Consider the daily stock return of the Citigroup (tick symbol C) and the Standard and Poor’s
500 Composite index from January 2001 to December 2008. The data are simple returns
and in the file d-csp0108.txt (three columns with date, C-rtn, SP-rtn).
(a) In previous assignment you have observed the superimposition of the normal density
separately for SP-rtn and C-rtn data. Now use your intuition or play trial and error method
1
to fit the same data sets with some t-distribution, double-exponential, cauchy as well as a
mixture of two normal distributions on the same graph. Which one is coming best ? What
is you intuition while making the trial and error for mixture distribution ? What is your
comment on the tail of cauchy distribution (something odd !!!! pay more attention !!!) (You
may illustrate the answer after making part (b) and part (c) too).
(b) Make different qqplots taking quantiles for each density you have chosen against the
empirical quantiles of the data. Give proper interpretation.
(c) Plot the empirical survival curve and superimpose survival curves for all the densities
you have chosen to fit the data. Comment on the picture.
Extra : If you find the task really interesting; Play a little more with mixture of two
cauchy distributions too.
500 Composite index from January 2001 to December 2008. The data are simple returns
and in the file d-csp0108.txt (three columns with date, C-rtn, SP-rtn).
(a) In previous assignment you have observed the superimposition of the normal density
separately for SP-rtn and C-rtn data. Now use your intuition or play trial and error method
1
to fit the same data sets with some t-distribution, double-exponential, cauchy as well as a
mixture of two normal distributions on the same graph. Which one is coming best ? What
is you intuition while making the trial and error for mixture distribution ? What is your
comment on the tail of cauchy distribution (something odd !!!! pay more attention !!!) (You
may illustrate the answer after making part (b) and part (c) too).
(b) Make different qqplots taking quantiles for each density you have chosen against the
empirical quantiles of the data. Give proper interpretation.
(c) Plot the empirical survival curve and superimpose survival curves for all the densities
you have chosen to fit the data. Comment on the picture.
Extra : If you find the task really interesting; Play a little more with mixture of two
cauchy distributions too.
Conclusion
Which one is
coming best ?
ANS:- As I see
Normal distribution has havier tail than all others and Cauchy
Distribution has lighter tail than all others. Similar for their
mixture distribution but tail of mixture distribution is slightly
lighter than actual normal distribution and similarly tail of mixture
of cauchy distribution is slightly lighter than actual cauchy
distribution.
According to my
observation Mixture of two normal distribution is best fitted
distribution with our C_rtn and SP_rtn data, hence it is best.
What is you
intuition while making the trial and error for mixture distribution ?
ANS:- I have
taken 90% of N(0,1) and 10% of N(0,25) for mixture of two normal
distribution and 90% of C(0,1) and 10% of C(0,5) for mixture of two
Cauchy distribution. Variance of mixture normal dis is 3.4, we get
different distribution of mixture of these two and N(0,3.4) although
both distribution have same mean and variance. Same for Cauchy
Distribution.
What is your
comment on the tail of cauchy distribution (something odd !!!! pay
more attention !!!)
ANS:- Tail of Cauchy distribution is lighter than all
other distribution drown and Tail of mixture of two cauchy
distribution is slightly lighter than actual cauchy distribution.
