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Copy pathMonte-Carlo-Simulation.R
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Monte-Carlo-Simulation.R
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# ---------------------------------------------------------------------------------------
# --------------- Reproducible Research -----------------------------------------------
# Script to reproduce the results on paper:
# Performance of some estimators of relative variability
#
# Created by Raydonal Ospina
# Modified by: Raydonal Ospina
#
# Raydonal 15/11/2017
# Updated 30/06/2019
# Contact: raydonal@de.ufpe.br
# ---------------------------------------------------------------------------------------
# # ---------------------------------------------------------------------------------------
# # Verify the packages
# if(!require(install.load)){install.packages("install.load", dep=TRUE); require("install.load")}
# # devtools::install_github("hrbrmstr/ggalt")
#
# # load the packages
# install_load("magrittr", "tidyr", "dplyr", "ggplot2", "leaflet",
# "reshape", "reshape2", "grid", "gridExtra", "data.table",
# "latex2exp", "gamlss", "plot3D", "compiler", "moments",
# "tables", "fitdistrplus", "RColorBrewer", "lmomco", "lattice",
# "seleniumPipes", "RSelenium", "readxl", "mailR",
# "sp", "stringr", "latticeExtra", "plyr", #"reshapeGUI",
# "gridBase", "gridExtra", "entropy", "EntropyEstimation",
# "infotheo", "distrEx", "gamlss", "betareg", "readxl", "haven",
# "survey", "sampling", "ncf", "spdep", "data.table", "compiler",
# "plot3D", "tidyverse", "tolerance")
library(tidyverse)
library(compiler)
library(gridExtra)
library(gamlss.dist)
library(gamlss)
library(data.table)
library(tolerance)
library(purrr)
#
# if (!require("devtools")){install.packages("devtools"); devtools::install_github("shiny")}
# # ---------------------------------------------------------------------------------------
#
#
# ---------------------------------------------------------------------------------------
#### Functions
# ---------------------------------------------------------------------------------------
## median
median <- function(x) as.numeric(quantile(x, probs = .5))
median <- cmpfun(median)
# ---------------------------------------------------------------------------------------
# ---------------------------------------------------------------------------------------
## classical coefficient of variation
old <- function(x) sd(x)/mean(x)
old <- cmpfun(old)
# ---------------------------------------------------------------------------------------
# ---------------------------------------------------------------------------------------
## edith
edith <- function(x){
q <- quantile(x, probs = c(.25, .75))
as.numeric((q[2] - q[1]) / (q[2] + q[1]))
}
edith <- cmpfun(edith)
# ---------------------------------------------------------------------------------------
# ---------------------------------------------------------------------------------------
## edith type 8
edith8 <- function(x){
q <- quantile(x, probs = c(.25, .75), type = 8)
as.numeric((q[2] - q[1]) / (q[2] + q[1]))
}
edith8 <- cmpfun(edith8)
# ---------------------------------------------------------------------------------------
# ---------------------------------------------------------------------------------------
## mad/median
madmedian <- function(x){
mdn <- median(x)
MAD <- 1.4826 * median(abs(x - mdn))
MAD/mdn
}
madmedian <- cmpfun(madmedian)
# ---------------------------------------------------------------------------------------
# ---------------------------------------------------------------------------------------
## mnad/median
MnADmedian <- function(x){
mdn <- median(x)
MnAD <- mean(abs(x - mdn))
MnAD/mdn
}
MnADmedian <- cmpfun(MnADmedian)
# ---------------------------------------------------------------------------------------
# ---------------------------------------------------------------------------------------
## all together
cvs <- function(x) c(old(x), edith(x), edith8(x), madmedian(x), MnADmedian(x))
cvs <- cmpfun(cvs)
# ---------------------------------------------------------------------------------------
#
#
## PLOTS
# ---------------------------------------------------------------------------------------
## Plot of CV performance in ggplot2
plot.CV.1 <- function(data=data, # data base
name.title="", # title of plot
name.distribution="", # Name of output files
...
