R help - Jan 2015 - Probability distribution of fitted gaussian distribution.

Hi,

I have a discrete set of data on the returns for 3 indices with 206 data
points. Since the number of points is less it doesnt exact look like a
gaussian distribution.

I wanted to fit the data to a gaussian distribution and have used the
fitdist function and have gotten the plots and the mean and sd estimates
for the gaussian that fits my data.

What I then want to do is to get a U=F(x) where U is the uniform variable
corresponding to the CDF function applied on the fitted theoritical CDF
curve. How can I get that?


Equivalent data that I find in matlab. Here the ksdensity gives an array of
f and xi values and I could use the f values for my usage. But I am trying
to work it out in R. The steps that I am going through in R are below. I
have also attached the input sheet that I am using for the indices. Sorry
in advance, case its a dumb one.

Estimate Density

Generate a sample data set from a mixture of two normal distributions.

rng default  % for reproducibility
x = [randn(30,1); 5+randn(30,1)];

Plot the estimated density.

[f,xi] = ksdensity(x);
figure
plot(xi,f);

Steps that I am following.

# Reading and finding the returns for 3 indices.
CDSPrices<-read.csv("CDS.csv")
 numRows=nrow(CDSPrices)
CDSReturnsN225=CDSPrices$N225[2:numRows]/CDSPrices$N225[1:numRows-1]-1
CDSReturnsSPX=CDSPrices$SPX[2:numRows]/CDSPrices$SPX[1:numRows-1]-1
CDSReturnsIBOVESPA=CDSPrices$IBOVESPA[2:numRows]/CDSPrices$IBOVESPA[1:numRows-1]-1
CDS_Returns<-cbind(CDSReturnsN225,CDSReturnsSPX,CDSReturnsIBOVESPA)

# Using fitdist to fit a gaussian distribution onto the discrete empirical
data I have.
library(fitdistrplus)
fittedNormal<-fitdist(CDS_Returns[,1],"norm")
plot(fittedNormal)

> fittedNormal[]
$estimate
        mean           sd
-0.002035951  0.028654032

$method
[1] "mle"

$sd
       mean          sd
0.001996421 0.001403953

Reference

http://cran.r-project.org/web/packages/fitdistrplus/fitdistrplus.pdf  ~
 Page 15


-- 
*Jacob Varughese*

On Jan 3, 2015, at 9:27 AM, Jacob Varughese wrote:
> Hi,
> 
> I have a discrete set of data on the returns for 3 indices with 206 data
> points. Since the number of points is less it doesnt exact look like a
> gaussian distribution.
> 
> I wanted to fit the data to a gaussian distribution and have used the
> fitdist function and have gotten the plots and the mean and sd estimates
> for the gaussian that fits my data.
> 
> What I then want to do is to get a U=F(x) where U is the uniform variable
> corresponding to the CDF function applied on the fitted theoritical CDF
> curve. How can I get that?
> 
> 
> Equivalent data that I find in matlab. Here the ksdensity gives an array of
> f and xi values and I could use the f values for my usage. But I am trying
> to work it out in R. The steps that I am going through in R are below. I
> have also attached the input sheet that I am using for the indices. Sorry
> in advance, case its a dumb one.
> 
> Estimate Density
> 
> Generate a sample data set from a mixture of two normal distributions.
> 
> rng default  % for reproducibility
> x = [randn(30,1); 5+randn(30,1)];
> 
> Plot the estimated density.
> 
> [f,xi] = ksdensity(x);
> figure
> plot(xi,f);
> 
> Steps that I am following.
> 
> # Reading and finding the returns for 3 indices.
> CDSPrices<-read.csv("CDS.csv")
> numRows=nrow(CDSPrices)
> CDSReturnsN225=CDSPrices$N225[2:numRows]/CDSPrices$N225[1:numRows-1]-1
> CDSReturnsSPX=CDSPrices$SPX[2:numRows]/CDSPrices$SPX[1:numRows-1]-1
>
CDSReturnsIBOVESPA=CDSPrices$IBOVESPA[2:numRows]/CDSPrices$IBOVESPA[1:numRows-1]-1
> CDS_Returns<-cbind(CDSReturnsN225,CDSReturnsSPX,CDSReturnsIBOVESPA)
> 
> # Using fitdist to fit a gaussian distribution onto the discrete empirical
> data I have.
> library(fitdistrplus)
> fittedNormal<-fitdist(CDS_Returns[,1],"norm")
> plot(fittedNormal)
> 
> 
>> fittedNormal[]
> $estimate
>        mean           sd
> -0.002035951  0.028654032
> 
> $method
> [1] "mle"
> 
> $sd
>       mean          sd
> 0.001996421 0.001403953
Wouldn't you get pretty much the same result from:

 list( mean=mean(CDS_Returns[,1], sd=sd(CDS_Returns[,1]) )  # ?

... since the sample mean is identical to the MLE estimate and the sample SD is
at worst only different by a factor of N/(N-1).

And for what you are calling " U=F(x) where U is the uniform variable
corresponding to the CDF function applied on the fitted theoritical CDF
curve", wouldn't that just involve the use of the `qnorm` function?

> 
> Reference
> 
> http://cran.r-project.org/web/packages/fitdistrplus/fitdistrplus.pdf  ~
> Page 15
> 
> 
> -- 
> *Jacob Varughese*
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius
Alameda, CA, USA