Q a >>>>>
Code for C_rtn
crtn=function()
{
####### --------- Lybraries ------------#####
library("MASS");
require(graphics);
data_set=read.table("d-csp0108.txt",header=TRUE);
date=data_set[1];
C=data_set[2];
SP=data_set[3];
mean_C=mean(C);
mean_SP=mean(SP);
var_C=var(C);
var_SP=var(SP);
c_rtn=t(C);
sp_rtn=t(SP);
# 4 figures arranged in 2 rows and 2 columns
#attach(mtcars)
par(mfrow=c(2,3))
###---------- Normal Plot- ------------####
h1=hist(c_rtn, breaks=400, col="red", xlab="c_rtn",
freq=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
x=seq(min(c_rtn),max(c_rtn),length=200)
ynorm=dnorm(x, mean=0, sd=0.012);
#ynorm=ynorm*diff(h1$mids[1:2])*length(c_rtn);
par(new=TRUE)
plot(x, ynorm, type="l", col="blue", lwd=2 ,
xlim=c(-0.2,0.2), ylim=c(0,40));
labels=c("normal Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
####--------student T plot ------------#######
h1=hist(c_rtn, breaks=400, col="red", xlab="c_rtn",
freq=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
x=seq(-15,15,length=200);
x1=seq(-0.2,0.2,length=200);
yt=dt(x, 200000);
yt=yt*diff(h1$mids[1:2])*length(c_rtn)*20;
par(new=TRUE)
plot(x1,yt, type="l", col="blue", lwd=2,
axes=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
labels=c("Student t Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
#####---------------- Double exponential or Laplace plot
----------##########
h1=hist(c_rtn, breaks=400, col="red", xlab="c_rtn",
freq=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
b=1;
mu=0;
ylap=(1/(2*b))*(exp(-abs(x-mu)/b))
ylap=ylap*diff(h1$mids[1:2])*length(c_rtn)*18;
par(new=TRUE)
plot(x1,ylap, type="l", col="blue", lwd=2,
axes=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
labels=c("laplace Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
######--------------- Cauchy Distribution ---------- #########
h1=hist(c_rtn, breaks=400, col="red", xlab="c_rtn",
freq=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
x=seq(-15,15,length=200);
x1=seq(-0.2,0.2,length=200);
gama=0.75;
x0=0;
yc=dcauchy(x,location=x0, scale=gama, log=FALSE)
yc=yc*diff(h1$mids[1:2])*length(c_rtn)*20;
par(new=TRUE)
plot(x1,yc, type="l", col="blue", lwd=2,
axes=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
labels=c("Cauchy Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
########---------- Mixture of two normal distribution
-------------########
h1=hist(c_rtn, breaks=400, col="red", xlab="c_rtn",
freq=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
x=seq(min(c_rtn),max(c_rtn),length=200)
ymnorm=0.9*dnorm(x,mean=0, sd=0.012) + 0.1*dnorm(x,mean=0, sd=0.009)
#ymnorm=ymnorm*diff(h1$mids[1:2])*length(c_rtn)*20;
par(new=TRUE)
plot(x,ymnorm, type="l", col="blue", lwd=2,
axes=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
labels=c("mixture of normal Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
######------------- Mixture of two Cauchy Distribution -------------
########
h1=hist(c_rtn, breaks=400, col="red", xlab="c_rtn",
freq=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
x=seq(-15,15,length=200);
x1=seq(-0.2,0.2,length=200);
ymc=0.9*dcauchy(x,location=0, scale=0.75, log=FALSE) +
0.1*dcauchy(x,location=0, scale=0.9, log=FALSE)
ymc=ymc*diff(h1$mids[1:2])*length(c_rtn)*20;
par(new=TRUE)
plot(x1,ymc, type="l", col="blue", lwd=2,
axes=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