)
{
set.seed(11)
data$Estimator <- factor(data$Estimator, levels=c("CQV7","CQV8","CVMAD","CQVMnAD"),
labels=c(expression(bolditalic(CQV)[7]),
expression(bolditalic(CQV)[8]),
expression(bolditalic(CQV)[MAD]),
expression(bolditalic(CQV)[MnAD]))
)
pl <- ggplot(data, aes(x=true, y=gamma, fill=n, color=n, size=n))
pl <-pl+ geom_jitter(alpha=0.6, shape=21, width = 0.05, height = 0.05)+
facet_wrap(~Estimator, ncol=4, labeller = label_parsed) +
scale_colour_brewer(palette = "Set1")+
scale_fill_brewer(palette = "Set1") #+scale_color_brewer(palette = "Spectral")
# geom_point(shape=1)
pl <- pl + theme(
legend.key = element_rect(colour = "white",
fill = "white"),
legend.key.size = unit(1.1, "cm"),
legend.text = element_text(face = "bold",
size=18),
legend.title = element_text(size=18, face="bold", hjust = 0.5),
panel.grid.major = element_line(colour = "gray70",
linetype = "dotted"),
# panel.grid.minor = element_line(colour = "red", linetype = "dotted"),
panel.background = element_rect(fill = "white",
colour="black"),
panel.spacing = unit(1.1, "cm"),
strip.text.x = element_text(size=18,
hjust=0.5,
vjust=0.5,
face="bold", lineheight = 0.5),
strip.background = element_rect(colour="black", fill="gray98"),
axis.text=element_text(size=17, face="plain", colour="gray24"),
axis.text.x = element_text(angle=0, vjust=0.5, size=17),
axis.title=element_text(size=22,face="plain"),
plot.title = element_text(size = 18, colour = "black", face="bold", hjust=0.5),
# legend.position = c(0.85, 0.85)
legend.position ="right", #c(0.1, 0.85)
legend.direction="vertical",
legend.title.align=0.5
) + guides(fill = guide_legend(label.position = "right", keywidth = 0.8,
label.hjust=0.5, title.hjust=0.5))
pl <- pl + labs(x = expression(theta), y=expression(gamma), title=paste(name.title))
# cartesian coordinate
a = pl+scale_x_continuous(breaks=seq(0.0, 1.0, 0.2), limits=c(0,1), expand=c(0.02,0.02))
# a <- a+scale_y_continuous(expand = expand_scale(mult = c(0, .1)))#scale_y_continuous(expand=c(0.1,0.1))
# polar coordinate
b = pl+coord_polar(theta = "x", start = 0, direction=1)+
scale_x_continuous(breaks=seq(0.0, 1.0, 0.1), limits=c(0,1), expand=c(0,0))
m = list(a=a,b=b)
# save the plots
ggsave(paste0(name.distribution,"-1.pdf"), m$a, width=16, height = 5)
ggsave(paste0(name.distribution,"-1-Polar.pdf"), m$b, width=16, height = 5)
# return the plots for modifications
return(m)
}
plot.CV.2 <- function(data=data, # data base
name.title="", # title of plot
name.distribution="", # Name of output files
...
)
{
set.seed(11)
data$Estimator <- factor(data$Estimator, levels=c("CQV7","CQV8","CVMAD","CQVMnAD"),
labels=c(expression(bolditalic(CQV)[7]),
expression(bolditalic(CQV)[8]),
expression(bolditalic(CQV)[MAD]),
expression(bolditalic(CQV)[MnAD])))
pl <- ggplot(data, aes(x=true, y=gamma, fill=n, color=n, size=n))
pl <-pl+ geom_jitter(alpha=0.6, shape=21, width = 0.05, height = 0.05)+
facet_wrap(~Estimator, ncol=4, labeller = label_parsed)
pl <- pl + theme(
legend.key = element_rect(colour = "white",
fill = "white"),
legend.key.size = unit(1.1, "cm"),
legend.text = element_text(face = "bold",
size=18),
legend.title = element_text(size=18, face="bold", hjust = 0.5),
panel.grid.major = element_line(colour = "gray70",
linetype = "dotted"),
# panel.grid.minor = element_line(colour = "red", linetype = "dotted"),
panel.background = element_rect(fill = "white",
colour="black"),
panel.spacing = unit(1.1, "cm"),
strip.text.x = element_text(size=18,
hjust=0.5,
vjust=0.5,
face="bold", lineheight = 0.5),
strip.background = element_rect(colour="black", fill="gray98"),
axis.text=element_text(size=17, face="plain", colour="gray24"),
axis.text.x = element_text(angle=0, vjust=0.5, size=17),
axis.title=element_text(size=22,face="plain"),
plot.title = element_text(size = 18, colour = "black", face="bold", hjust=0.5),
# legend.position = c(0.85, 0.85)
legend.position ="right", #c(0.1, 0.85)
legend.direction="vertical",
legend.title.align=0.5
) + guides(fill = guide_legend(label.position = "right", keywidth = 0.8,
label.hjust=0.5, title.hjust=0.5))
pl <- pl + labs(x = expression(theta), y=expression(gamma), title=paste(name.title))
# cartesian coordinate
a = pl+scale_x_continuous(breaks=seq(0.0, 1.0, 0.2), limits=c(0,1), expand=c(0.02,0.02))
# a <- a+scale_y_continuous(expand = expand_scale(mult = c(0, .1)))#scale_y_continuous(expand=c(0.1,0.1))
# polar coordinate
b = pl+coord_polar(theta = "x", start = 0, direction=1)+
scale_x_continuous(breaks=seq(0.0, 1.0, 0.1), limits=c(0,1), expand=c(0,0))
m = list(a=a,b=b)
# save the plots
ggsave(paste0(name.distribution,"-2.pdf"), m$a, width=16, height = 5)
ggsave(paste0(name.distribution,"-2-Polar.pdf"), m$b, width=16, height = 5)
# return the plots for modifications
return(m)
}
#-----------------------------------------
plot.CV.3 <- function(data=data, # data base
name.title="", # title of plot
name.distribution="", # Name of output files
...
