# How to fit an uniform distribution to a histogram?

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hmhuang on 12 Jan 2022
Commented: Jeff Miller on 15 Jan 2022
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... As a workaround, I would like to do it manually but I have no ideas. 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?
Torsten on 13 Jan 2022
They are not free, they are known.

John D'Errico on 13 Jan 2022
If you have histfit, then you would also have unifit.
data = unifrnd(-100,100,1000,1);
[AHAT,BHAT,ACI,BCI] = unifit(data)
AHAT = -99.8483
BHAT = 99.9082
ACI = 2×1
-100.4476 -99.8483
BCI = 2×1
99.9082 100.5076
histogram(data,'norm','pdf')
hold on
fplot(@(x) unifpdf(x,AHAT,BHAT))

Jeff Miller on 12 Jan 2022
histogram(data, numBars);
avgHeight = numel(data)/numBars;
hold on;
plot([min(data), max(data)],[avgHeight, avgHeight])
Jeff Miller on 15 Jan 2022
Apparently the OP wanted the histogram's y-axis scaled in terms of in terms of probability density, as in John's answer, rather than in terms of counts, as in the original posted figure.

Walter Roberson on 12 Jan 2022
Calculate the 98th prctile of the counts; that corresponds to 2 standard deviations. Min and max of the x gives you the other bounds. You might also want to mark the mean of the counts.
If you record the handle returned by histogram() then the counts is the BinCounts property of the handle.