labels=c("Mixture of cauchy Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
########## Labels and legends ###################
#labels=c("normal = points", "student t = lines",
"laplace = both", "cauchy = both overplotted",
"Mixture of normal = steps", "Mixture of cauchy =
other steps")
#legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
#title(" Distribution Plots of SP_rtn with different density
functions")
}
Q a >>>>>
Code for SP_rtn
sprtn=function()
{
####### --------- Lybraries ------------#####
library("MASS");
require(graphics);
data_set=read.table("d-csp0108.txt",header=TRUE);
date=data_set[1];
C=data_set[2];
SP=data_set[3];
mean_C=mean(C);
mean_SP=mean(SP);
var_C=var(C);
var_SP=var(SP);
c_rtn=t(C);
sp_rtn=t(SP);
# 4 figures arranged in 2 rows and 2 columns
#attach(mtcars)
par(mfrow=c(2,3))
###---------- Normal Plot- ------------####
h1=hist(sp_rtn, breaks=400, col="red", xlab="sp_rtn",
freq=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
x=seq(min(sp_rtn),max(sp_rtn),length=200)
ynorm=dnorm(x, mean=0, sd=0.0065);
#ynorm=ynorm*diff(h1$mids[1:2])*length(c_rtn);
par(new=TRUE)
plot(x, ynorm, type="l", col="blue", lwd=2 ,
xlim=c(-0.1,0.1), ylim=c(0,80));
labels=c("normal Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
####--------student T plot ------------#######
h1=hist(sp_rtn, breaks=400, col="red", xlab="sp_rtn",
freq=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
x=seq(-15,15,length=200);
x1=seq(-0.1,0.1,length=200);
yt=dt(x, 200000);
yt=yt*diff(h1$mids[1:2])*length(c_rtn)*160;
par(new=TRUE)
plot(x1,yt, type="l", col="blue", lwd=2,
axes=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
labels=c("Student t Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
#####---------------- Double exponential or Laplace plot
----------##########
h1=hist(sp_rtn, breaks=400, col="red", xlab="sp_rtn",
freq=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
b=1;
mu=0;
ylap=(1/(2*b))*(exp(-abs(x-mu)/b))
ylap=ylap*diff(h1$mids[1:2])*length(c_rtn)*135;
par(new=TRUE)
plot(x1,ylap, type="l", col="blue", lwd=2,
axes=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
labels=c("laplace Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
######--------------- Cauchy Distribution ---------- #########
h1=hist(sp_rtn, breaks=400, col="red", xlab="sp_rtn",
freq=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
x=seq(-15,15,length=200);
x1=seq(-0.1,0.1,length=200);
gama=0.75;
x0=0;
yc=dcauchy(x,location=x0, scale=gama, log=FALSE)
yc=yc*diff(h1$mids[1:2])*length(c_rtn)*150;
par(new=TRUE)
plot(x1,yc, type="l", col="blue", lwd=2,
axes=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
labels=c("Cauchy Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
########---------- Mixture of two normal distribution
-------------########
h1=hist(sp_rtn, breaks=400, col="red", xlab="sp_rtn",
freq=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
x=seq(min(sp_rtn),max(sp_rtn),length=200)
ymnorm=0.9*dnorm(x,mean=0, sd=0.0061) + 0.1*dnorm(x,mean=0,
sd=0.0099)
#ymnorm=ymnorm*diff(h1$mids[1:2])*length(c_rtn)*20;
par(new=TRUE)
plot(x,ymnorm, type="l", col="blue", lwd=2,
axes=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
labels=c("mixture of normal Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
######------------- Mixture of two Cauchy Distribution -------------
########
h1=hist(sp_rtn, breaks=400, col="red", xlab="sp_rtn",
