MATLAB: Probability distribution

distributionprobabilityreturns

Hi there, I have a series of 1277 daily returns on a asset. I want to see what distribution these returns follow (Eg, Levy, Normal). Does anybody know how I can show which distribution it is??

I look forward to a reply.

Best Answer

If you have a univariate data then you can test it for normality using Anderson-Daarling test [1] or Kolmogorv-Smirnov test [2].

[1] http://www.mathworks.com/matlabcentral/fileexchange/14807-andartest ... you will have to modify the code slightly to get the p-value

[2] implemented as 'kstest' function in Statistics Toolbox

Unfortunately, I am not familiar with other tests to see if the data was drawn from other types of distributions ...

Related Solutions

MATLAB: Evaluate a distribution programmatically

The fitdist (link) function will fit a distribution to data, producing a probability distribution object:

pd = fitdist(x,distname)

You can then calculate the probabilities with it using the Plot Standard Normal Distribution cdf (link) or Plot the pdf of a Standard Normal Distribution (link) functions:

data = 5 + 2*randn(1, 100);                         % Create Data
pd = fitdist(data(:), 'Normal');
x = linspace(-2, 12);
Npdf = pdf(pd, x);
Ncdf = cdf(pd, x);
figure
plot(x, Npdf,   x, Ncdf)
grid

MATLAB: Question about Anderson-Darling (adtest)

Not using adtest. Like the Ford Model T, which Henry Ford sold in any color as long as the color you wanted was black, adtest tests to see if your distriution is any distribution, as long as normal is the distribution you want to test against.

Instead, you probably want to use a Kolmogorov-Smirnov test.

http://www.mit.edu/~6.s085/notes/lecture5.pdf

From the help for kstest2:

kstest2 Two-sample Kolmogorov-Smirnov goodness-of-fit hypothesis test.
    H = kstest2(X1,X2) performs a Kolmogorov-Smirnov (K-S) test 
    to determine if independent random samples, X1 and X2, are drawn from 
    the same underlying continuous population.

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MATLAB: Evaluate a distribution programmatically

MATLAB: Question about Anderson-Darling (adtest)

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