)
{
# set.seed(11)
data$Estimator <- factor(data$Estimator, levels=c("CQV7","CQV8","CVMAD","CQVMnAD"),
labels=c(expression(bolditalic(CQV)[7]),
expression(bolditalic(CQV)[8]),
expression(bolditalic(CV)[MAD]),
expression(bolditalic(CV)[MnAD]))
)
pl <- ggplot(data, aes(x = true, y=lgamma, fill = n, color = n, size = n))
pl <- pl + geom_point(alpha = 0.7, shape=21) + #, width = 0.05, height = 0.5) +
facet_wrap(~Estimator, ncol = 4, labeller = label_parsed) +
scale_color_manual(values = c("blue",
"red",
"green",
"brown",
"orange")) +
scale_fill_manual(values = c("blue",
"red",
"green",
"brown",
"orange"))+
geom_hline(aes(yintercept = 0), col="red")
#
#
# scale_colour_brewer(palette = "Set1")+
# scale_fill_brewer(palette = "Set1") #+scale_color_brewer(palette = "Spectral")
# geom_point(shape=1)
pl <- pl + theme(
legend.key = element_rect(colour = "white",
fill = "white"),
legend.key.size = unit(1.1, "cm"),
legend.text = element_text(face = "bold",
size=18),
legend.title = element_text(size=18, face="bold", hjust = 0.5),
panel.grid.major = element_line(colour = "gray70",
linetype = "dotted"),
# panel.grid.minor = element_line(colour = "red", linetype = "dotted"),
panel.background = element_rect(fill = "white",
colour="black"),
panel.spacing = unit(1.1, "cm"),
strip.text.x = element_text(size=18,
hjust=0.5,
vjust=0.5,
face="bold", lineheight = 0.5),
strip.background = element_rect(colour="black", fill="gray98"),
axis.text=element_text(size=17, face="plain", colour="gray24"),
axis.text.x = element_text(angle=0, vjust=0.5, size=17),
axis.title=element_text(size=22,face="plain"),
plot.title = element_text(size = 18, colour = "black", face="bold", hjust=0.5),
# legend.position = c(0.85, 0.85)
legend.position ="right", #c(0.1, 0.85)
legend.direction="vertical",
legend.title.align=0.5
) + guides(fill = guide_legend(label.position = "right", keywidth = 0.8,
label.hjust=0.5, title.hjust=0.5))
pl <- pl + labs(x = expression(theta), y=expression(log[10](gamma)), title=paste(name.title))
# cartesian coordinate
a = pl+scale_x_continuous(breaks=seq(0.0, 1.0, 0.2), limits=c(0,1), expand=c(0.02,0.02))
# a <- a+scale_y_continuous(limits=c(0,max(data_long$gamma)),
# breaks = seq(0,max(data_long$gamma), by = 2000),
# expand = c(0,0))
#
# polar coordinate
b = pl+coord_polar(theta = "x", start = 0, direction=1)+
scale_x_continuous(breaks=seq(0.0, 1.0, 0.1), limits=c(0,1), expand=c(0,0))
m = list(a=a,b=b)
# save the plots
ggsave(paste0(name.distribution,"-4.pdf"), m$a, width=16, height = 5)
ggsave(paste0(name.distribution,"-4-Polar.pdf"), m$b, width=16, height = 5)
# return the plots for modifications
return(m)
}
# #################################################
#
#-----------------------------------------
plot.CV.4 <- function(data=data, # data base
name.title="", # title of plot
name.distribution="", # Name of output files
...