freq=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
x=seq(-15,15,length=200);
x1=seq(-0.1,0.1,length=200);
ymc=0.9*dcauchy(x,location=0, scale=0.75, log=FALSE) +
0.1*dcauchy(x,location=0, scale=0.9, log=FALSE)
ymc=ymc*diff(h1$mids[1:2])*length(c_rtn)*150;
par(new=TRUE)
plot(x1,ymc, type="l", col="blue", lwd=2,
axes=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
labels=c("Mixture of cauchy Distribution ")
legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
########## Labels and legends ###################
#labels=c("normal = points", "student t = lines",
"laplace = both", "cauchy = both overplotted",
"Mixture of normal = steps", "Mixture of cauchy =
other steps")
#legend("topleft", border="white", inset=0,
title="Distributions", labels, lwd=2, lty=c(1,1,1,1,2))
#title(" Distribution Plots of SP_rtn with different density
functions")
}
Q b >>>>>>>>>>>>
Code for C_rtn
qbc=function()
{
####### --------- Lybraries ------------#####
library("MASS");
require(graphics)
data_set=read.table("d-csp0108.txt",header=TRUE);
date=data_set[1];
C=data_set[2];
SP=data_set[3];
mean_C=mean(C);
mean_SP=mean(SP);
var_C=var(C);
var_SP=var(SP);
c_rtn=t(C);
sp_rtn=t(SP);
# 4 figures arranged in 2 rows and 2 columns
#attach(mtcars)
par(mfrow=c(2,3))
x=seq(-10,10,length=10000);
qc_rtn=quantile(c_rtn,prob=seq(0,1,.0001))
###---------- Normal Plot- ------------####
yqnorm=qnorm(x, mean=0, sd=1, lower.tail = TRUE, log.p = FALSE);
qqplot(yqnorm,qc_rtn)
qqline(qc_rtn)
labels=c("Normal Distribution")
legend("topright", inset=.05, title="Q-Q Plots
c_rtn", labels, lwd=2)
####--------student T plot ------------#######
yqt=qt(x, 3, lower.tail = TRUE, log.p = FALSE);
qqplot(yqt,qc_rtn)
qqline(qc_rtn)
labels=c("Student t Distribution")
legend("topright", inset=.05, title="Q-Q Plots c_rtn
", labels, lwd=2)
#####---------------- Double exponential or Laplace plot
----------##########
#ylap=dlaplace(x,location=0,scale=1)
b=1;
mu=0;
ylap=(1/(2*b))*(exp(-abs(x-mu)/b))
yqlap=quantile(ylap)
qqplot(yqlap,qc_rtn)
qqline(qc_rtn)
labels=c("Laplace Distribution")
legend("topright", inset=.05, title="Q-Q Plots c_rtn
", labels, lwd=2)
######--------------- Cauchy Distribution ---------- #########
yqcauchy=qcauchy(x, location=0, scale=1, lower.tail = TRUE, log.p =
FALSE);
qqplot(yqcauchy,qc_rtn)
qqline(qc_rtn)
labels=c("Cauchy Distribution")
legend("topright", inset=.05, title="Q-Q Plots c_rtn
", labels, lwd=2)
########---------- Mixture of two normal distribution
-------------########
yqmnorm=0.9*qnorm(x,mean=0, sd=1) + 0.1*qnorm(x,mean=0, sd=5)
qqplot(yqmnorm,qc_rtn)
qqline(qc_rtn)
labels=c("Mixture of Two Normal")
legend("topright", inset=.05, title="Q-Q Plots c_rtn
", labels, lwd=2)
######------------- Mixture of two Cauchy Distribution -------------
########
yqmc=0.9*qcauchy(x,location=0, scale=1, log=FALSE) +
0.1*qcauchy(x,location=0, scale=5, log=FALSE)
qqplot(yqmc,qc_rtn)
qqline(qc_rtn)
labels=c("Mixture of Two cauchy")
legend("topright", inset=.05, title="Q-Q Plots c_rtn
", labels, lwd=2)
########## Labels and legends ###################
#labels=c("normal = p", "student t = l",
"laplace = b", "cauchy = o", "Mixture of
normal = s", "Mixture of cauchy = S")
#legend("topright", inset=.05, title="Distributions",
labels, lwd=2, lty=c(1,1,1,1,2))
}
Q b >>>>>
code for SP_rtn
qbsp=function()
{
####### --------- Lybraries ------------#####
