MATLAB: How to fit a custom probability distribution to the data

probabilityrandom number generatorstatistics

I have a set of data characterised by a high frequency (60-70%) of zero values. I think that the best probability density function to fit my data is something like f(x)=a*exp(-b*x), a two-parameters negative exponential which is not implemented in the software. What I need to do is to fit this equation to my data and generate random numbers inside that distribution. How can I do that?

Best Answer

Since the integral from 0 to Inf must be equal to 1, it follows that a = b = lambda. This is the usual exponential distribution which can be chosen for fitting:

https://de.mathworks.com/help/stats/mle.html

Best wishes

Torsten.

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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: Probability distribution

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 ...

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MATLAB: Evaluate a distribution programmatically

MATLAB: Probability distribution

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