)
{
# set.seed(11)
data$Estimator <- factor(data$Estimator, levels=c("CQV7","CQV8","CVMAD","CQVMnAD"),
labels=c(expression(bolditalic(CQV)[7]),
expression(bolditalic(CQV)[8]),
expression(bolditalic(CV)[MAD]),
expression(bolditalic(CV)[MnAD]))
)
pl <- ggplot(data, aes(x = true, y=lgamma, shape=n))
pl <- pl + geom_point(alpha = 0.7, color = "black", size=1) + #, width = 0.05, height = 0.5) +
facet_wrap(~Estimator, ncol = 4, labeller = label_parsed) +
scale_shape_manual(values = c(0,1,2,5,6))
# "red",
# "green",
# "brown",
# "orange")) +
# scale_fill_manual(values = c("blue",
# "red",
# "green",
# "brown",
# "orange"))+
geom_hline(aes(yintercept = 0), col="red")
#
#
# scale_colour_brewer(palette = "Set1")+
# scale_fill_brewer(palette = "Set1") #+scale_color_brewer(palette = "Spectral")
# geom_point(shape=1)
pl <- pl + theme(
legend.key = element_rect(colour = "white",
fill = "white"),
legend.key.size = unit(1.1, "cm"),
legend.text = element_text(face = "bold",
size=18),
legend.title = element_text(size=18, face="bold", hjust = 0.5),
panel.grid.major = element_line(colour = "gray70",
linetype = "dotted"),
# panel.grid.minor = element_line(colour = "red", linetype = "dotted"),
panel.background = element_rect(fill = "white",
colour="black"),
panel.spacing = unit(1.1, "cm"),
strip.text.x = element_text(size=18,
hjust=0.5,
vjust=0.5,
face="bold", lineheight = 0.5),
strip.background = element_rect(colour="black", fill="gray98"),
axis.text=element_text(size=17, face="plain", colour="gray24"),
axis.text.x = element_text(angle=0, vjust=0.5, size=17),
axis.title=element_text(size=22,face="plain"),
plot.title = element_text(size = 18, colour = "black", face="bold", hjust=0.5),
# legend.position = c(0.85, 0.85)
legend.position ="right", #c(0.1, 0.85)
legend.direction="vertical",
legend.title.align=0.5
) + guides(fill = guide_legend(label.position = "right", keywidth = 0.8,
label.hjust=0.5, title.hjust=0.5))
pl <- pl + labs(x = expression(theta), y=expression(log[10](gamma)), title=paste(name.title))
# cartesian coordinate
a = pl+scale_x_continuous(breaks=seq(0.0, 1.0, 0.2), limits=c(0,1), expand=c(0.02,0.02))
# a <- a+scale_y_continuous(limits=c(0,max(data_long$gamma)),
# breaks = seq(0,max(data_long$gamma), by = 2000),
# expand = c(0,0))
#
# polar coordinate
b = pl+coord_polar(theta = "x", start = 0, direction=1)+
scale_x_continuous(breaks=seq(0.0, 1.0, 0.1), limits=c(0,1), expand=c(0,0))
m = list(a=a,b=b)
# save the plots
ggsave(paste0(name.distribution,"-4.pdf"), m$a, width=16, height = 5)
ggsave(paste0(name.distribution,"-4-Polar.pdf"), m$b, width=16, height = 5)
# return the plots for modifications
return(m)
}
# ---------------------------------------------------------------------------------------
# ---------------------------------------------------------------------------------------
## Monte Carlo Simulation
## Parameters of simulation
## random seed
set.seed(121)
# Sample size
n <- c(10, 25, 50, 100, 200)
# mean
mu <- c(0.1, 0.4, 0.7, 1, 5, 15, 30)
# dispersion
s <- c(.1, 0.3, 0.6, 1, 3, 5)
## number of Monte Carlo replicates
B <- 10000
# ---------------------------------------------------------------------------------------
ptm <- proc.time()
#########################################################################################
## ------------------------
## Normal
# E(X) = mu
# VarX = sigma^2
## ------------------------
params <- expand.grid(n = n, mu = mu, s = s)
NROW(params)
params$true <- with(params, s/mu)
params <- params[(0 <= params$true) & (params$true <= 1), ]
save(params, file="Normal-params.Rdata")
L <- matrix(NA_real_, nrow = NROW(params), ncol = 5)
colnames(L) <- c('old','edith','edith8', 'MADmedian','MnADmedian')
for(i in 1:NROW(params)){
r <- as.numeric(unlist(params[i,]))
## replicates
res <- parallel:::mclapply(1:B, function(i){
x <- rnorm(n = r[1], mean = r[2], s = r[3])
cvs(x)
}, mc.cores = 4)
res <- do.call(rbind, res)
L[i, ] <- colMeans((res-r[4])^2, na.rm = TRUE)
