \code{\link{pareto2.confint.h}} for details.
# #'
# #' @references
# #' Gagolewski M., Grzegorzewski P., S-Statistics and Their Basic Properties, In: Borgelt C. et al (Eds.),
# #' Combining Soft Computing and Statistical Methods in Data Analysis, Springer-Verlag, 2010, 281-288.\cr
# #'
# #' @title Right-sided exact confidence interval for the theoretical h-index
# #' @param h observed value of the \eqn{h}-index
# #' @param s scale parameter, \eqn{s>0}.
# #' @param n sample size.
# #' @param conf.level confidence level; defaults 0.95.
# #' @param tol the desired accuracy (convergence tolerance).
# #' @return Upper bound of the confidence interval.
# #' @export
# #' @seealso \code{\link{index.h}}, \code{\link{ppareto2}}, \code{\link{rho.get}},
# #' \code{\link{pareto2.confint.rho}},\cr
# #' \code{\link{pareto2.confint.h}}, \code{\link{pareto2.confint.h.lower}}
# pareto2.confint.h.upper <- function(h, s, n, conf.level=0.95, tol=1e-12)
# {
# 	gamma <- 1-conf.level;
#
# 	if (mode(s) != "numeric" || length(s) != 1 || s <= 0) stop("'s' should be > 0");
#
# 	if (length(h) != 1 || h < 0 || h > n)
# 		stop("Incorrect h value!");
# 	h <- round(h);
#
# 	if (h > n-1e-9) return(n);
# 	if (gamma < 1e-9) return(n);
#
#
# 	xsol <- uniroot(function(x,h,s,n,gamma) {
# 		pareto2.phirsch(h+1e-9,n,x,s)-gamma;
# 	}, c(0,1e25),h,s,n,gamma, tol=tol, maxiter=1000)$root;
#
# 	n*rho.get(ppareto2, function(x) { pmin(1,pmax(0,x))*n }, xsol, s); # return value
# }
#
#
#
#
# #' Computes the exact left-sided confidence interval for the theoretical \eqn{h}-index
# #' of a probability distribution in an \eqn{(X_1,\dots,X_n)} i.i.d. Pareto-type II
# #' model with known scale parameter \eqn{s>0}.
# #'
# #' See \code{\link{pareto2.confint.h}} for details.
# #'
# #' @references
# #' Gagolewski M., Grzegorzewski P., S-Statistics and Their Basic Properties, In: Borgelt C. et al (Eds.),
# #' Combining Soft Computing and Statistical Methods in Data Analysis, Springer-Verlag, 2010, 281-288.\cr
# #'
# #' @title Left-sided exact confidence interval for the theoretical h-index
# #' @param h observed value of the \eqn{h}-index
# #' @param s scale parameter, \eqn{s>0}.
# #' @param n sample size.
# #' @param conf.level confidence level; defaults 0.95.
# #' @param tol the desired accuracy (convergence tolerance).
# #' @return Lower bound of the confidence interval.
# #' @export
# #' @seealso \code{\link{index.h}}, \code{\link{ppareto2}}, \code{\link{rho.get}},
# #' \code{\link{pareto2.confint.rho}},\cr
# #' \code{\link{pareto2.confint.h}}, \code{\link{pareto2.confint.h.lower}}
# pareto2.confint.h.lower <- function(h, s, n, conf.level=0.95, tol=1e-12)
# {
# 	gamma <- 1-conf.level;
#
# 	if (mode(s) != "numeric" || length(s) != 1 || s <= 0) stop("'s' should be > 0");
#
# 	if (length(h) != 1 || h < 0 || h > n)
# 		stop("Incorrect h value!");
# 	h <- round(h);
#
# 	if (h < 1e-9) return(0);
# 	if (gamma < 1e-9) return(0);
#
#
# 	xsol <- uniroot(function(x,h,s,n,gamma) {
# 		pareto2.phirsch(h-1+1e-9,n,x,s)-1+gamma;
# 	}, c(0,1e25),h,s,n,gamma, tol=tol, maxiter=1000)$root;
#
# 	n*rho.get(ppareto2, function(x) { pmin(1,pmax(0,x))*n }, xsol, s); # return value
# }
#
#
#
# #' Computes the exact two-sided confidence interval for the theoretical \eqn{h}-index
# #' of a probability distribution in an \eqn{(X_1,\dots,X_n)} i.i.d. Pareto-type II
# #' model with known scale parameter \eqn{s>0}.
# #'
# #' The \dfn{Theoretical \eqn{h}-index} for a sequence of \eqn{n} i.i.d. random variables
# #' with common increasing and continuous c.d.f. \eqn{F} defined on \eqn{[0,\infty)}
# #' is equal to \eqn{n\varrho_\kappa}{n*\rho_\kappa}, where \eqn{\rho_\kappa}
# #' is the \eqn{\rho}-index of \eqn{F} for \eqn{\kappa(x)=nx}, see \code{\link{rho.get}} for details.
# #'
# #' @references
# #' Gagolewski M., Grzegorzewski P., S-Statistics and Their Basic Properties, In: Borgelt C. et al (Eds.),
# #' Combining Soft Computing and Statistical Methods in Data Analysis, Springer-Verlag, 2010, 281-288.\cr
# #'
# #' @title Two-sided exact confidence interval for the theoretical h-index
# #' @param h observed value of the \eqn{h}-index
# #' @param s scale parameter, \eqn{s>0}.
# #' @param n sample size.
# #' @param conf.level confidence level; defaults 0.95.
# #' @param tol the desired accuracy (convergence tolerance).
# #' @return Vector of length 2 with the computed bounds of the confidence interval.
# #' @export
# #' @seealso \code{\link{index.h}}, \code{\link{ppareto2}}, \code{\link{rho.get}},
# #' \code{\link{pareto2.confint.rho}},\cr
# #' \code{\link{pareto2.confint.h.upper}}, \code{\link{pareto2.confint.h.upper}}
# pareto2.confint.h <- function(h, s, n, conf.level=0.95, tol=1e-12)
# {
# 	gamma <- 1-conf.level;
# 	return(c(
# 		pareto2.confint.h.lower(h,s,n,1-gamma*0.5,tol),
# 		pareto2.confint.h.upper(h,s,n,1-gamma*0.5,tol)
# 	));
# }