matlabhistogramuniform-distribution

How to fit an uniform distribution to a histogram?

I have a set of data that is generated from an uniform distribution. Now I want to fit the corresponding histogram to an uniform distribution, such that there is a 'ㄇ' shape of line plotted on that histogram. I tried to fit it by using the MATLAB built-in function histfit, but there is no such an option of uniform distribution for histfit. How can I do it?

data = unifrnd(-100,100,1000,1);

%% MATLAB built-in function: 'histfit'
figure(1);
hh = histfit(data); % No options for 'histfit' to fit data to an uniform distribution

%% Manually fitting a histogram to an uniform distribution
figure(2);
numBars = length(hh(1).XData);
histogram(data, numBars);
% TODO: How to do next to plot a line that fits the data to an uniform distribution?
Solution

  • Since a uniform distribution is just 1/(b-a) for a region [a, b), you can define a function that calculates this

    x = -200:200;
y = unifdist(x, -100, 100);

figure;
plot(x, y)

function ret = unifdist(x, a, b)
  ret = ones(length(x), 1)/(b-a);
  ret(x < a | x >= b) = 0;
end

    There's probably a much simpler and faster way to do this, but it works.