if(i %% 10 == 0) cat(i, " ")
# if(i == NROW(params)) cat("\n")
}
out <- cbind(params, L)
# Add the Gamma measures
out$CQV7=out$edith/out$old
out$CQV8=out$edith8/out$old
out$CVMAD=out$MADmedian/out$old
out$CQVMnAD=out$MnADmedian/out$old
save(out, file="Normal-Sim-Wide.Rdata")
load("Normal-Sim-Wide.Rdata")
data_long <- gather(out, Estimator, gamma, CQV7:CQVMnAD, factor_key=TRUE)
data_long$n=as.factor(data_long$n)
# data_long$m=as.factor(data_long$m)
# data_long$p=as.factor(format(data_long$p, digits=2) )
data_long$lgamma = log10(data_long$gamma)
data_long$ltrue = log10(data_long$true)
# remove the infnite values
data_long <- data_long[!is.infinite((data_long$gamma)), ]
save(data_long, file="Normal-Sim-Long.Rdata")
Normal = data_long %>% group_by(n, Estimator) %>% summarise(med=median(lgamma))
save(Normal, file="Normal-Table.Rdata")
# v.1 = plot.CV.1(data=data_long, name.distribution="Normal")
# v.2 = plot.CV.2(data=data_long, name.distribution="Normal")
load("Normal-Sim-Long.Rdata")
v.3 = plot.CV.3(data=data_long, name.distribution="Normal")
#########################################################################################
#########################################################################################
# MIXTURES
## ------------------------
## Normal Contaminated 5% lambda=3 MIXTURES
# E(X) = mu
# VarX = sigma^2
## ------------------------
params <- expand.grid(n = n, mu = mu, s = s)
NROW(params)
params$true <- with(params, s/mu)
params <- params[(0 <= params$true) & (params$true <= 1), ]
save(params, file="Normal-5-params.Rdata")
L <- matrix(NA_real_, nrow = NROW(params), ncol = 5)
colnames(L) <- c('old','edith','edith8', 'MADmedian','MnADmedian')
for(i in 1:NROW(params)){
r <- as.numeric(unlist(params[i,]))
## replicates
res <- parallel:::mclapply(1:B, function(i){
x <- (1-(5/100))*rnorm(n = r[1], mean = r[2], s = r[3])+
(5/100)*rnorm(n = r[1], mean = r[2], s = sqrt(3)*r[3])
cvs(x)
}, mc.cores = 4)
res <- do.call(rbind, res)
L[i, ] <- colMeans((res-r[4])^2, na.rm = TRUE)
if(i %% 10 == 0) cat(i, " ")
# if(i == NROW(params)) cat("\n")
}
out <- cbind(params, L)
# Add the Gamma measures
out$CQV7=out$edith/out$old
out$CQV8=out$edith8/out$old
out$CVMAD=out$MADmedian/out$old
out$CQVMnAD=out$MnADmedian/out$old
save(out, file="Normal-5-Sim-Wide.Rdata")
load("Normal-5-Sim-Wide.Rdata")
data_long <- gather(out, Estimator, gamma, CQV7:CQVMnAD, factor_key=TRUE)
data_long$n=as.factor(data_long$n)
# data_long$m=as.factor(data_long$m)
# data_long$p=as.factor(format(data_long$p, digits=2) )
data_long$lgamma = log10(data_long$gamma)
data_long$ltrue = log10(data_long$true)
# remove the infnite values
data_long <- data_long[!is.infinite((data_long$gamma)), ]
save(data_long, file="Normal-5-Sim-Long.Rdata")
Normal.5 = data_long %>% group_by(n, Estimator) %>% summarise(med=median(lgamma))
save(Normal.5, file="Normal.5-Table.Rdata")
# v.1 = plot.CV.1(data=data_long, name.distribution="Normal-5")
# v.2 = plot.CV.2(data=data_long, name.distribution="Normal-5")
load("Normal-5-Sim-Long.Rdata")
v.3 = plot.CV.3(data=data_long, name.distribution="Normal-5")
#########################################################################################
#
#
#
#########################################################################################
## ------------------------
## Normal Contaminated 10% lambda=3 MIXTURES
# E(X) = mu
# VarX = sigma^2
## ------------------------
params <- expand.grid(n = n, mu = mu, s = s)
NROW(params)
params$true <- with(params, s/mu)
params <- params[(0 <= params$true) & (params$true <= 1), ]
save(params, file="Normal-10-params.Rdata")
L <- matrix(NA_real_, nrow = NROW(params), ncol = 5)
colnames(L) <- c('old','edith','edith8', 'MADmedian','MnADmedian')
for(i in 1:NROW(params)){
r <- as.numeric(unlist(params[i,]))
## replicates
res <- parallel:::mclapply(1:B, function(i){
x <- (1-(10/100))*rnorm(n = r[1], mean = r[2], s = r[3])+
(10/100)*rnorm(n = r[1], mean = r[2], s = sqrt(3)*r[3])