library("MASS");
require(graphics)
data_set=read.table("d-csp0108.txt",header=TRUE);
date=data_set[1];
C=data_set[2];
SP=data_set[3];
mean_C=mean(C);
mean_SP=mean(SP);
var_C=var(C);
var_SP=var(SP);
c_rtn=t(C);
sp_rtn=t(SP);
# 4 figures arranged in 2 rows and 2 columns
#attach(mtcars)
par(mfrow=c(2,3))
x=seq(-10,10,length=10000);
qsp_rtn=quantile(sp_rtn,prob=seq(0,1,.0001))
###---------- Normal Plot- ------------####
yqnorm=qnorm(x, mean=0, sd=1, lower.tail = TRUE, log.p = FALSE);
qqplot(yqnorm,qsp_rtn)
qqline(qsp_rtn)
labels=c("Normal Distribution")
legend("topright", inset=.05, title="Q-Q Plots
sp_rtn", labels, lwd=2)
####--------student T plot ------------#######
yqt=qt(x, 3, lower.tail = TRUE, log.p = FALSE);
qqplot(yqt,qsp_rtn)
qqline(qsp_rtn)
labels=c("Student t Distribution")
legend("topright", inset=.05, title="Q-Q Plots
sp_rtn", labels, lwd=2)
#####---------------- Double exponential or Laplace plot
----------##########
#ylap=dlaplace(x,location=0,scale=1)
b=1;
mu=0;
ylap=(1/(2*b))*(exp(-abs(x-mu)/b))
yqlap=quantile(ylap)
qqplot(yqlap,qsp_rtn)
qqline(qsp_rtn)
labels=c("Laplace Distribution")
legend("topright", inset=.05, title="Q-Q Plots
sp_rtn", labels, lwd=2)
######--------------- Cauchy Distribution ---------- #########
yqcauchy=qcauchy(x, location=0, scale=1, lower.tail = TRUE, log.p =
FALSE);
qqplot(yqcauchy,qsp_rtn)
qqline(qsp_rtn)
labels=c("Cauchy Distribution")
legend("topright", inset=.05, title="Q-Q Plots
sp_rtn", labels, lwd=2)
########---------- Mixture of two normal distribution
-------------########
yqmnorm=0.9*qnorm(x,mean=0, sd=1) + 0.1*qnorm(x,mean=0, sd=5)
qqplot(yqmnorm,qsp_rtn)
qqline(qsp_rtn)
labels=c("Mixture of Two Normal")
legend("topright", inset=.05, title="Q-Q Plots
sp_rtn", labels, lwd=2)
######------------- Mixture of two Cauchy Distribution -------------
########
yqmc=0.9*qcauchy(x,location=0, scale=1, log=FALSE) +
0.1*qcauchy(x,location=0, scale=5, log=FALSE)
qqplot(yqmc,qsp_rtn)
qqline(qsp_rtn)
labels=c("Mixture of Two cauchy")
legend("topright", inset=.05, title="Q-Q Plots
sp_rtn", labels, lwd=2)
########## Labels and legends ###################
#labels=c("normal = p", "student t = l",
"laplace = b", "cauchy = o", "Mixture of
normal = s", "Mixture of cauchy = S")
#legend("topright", inset=.05, title="Distributions",
labels, lwd=2, lty=c(1,1,1,1,2))
}
Q c >>>>>>>>
Code for C_rtn
qcc=function()
{
####### --------- Lybraries ------------#####
library("MASS");
require(graphics)
data_set=read.table("d-csp0108.txt",header=TRUE);
date=data_set[1];
C=data_set[2];
SP=data_set[3];
mean_C=mean(C);
mean_SP=mean(SP);
var_C=var(C);
var_SP=var(SP);
c_rtn=t(C);
sp_rtn=t(SP);
# 4 figures arranged in 2 rows and 2 columns
#attach(mtcars)
par(mfrow=c(3,3))
#x=seq(-10,10,length=1000);
#x=seq(min(c_rtn), max(c_rtn), length=length(c_rtn))
h1=hist(c_rtn, breaks=400, col="red", xlab="c_rtn",
freq=FALSE, xlim=c(-0.2,0.2), ylim=c(0,40))
###---------- Normal Plot- ------------####
x=seq(min(c_rtn),max(c_rtn),length=200)
ydnorm=dnorm(x, mean=0, sd=0.012);
plot.stepfun(ydnorm, col.vert = "gray20", main =
"empirical survival curve c_rtn of Normal distribution ",
axes=FALSE, xlim=c(-.2,.6) , col="red")
par(new=TRUE)
plot.stepfun(c_rtn,col.vert="gray20" , main = "empirical
survival curve c_rtn of Normal distribution " , xlim=c(-.2,.6),
col="blue");
###--------student T plot ------------#######
