.devel/R-old/p2.confint.rho.approx.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.
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## 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/>.


invisible(NULL)

# #' Computes the approximate (asymptotic) left-sided confidence interval for the \eqn{\rho}-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 confidence interval bases on the observed value
# #' of S-statistic w.r.t. to the given control function \eqn{\kappa}.
# #'
# #'
# #' For more information see man page on  \code{\link{rho.get}}, \code{\link{Sstat}} and the paper (Gagolewski, Grzegorzewski, 2010).
# #'
# #' @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 approximate confidence interval for the rho-index
# #' @param v observed value of the S-statistic w.r.t. \eqn{\kappa}.
# #' @param kappa an increasing function, \eqn{\kappa}, a so-called control function.
# #' @param kappaInvDer the derivative of the inverse of \eqn{\kappa}.
# #' @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.
# #' @seealso \code{\link{ppareto2}}, \code{\link{pareto2.confint.rho}}, \code{\link{Sstat}},
# #' \code{\link{pareto2.confint.rho.approx.upper}},
# #' \code{\link{pareto2.confint.rho.approx}}, \code{\link{rho.get}}
# #' @export
# pareto2.confint.rho.approx.lower <- function(v, kappa, kappaInvDer, s, n, conf.level=0.95, tol=1e-20)
# {
# 	gamma <- 1-conf.level;
#
# 	if (!is.numeric(v) || length(v) != 1)
# 		stop("v must be a single numeric value");
#
# 	if (mode(s) != "numeric" || length(s) != 1 || s <= 0) stop("'s' should be > 0");
#
# 	if (v < 1e-6) return(0.0);
# # 	if (v > 1-1e-13) return (1.0);
# 	if (gamma < 1e-5) return(0.0);
#
#
# 	bord <- uniroot(function(rho, v, kappa, kappaInvDer, s, n, gamma)
# 	{
# 		k <- uniroot(function(k, s, kappa, rho) {
# 				1-ppareto2(kappa(rho), k, s)-rho
# 			}, c(1e-15,1e10), s, kappa, rho, tol=tol)$root;
#
# # 		k <- log(rho)/(log(s/(s+rho))); # round-off errors :-(
# # 		k <- log1p(rho-1)/(log1p(s/(s+rho)-1)); # round-off errors :-(
#
# 		gprimerho <- dpareto2(kappa(rho), k, s)/abs(kappaInvDer(kappa(rho)));
#
# 		qnorm(1-gamma, rho, sqrt(rho*(1-rho)/n)/(1+gprimerho))-v;
# 	}, c(1e-7,1-1e-7), v, kappa, kappaInvDer, s, n, gamma, tol=tol)$root;
#
# 	return(bord);
#
# # 	return(qnorm(gamma/2, v, sqrt(v*(1-v)/n)/(1+gprime)));
# }
#
#
#
#
#
#
# #' Computes the approximate (asymptotic) right-sided confidence interval for the \eqn{\rho}-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 confidence interval bases on the observed value
# #' of S-statistic w.r.t. to the given control function \eqn{\kappa}.
# #'
# #'
# #' For more information see man page on  \code{\link{rho.get}}, \code{\link{Sstat}} and the paper (Gagolewski, Grzegorzewski, 2010).
# #'
# #' @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 approximate confidence interval for the rho-index
# #' @param v observed value of the S-statistic w.r.t. \eqn{\kappa}.
# #' @param kappa an increasing function, \eqn{\kappa}, a so-called control function.
# #' @param kappaInvDer the derivative of the inverse of \eqn{\kappa}.
# #' @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.
# #' @seealso \code{\link{ppareto2}}, \code{\link{pareto2.confint.rho}}, \code{\link{Sstat}},
# #' \code{\link{pareto2.confint.rho.approx.lower}},
# #' \code{\link{pareto2.confint.rho.approx}}, \code{\link{rho.get}}
# #' @export
# pareto2.confint.rho.approx.upper <- function(v, kappa, kappaInvDer, s, n, conf.level=0.95, tol=1e-20)
# {
# 	gamma <- 1-conf.level;
#
# 	if (!is.numeric(v) || length(v) != 1)
# 		stop("v must be a single numeric value");
#
# 	if (mode(s) != "numeric" || length(s) != 1 || s <= 0) stop("'s' should be > 0");
#
# 	if (v > 1-1e-6) return(1.0);
# # 	if (v < 1e-13) return (0.0);
# 	if (gamma < 1e-5) return(1.0);
#
#
# 	bord <- uniroot(function(rho, v, kappa, kappaInvDer, s, n, gamma)
# 	{
# 		k <- uniroot(function(k, s, kappa, rho) {
# 				1-ppareto2(kappa(rho), k, s)-rho
# 			}, c(1e-15,1e10), s, kappa, rho, tol=tol)$root;
#
# # 		k <- log(rho)/(log(s/(s+rho))); # round-off errors :-(
# # 		k <- log1p(rho-1)/(log1p(s/(s+rho)-1)); # round-off errors :-(
#
# 		gprimerho <- dpareto2(kappa(rho), k, s)/abs(kappaInvDer(kappa(rho)));
#
# 		qnorm(gamma, rho, sqrt(rho*(1-rho)/n)/(1+gprimerho))-v;
# 	}, c(1e-7,1-1e-7), v, kappa, kappaInvDer, s, n, gamma, tol=tol)$root;
#
# 	return(bord);
#
# # 	return(qnorm(gamma/2, v, sqrt(v*(1-v)/n)/(1+gprime)));
# }
#
#
#
#
#
#
#
# #' Computes the approximate (asymptotic) two-sided confidence interval for the \eqn{\rho}-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 confidence interval bases on the observed value
# #' of S-statistic w.r.t. to the given control function \eqn{\kappa}.
# #'
# #'
# #' For more information see man page on  \code{\link{rho.get}}, \code{\link{Sstat}} and the paper (Gagolewski, Grzegorzewski, 2010).
# #'
# #' @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 approximate confidence interval for the rho-index
# #' @param v observed value of the S-statistic w.r.t. \eqn{\kappa}.
# #' @param kappa an increasing function, \eqn{\kappa}, a so-called control function.
# #' @param kappaInvDer the derivative of the inverse of \eqn{\kappa}.
# #' @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.
# #' @seealso \code{\link{ppareto2}}, \code{\link{pareto2.confint.rho}}, \code{\link{Sstat}},
# #' \code{\link{pareto2.confint.rho.approx.lower}},
# #' \code{\link{pareto2.confint.rho.approx.upper}}, \code{\link{rho.get}}
# #' @export
# pareto2.confint.rho.approx <- function(v, kappa, kappaInvDer, s, n, conf.level=0.95, tol=1e-20)
# {
# 	gamma <- 1-conf.level;
# 	return(c(
# 		pareto2.confint.rho.approx.lower(v,kappa, kappaInvDer,s,n,1-gamma*0.5,tol),
# 		pareto2.confint.rho.approx.upper(v,kappa, kappaInvDer,s,n,1-gamma*0.5,tol)
# 	));
# }