cvs(x)
}, mc.cores = 4)
res <- do.call(rbind, res)
L[i, ] <- colMeans((res-r[4])^2, na.rm = TRUE)
if(i %% 10 == 0) cat(i, " ")
# if(i == NROW(params)) cat("\n")
}
out <- cbind(params, L)
# Add the Gamma measures
out$CQV7=out$edith/out$old
out$CQV8=out$edith8/out$old
out$CVMAD=out$MADmedian/out$old
out$CQVMnAD=out$MnADmedian/out$old
save(out, file="Normal-10-Sim-Wide.Rdata")
load("Normal-10-Sim-Wide.Rdata")
data_long <- gather(out, Estimator, gamma, CQV7:CQVMnAD, factor_key=TRUE)
data_long$n=as.factor(data_long$n)
# data_long$m=as.factor(data_long$m)
# data_long$p=as.factor(format(data_long$p, digits=2) )
data_long$lgamma = log10(data_long$gamma)
data_long$ltrue = log10(data_long$true)
# remove the infnite values
data_long <- data_long[!is.infinite((data_long$gamma)), ]
save(data_long, file="Normal-10-Sim-Long.Rdata")
Normal.10 = data_long %>% group_by(n, Estimator) %>% summarise(med=median(lgamma))
save(Normal.10, file="Normal.10-Table.Rdata")
# v.1 = plot.CV.1(data=data_long, name.distribution="Normal-10")
# v.2 = plot.CV.2(data=data_long, name.distribution="Normal-10")
load("Normal-10-Sim-Long.Rdata")
v.3 = plot.CV.3(data=data_long, name.distribution="Normal-10")
#########################################################################################
#########################################################################################
## ------------------------
## Normal Contaminated 15% lambda=3 MIXTURES
# E(X) = mu
# VarX = sigma^2
## ------------------------
params <- expand.grid(n = n, mu = mu, s = s)
NROW(params)
params$true <- with(params, s/mu)
params <- params[(0 <= params$true) & (params$true <= 1), ]
save(params, file="Normal-15-params.Rdata")
L <- matrix(NA_real_, nrow = NROW(params), ncol = 5)
colnames(L) <- c('old','edith','edith8', 'MADmedian','MnADmedian')
for(i in 1:NROW(params)){
r <- as.numeric(unlist(params[i,]))
## replicates
res <- parallel:::mclapply(1:B, function(i){
x <- (1-(15/100))*rnorm(n = r[1], mean = r[2], s = r[3])+
(15/100)*rnorm(n = r[1], mean = r[2], s = sqrt(3)*r[3])
cvs(x)
}, mc.cores = 4)
res <- do.call(rbind, res)
L[i, ] <- colMeans((res-r[4])^2, na.rm = TRUE)
if(i %% 10 == 0) cat(i, " ")
# if(i == NROW(params)) cat("\n")
}
out <- cbind(params, L)
# Add the Gamma measures
out$CQV7=out$edith/out$old
out$CQV8=out$edith8/out$old
out$CVMAD=out$MADmedian/out$old
out$CQVMnAD=out$MnADmedian/out$old
save(out, file="Normal-15-Sim-Wide.Rdata")
load("Normal-15-Sim-Wide.Rdata")
data_long <- gather(out, Estimator, gamma, CQV7:CQVMnAD, factor_key=TRUE)
data_long$n=as.factor(data_long$n)
# data_long$m=as.factor(data_long$m)
# data_long$p=as.factor(format(data_long$p, digits=2) )
data_long$lgamma = log10(data_long$gamma)
data_long$ltrue = log10(data_long$true)
# remove the infnite values
data_long <- data_long[!is.infinite((data_long$gamma)), ]
save(data_long, file="Normal-15-Sim-Long.Rdata")
Normal.15 = data_long %>% group_by(n, Estimator) %>% summarise(med=median(lgamma))
save(Normal.15, file="Normal.15-Table.Rdata")
# v.1 = plot.CV.1(data=data_long, name.distribution="Normal-15")
# v.2 = plot.CV.2(data=data_long, name.distribution="Normal-15")
load("Normal-15-Sim-Long.Rdata")
v.3 = plot.CV.3(data=data_long, name.distribution="Normal-15")
#########################################################################################
#########################################################################################
## ------------------------
## Normal Contaminated 20% lambda=3 MIXTURES
# E(X) = mu
# VarX = sigma^2
## ------------------------
params <- expand.grid(n = n, mu = mu, s = s)
NROW(params)
params$true <- with(params, s/mu)
params <- params[(0 <= params$true) & (params$true <= 1), ]
save(params, file="Normal-20-params.Rdata")
L <- matrix(NA_real_, nrow = NROW(params), ncol = 5)
colnames(L) <- c('old','edith','edith8', 'MADmedian','MnADmedian')
for(i in 1:NROW(params)){
r <- as.numeric(unlist(params[i,]))
## replicates
res <- parallel:::mclapply(1:B, function(i){