x=seq(-15,15,length=200);
x1=seq(-0.2,0.2,length=200);
yt=dt(x, 200000);
ydt=yt*diff(h1$mids[1:2])*length(c_rtn)*20;
plot.stepfun(ydt, col.vert = "gray20", main = "empirical
survival curve c_rtn of Student t distribution " , axes=FALSE,
xlim=c(-.2,.6), col="red")
par(new=TRUE)
plot.stepfun(c_rtn,col.vert="gray20", main = "empirical
survival curve c_rtn of Student i distribution " ,
xlim=c(-.2,.6) , col="blue");
#####---------------- Double exponential or Laplace plot
----------##########
#ylap=dlaplace(x,location=0,scale=1)
b=1;
mu=0;
ylap=(1/(2*b))*(exp(-abs(x-mu)/b))
ylap=ylap*diff(h1$mids[1:2])*length(c_rtn)*18;
plot.stepfun(ylap, col.vert = "gray20", main = "empirical
survival curve c_rtn of Laplace distribution " , axes=FALSE,
xlim=c(-.2,.6) , col="red")
par(new=TRUE)
plot.stepfun(c_rtn,col.vert="gray20", main = "empirical
survival curve c_rtn of Laplace distribution " , xlim=c(-.2,.6)
, col="blue" );
######--------------- Cauchy Distribution ---------- #########
x=seq(-15,15,length=200);
x1=seq(-0.2,0.2,length=200);
gama=0.75;
x0=0;
yc=dcauchy(x,location=x0, scale=gama, log=FALSE)
ydc=yc*diff(h1$mids[1:2])*length(c_rtn)*20;
plot.stepfun(ydc, col.vert = "gray20", main = "empirical
survival curve c_rtn of Cauchy distribution " , axes=FALSE,
xlim=c(-.2,.6) , col="red")
par(new=TRUE)
plot.stepfun(c_rtn,col.vert="gray20", main = "empirical
survival curve c_rtn of Cauchy distribution " , xlim=c(-.2,.6) ,
col="blue");
########---------- Mixture of two normal distribution
-------------########
x=seq(min(c_rtn),max(c_rtn),length=200)
ydmnorm=0.9*dnorm(x,mean=0, sd=0.012) + 0.1*dnorm(x,mean=0,
sd=0.009)
plot.stepfun(ydmnorm, col.vert = "gray20", main =
"empirical survival curve c_rtn of Mixture of normal
distribution " , axes=FALSE, xlim=c(-.2,.6) , col="red")
par(new=TRUE)
plot.stepfun(c_rtn,col.vert="gray20", main = "empirical
survival curve c_rtn of Mixture of Normal distribution " ,
xlim=c(-.2,.6) , col="blue");
######------------- Mixture of two Cauchy Distribution -------------
########
x=seq(-15,15,length=200);
x1=seq(-0.2,0.2,length=200);
ymc=0.9*dcauchy(x,location=0, scale=0.75, log=FALSE) +
0.1*dcauchy(x,location=0, scale=0.9, log=FALSE)
ydmc=ymc*diff(h1$mids[1:2])*length(c_rtn)*20;
plot.stepfun(ydmc, col.vert = "gray20", main = "empirical
survival curve c_rtn of Mixture of cauchy distribution " ,
axes=FALSE, xlim=c(-.2,.6) , col="red")
par(new=TRUE)
plot.stepfun(c_rtn,col.vert="gray20", main = "empirical
survival curve c_rtn of Mixture of cauchy distribution " ,
xlim=c(-.2,.6) , col="blue");
########## Labels and legends ###################
#labels=c("normal = p", "student t = l",
"laplace = b", "cauchy = o", "Mixture of
normal = s", "Mixture of cauchy = S")
#legend("topright", inset=.05, title="Distributions",
labels, lwd=2, lty=c(1,1,1,1,2))
}
Q c >>>>>>>>
Code for SP_rtn
qcsp=function()
{
####### --------- Lybraries ------------#####
library("MASS");
require(graphics)
data_set=read.table("d-csp0108.txt",header=TRUE);
date=data_set[1];
C=data_set[2];
SP=data_set[3];
mean_C=mean(C);
mean_SP=mean(SP);
var_C=var(C);
var_SP=var(SP);
c_rtn=t(C);
sp_rtn=t(SP);
# 4 figures arranged in 2 rows and 2 columns
#attach(mtcars)
par(mfrow=c(3,3))
#x=seq(-10,10,length=1000);
#x=seq(min(sp_rtn), max(sp_rtn), length=length(sp_rtn))
h1=hist(sp_rtn, breaks=400, col="red", xlab="sp_rtn",
freq=FALSE, xlim=c(-0.1,0.1), ylim=c(0,80))
