CODEWITHSUNDEEP
matlabdistributionmodel-fitting
Tao Liu
Tao Liu

Reputation: 35

uniform distribution fitting in matlab

I have a data set and would like to fit them to uniform distribution and calculate goodness of fit with Matlab. However, I found that uniform is not included in function 'fitdist'. Is there any method to do uniform distribution fitting in Matlab?

Upvotes: 2

Views: 6310

Answers (4)

Rafnuss
Rafnuss

Reputation: 119

Just to expand of Alan answer, to know how to properly used Pearson's chi-squared test

Setting Parameters

N=100; % sample size
a=0; % lower boundary
b=1; % higher boundary

Sample N uniformly distributed values between a and b. And in the second line add some bais to make it not uniform if you want to test the code.

x=unifrnd(a,b,N,1);
%x(x<.9) = rand(sum(x<.9),1);

Using chi2gof

As described here, with chi2gof, you can't use the 'cdf of the hypothesized distribution' and need to specified the bins, the edges and the expected values.

nbins = 10; % number of bin
edges = linspace(a,b,nbins+1); % edges of the bins
E = N/nbins*ones(nbins,1); % expected value (equal for uniform dist)

[h,p,stats] = chi2gof(x,'Expected',E,'Edges',edges)

Using chi2cdf

With this function you need to supply the chi-squared test statistic, $\displaystyle \chi ^{2}$ which can be computed with the function histogramm:

h = histogram(x,edges);
chi = sum((h.Values - N/nbins).^2 / (N/nbins));
k = nbins-1; % degree of freedom
chi2cdf(chi, k)

Note, that if you don't use the edges to compute the number of value per bins, histogramm will choose them from the lower value to the highest and therefore the final score will be different than with chi2gof

At the end, you want to use the p value to answer the question "Can I safely reject the null hypothesis (i.e. x is not a coming from a uniform distribution) ? ". Yes, you can safely say that x is not coming from a uniform distribution if p is lower than a significant level (alpha).

Upvotes: 0

Peter Pallesen
Peter Pallesen

Reputation: 21

Transform your variable to a normal distributed variable and use "kstest". So if you have a variable X that is uniform from a to b make the following code

X_uni=(X-a)/(b-a); %Uniform 0,1 variable

X_norm=norminv(X_uni); % transform to normal distributed variable
[h,P]=kstest(X_norm) ; %P is the test statistic

Upvotes: 2

Alan
Alan

Reputation: 3417

Further to Colin's answer, goodness of fit for uniform distribution can be calculated using a Pearson's chi-squared test.

If you have access to the Matlab stats toolbox you can perform this fairly simply by using the chi2gof function. Example 3 in the documentation shows how to apply it to a uniform distribution.

Upvotes: 2

Colin T Bowers
Colin T Bowers

Reputation: 18560

When you say you would like to fit the dataset to the uniform, I'm assuming that what you mean is that you would like to estimate the parameters of a uniform distribution that best fit your dataset.

This is actually quite an interesting question. I'm not surprised that fitdist was no help as the uniform distribution is a bit of a special case. For example, it can be shown that under some circumstances, the maximum likelihood estimate of the parameters of a uniform distribution does not exist, and under other circumstances, has no unique solution.

So, what to do? Well, a uniform distribution has two parameters, a and b, which define the lower and upper bound of the density. Let X denote your dataset (say, a column vector of observations). A naive estimator of a and b is:

a = min(X);
b = max(X);

Of course these estimates will over-estimate (for a) and under-estimate (for b) the true parameters almost surely, since it is unlikely that a random sample drawn from the density will fall right on the boundary.

For the case where it is known that a is 0, the minimum variance unbiased estimator of b is:

b = max(X) + (max(X) / length(X))

This estimator is related to the famous German Tank Problem. For the general case, I don't actually know any estimation theory (although I'm sure there must be some). My first guess would be to use the naive min/max estimator, but subtract and add the average distance between the observations in your dataset, ie:

a = min(X) - c;
b = max(X) + c;

where

c = (max(X) - min(X)) / length(X)

As for goodness-of-fit, hopefully someone else on SO knows something, as I'd need to do a fair bit of research myself to answer that. Good Luck!

Upvotes: 6

Related Questions