x <- (1-(20/100))*rnorm(n = r[1], mean = r[2], s = r[3])+
(20/100)*rnorm(n = r[1], mean = r[2], s = sqrt(3)*r[3])
cvs(x)
}, mc.cores = 4)
res <- do.call(rbind, res)
L[i, ] <- colMeans((res-r[4])^2, na.rm = TRUE)
if(i %% 10 == 0) cat(i, " ")
# if(i == NROW(params)) cat("\n")
}
out <- cbind(params, L)
# Add the Gamma measures
out$CQV7=out$edith/out$old
out$CQV8=out$edith8/out$old
out$CVMAD=out$MADmedian/out$old
out$CQVMnAD=out$MnADmedian/out$old
save(out, file="Normal-20-Sim-Wide.Rdata")
load("Normal-20-Sim-Wide.Rdata")
data_long <- gather(out, Estimator, gamma, CQV7:CQVMnAD, factor_key=TRUE)
data_long$n=as.factor(data_long$n)
# data_long$m=as.factor(data_long$m)
# data_long$p=as.factor(format(data_long$p, digits=2) )
data_long$lgamma = log10(data_long$gamma)
data_long$ltrue = log10(data_long$true)
# remove the infnite values
data_long <- data_long[!is.infinite((data_long$gamma)), ]
save(data_long, file="Normal-20-Sim-Long.Rdata")
Normal.20 = data_long %>% group_by(n, Estimator) %>% summarise(med=median(lgamma))
save(Normal.20, file="Normal.20-Table.Rdata")
# v.1 = plot.CV.1(data=data_long, name.distribution="Normal-20")
# v.2 = plot.CV.2(data=data_long, name.distribution="Normal-20")
load("Normal-20-Sim-Long.Rdata")
v.3 = plot.CV.3(data=data_long, name.distribution="Normal-20")
#########################################################################################
#########################################################################################
# Really contaminated with Heavy tails
# ------------------------
# Normal Contaminated with 5% of Heavy tails (t-distribution with 2.5df)
# E(X) = mu
# VarX = sigma^2
## ------------------------
params <- expand.grid(n = n, mu = mu, s = s)
NROW(params)
params$true <- with(params, s/mu)
params <- params[(0 <= params$true) & (params$true <= 1), ]
save(params, file="Normal-Heavy-5-params.Rdata")
L <- matrix(NA_real_, nrow = NROW(params), ncol = 5)
colnames(L) <- c('old','edith','edith8', 'MADmedian','MnADmedian')
for(i in 1:NROW(params)){
r <- as.numeric(unlist(params[i,]))
## replicates
res <- parallel:::mclapply(1:B, function(i){
# x <- (1-(20/100))*rnorm(n = r[1], mean = r[2], s = r[3])+
# (20/100)*rnorm(n = r[1], mean = r[2], s = sqrt(3)*r[3])
x <- c(rnorm(n=r[1]*0.95, mean = r[2], s = r[3]), rt(n=r[1]*0.05, df = 2.5) )
cvs(x)
}, mc.cores = 4)
res <- do.call(rbind, res)
L[i, ] <- colMeans((res-r[4])^2, na.rm = TRUE)
if(i %% 10 == 0) cat(i, " ")
# if(i == NROW(params)) cat("\n")
}
out <- cbind(params, L)
# Add the Gamma measures
out$CQV7=out$edith/out$old
out$CQV8=out$edith8/out$old
out$CVMAD=out$MADmedian/out$old
out$CQVMnAD=out$MnADmedian/out$old
save(out, file="Normal-Heavy-5-Sim-Wide.Rdata")
load("Normal-Heavy-5-Sim-Wide.Rdata")
data_long <- gather(out, Estimator, gamma, CQV7:CQVMnAD, factor_key=TRUE)
data_long$n=as.factor(data_long$n)
# data_long$m=as.factor(data_long$m)
# data_long$p=as.factor(format(data_long$p, digits=2) )
data_long$lgamma = log10(data_long$gamma)
data_long$ltrue = log10(data_long$true)
# remove the infnite values
data_long <- data_long[!is.infinite((data_long$gamma)), ]
save(data_long, file="Normal-Heavy-5-Sim-Long.Rdata")
Normal.Heavy5 = data_long %>% group_by(n, Estimator) %>% summarise(med=median(lgamma))
save(Normal.Heavy5, file="Normal.Heavy-5-Table.Rdata")
# v.1 = plot.CV.1(data=data_long, name.distribution="Normal-20")
# v.2 = plot.CV.2(data=data_long, name.distribution="Normal-20")
load("Normal-Heavy-5-Sim-Long.Rdata")
v.3 = plot.CV.3(data=data_long, name.distribution="Normal-Heavy-5")
#########################################################################################
#########################################################################################
# Really contaminated with Heavy tails
# ------------------------
# Normal Contaminated with 10% of Heavy tails (t-distribution with 2.5df)
# E(X) = mu
# VarX = sigma^2
## ------------------------
params <- expand.grid(n = n, mu = mu, s = s)