###---------- Normal Plot- ------------####
x=seq(min(sp_rtn),max(sp_rtn),length=200)
ydnorm=dnorm(x, mean=0, sd=0.0065);
plot.stepfun(ydnorm, col.vert = "gray20", main =
"empirical survival curve SP_rtn of Normal distribution ",
axes=FALSE, xlim=c(-.2,.6) , col="red")
par(new=TRUE)
plot.stepfun(sp_rtn,col.vert="gray20" , main = "empirical
survival curve SP_rtn of Normal distribution " , xlim=c(-.2,.6),
col="blue");
###--------student T plot ------------#######
x=seq(-15,15,length=200);
x1=seq(-0.1,0.1,length=200);
yt=dt(x, 200000);
ydt=yt*diff(h1$mids[1:2])*length(c_rtn)*160;
plot.stepfun(ydt, col.vert = "gray20", main = "empirical
survival curve sp_rtn of Student t distribution " , axes=FALSE,
xlim=c(-.2,.6), col="red")
par(new=TRUE)
plot.stepfun(sp_rtn,col.vert="gray20", main = "empirical
survival curve sp_rtn of Student i distribution " ,
xlim=c(-.2,.6) , col="blue");
#####---------------- Double exponential or Laplace plot
----------##########
#ylap=dlaplace(x,location=0,scale=1)
b=1;
mu=0;
ylap=(1/(2*b))*(exp(-abs(x-mu)/b))
ylap=ylap*diff(h1$mids[1:2])*length(c_rtn)*135;
plot.stepfun(ylap, col.vert = "gray20", main = "empirical
survival curve sp_rtn of Laplace distribution " , axes=FALSE,
xlim=c(-.2,.6) , col="red")
par(new=TRUE)
plot.stepfun(sp_rtn,col.vert="gray20", main = "empirical
survival curve sp_rtn of Laplace distribution " , xlim=c(-.2,.6)
, col="blue" );
######--------------- Cauchy Distribution ---------- #########
x=seq(-15,15,length=200);
x1=seq(-0.1,0.1,length=200);
gama=0.75;
x0=0;
yc=dcauchy(x,location=x0, scale=gama, log=FALSE)
ydc=yc*diff(h1$mids[1:2])*length(c_rtn)*150;
plot.stepfun(ydc, col.vert = "gray20", main = "empirical
survival curve sp_rtn of Cauchy distribution " , axes=FALSE,
xlim=c(-.2,.6) , col="red")
par(new=TRUE)
plot.stepfun(sp_rtn,col.vert="gray20", main = "empirical
survival curve sp_rtn of Cauchy distribution " , xlim=c(-.2,.6)
, col="blue");
########---------- Mixture of two normal distribution
-------------########
x=seq(min(sp_rtn),max(sp_rtn),length=200)
ydmnorm=0.9*dnorm(x,mean=0, sd=0.0061) + 0.1*dnorm(x,mean=0,
sd=0.0099)
plot.stepfun(ydmnorm, col.vert = "gray20", main =
"empirical survival curve sp_rtn of Mixture of normal
distribution " , axes=FALSE, xlim=c(-.2,.6) , col="red")
par(new=TRUE)
plot.stepfun(sp_rtn,col.vert="gray20", main = "empirical
survival curve sp_rtn of Mixture of Normal distribution " ,
xlim=c(-.2,.6) , col="blue");
######------------- Mixture of two Cauchy Distribution -------------
########
x=seq(-15,15,length=200);
x1=seq(-0.1,0.1,length=200);
ymc=0.9*dcauchy(x,location=0, scale=0.75, log=FALSE) +
0.1*dcauchy(x,location=0, scale=0.9, log=FALSE)
ydmc=ymc*diff(h1$mids[1:2])*length(c_rtn)*150;
plot.stepfun(ydmc, col.vert = "gray20", main = "empirical
survival curve sp_rtn of Mixture of cauchy distribution " ,
axes=FALSE, xlim=c(-.2,.6) , col="red")
par(new=TRUE)
plot.stepfun(sp_rtn,col.vert="gray20", main = "empirical
survival curve sp_rtn of Mixture of cauchy distribution " ,
xlim=c(-.2,.6) , col="blue");
########## Labels and legends ###################
#labels=c("normal = p", "student t = l",
"laplace = b", "cauchy = o", "Mixture of
normal = s", "Mixture of cauchy = S")
#legend("topright", inset=.05, title="Distributions",
labels, lwd=2, lty=c(1,1,1,1,2))
}
********* End ********
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