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... 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?

[hmhuang]

Any ideas?

[Torsten]

What do you think is a free parameter for the uniform distribution that can be fitted ?

[hmhuang]

@Torsten min(data) and max(data)?

[Torsten]

They are not free, they are known.

Answer 1

[John D'Errico]

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))

Answer 2

[Jeff Miller]

histogram(data, numBars);
avgHeight = numel(data)/numBars;
hold on;
plot([min(data), max(data)],[avgHeight, avgHeight])

[Image Analyst]

This one seems to answer the question best to me. You wanted to know what a histogram would look like it it were uniform - perfectly flat, and this will do that.

[Torsten]

The accepted answer is also correct since the y-axis is scaled by 1e-3.

[Image Analyst]

Yes, the blue bars are from a limited number of points drawn from a random, uniform distribution, and the thin orange line in John's plot is the height the bars would be at if the sample distribution was perfectly flat, like if you had no randomness and an infinite number of points.

[Jeff Miller]

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.

Answer 3

[Walter Roberson]

https://www.mathworks.com/help/stats/prctile.html

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.