NROW(params)
params$true <- with(params, s/mu)
params <- params[(0 <= params$true) & (params$true <= 1), ]
save(params, file="Normal-Heavy-10-params.Rdata")
L <- matrix(NA_real_, nrow = NROW(params), ncol = 5)
colnames(L) <- c('old','edith','edith8', 'MADmedian','MnADmedian')
for(i in 1:NROW(params)){
r <- as.numeric(unlist(params[i,]))
## replicates
res <- parallel:::mclapply(1:B, function(i){
# x <- (1-(20/100))*rnorm(n = r[1], mean = r[2], s = r[3])+
# (20/100)*rnorm(n = r[1], mean = r[2], s = sqrt(3)*r[3])
x <- c(rnorm(n=r[1]*0.9, mean = r[2], s = r[3]), rt(n=r[1]*0.1, df = 2.5) )
cvs(x)
}, mc.cores = 4)
res <- do.call(rbind, res)
L[i, ] <- colMeans((res-r[4])^2, na.rm = TRUE)
if(i %% 10 == 0) cat(i, " ")
# if(i == NROW(params)) cat("\n")
}
out <- cbind(params, L)
# Add the Gamma measures
out$CQV7=out$edith/out$old
out$CQV8=out$edith8/out$old
out$CVMAD=out$MADmedian/out$old
out$CQVMnAD=out$MnADmedian/out$old
save(out, file="Normal-Heavy-10-Sim-Wide.Rdata")
load("Normal-Heavy-10-Sim-Wide.Rdata")
data_long <- gather(out, Estimator, gamma, CQV7:CQVMnAD, factor_key=TRUE)
data_long$n=as.factor(data_long$n)
# data_long$m=as.factor(data_long$m)
# data_long$p=as.factor(format(data_long$p, digits=2) )
data_long$lgamma = log10(data_long$gamma)
data_long$ltrue = log10(data_long$true)
# remove the infnite values
data_long <- data_long[!is.infinite((data_long$gamma)), ]
save(data_long, file="Normal-Heavy-10-Sim-Long.Rdata")
Normal.Heavy10 = data_long %>% group_by(n, Estimator) %>% summarise(med=median(lgamma))
save(Normal.Heavy10, file="Normal.Heavy-10-Table.Rdata")
# v.1 = plot.CV.1(data=data_long, name.distribution="Normal-20")
# v.2 = plot.CV.2(data=data_long, name.distribution="Normal-20")
load("Normal-Heavy-10-Sim-Long.Rdata")
v.3 = plot.CV.3(data=data_long, name.distribution="Normal-Heavy-10")
#########################################################################################
#########################################################################################
# Really contaminated with Heavy tails
# ------------------------
# Normal Contaminated with 15% of Heavy tails (t-distribution with 2.5df)
# E(X) = mu
# VarX = sigma^2
## ------------------------
params <- expand.grid(n = n, mu = mu, s = s)
NROW(params)
params$true <- with(params, s/mu)
params <- params[(0 <= params$true) & (params$true <= 1), ]
save(params, file="Normal-Heavy-15-params.Rdata")
L <- matrix(NA_real_, nrow = NROW(params), ncol = 5)
colnames(L) <- c('old','edith','edith8', 'MADmedian','MnADmedian')
for(i in 1:NROW(params)){
r <- as.numeric(unlist(params[i,]))
## replicates
res <- parallel:::mclapply(1:B, function(i){
# x <- (1-(20/100))*rnorm(n = r[1], mean = r[2], s = r[3])+
# (20/100)*rnorm(n = r[1], mean = r[2], s = sqrt(3)*r[3])
x <- c(rnorm(n=r[1]*0.85, mean = r[2], s = r[3]), rt(n=r[1]*0.15, df = 2.5) )
cvs(x)
}, mc.cores = 4)
res <- do.call(rbind, res)
L[i, ] <- colMeans((res-r[4])^2, na.rm = TRUE)
if(i %% 10 == 0) cat(i, " ")
# if(i == NROW(params)) cat("\n")
}
out <- cbind(params, L)
# Add the Gamma measures
out$CQV7=out$edith/out$old
out$CQV8=out$edith8/out$old
out$CVMAD=out$MADmedian/out$old
out$CQVMnAD=out$MnADmedian/out$old
save(out, file="Normal-Heavy-15-Sim-Wide.Rdata")
load("Normal-Heavy-15-Sim-Wide.Rdata")
data_long <- gather(out, Estimator, gamma, CQV7:CQVMnAD, factor_key=TRUE)
data_long$n=as.factor(data_long$n)
# data_long$m=as.factor(data_long$m)
# data_long$p=as.factor(format(data_long$p, digits=2) )
data_long$lgamma = log10(data_long$gamma)
data_long$ltrue = log10(data_long$true)
# remove the infnite values
data_long <- data_long[!is.infinite((data_long$gamma)), ]
save(data_long, file="Normal-Heavy-15-Sim-Long.Rdata")
Normal.Heavy15 = data_long %>% group_by(n, Estimator) %>% summarise(med=median(lgamma))
save(Normal.Heavy15, file="Normal.Heavy-15-Table.Rdata")
# v.1 = plot.CV.1(data=data_long, name.distribution="Normal-20")
# v.2 = plot.CV.2(data=data_long, name.distribution="Normal-20")