Does MatLab have any built in function to evaluate the density of a random variable from a custom histogram? (I suspect there are probably lots of ways to do this, I am just looking to see if there is already any builtin MatLab functionality). Thanks.

Answer:

The function `hist`

gives you an approximation of the probability density you are evaluating.

If you want a continuous representation of it, this article from the Matlab documentation explains how to get one using the `spline`

command from the Curve Fitting Toolbox. Basically the article explains how to make a cubic interpolation of your histogram.

The resulting code is :

```
y = randn(1,5001); % Replace y by your own dataset
[heights,centers] = hist(y);
hold on
n = length(centers);
w = centers(2)-centers(1);
t = linspace(centers(1)-w/2,centers(end)+w/2,n+1);
dt = diff(t);
Fvals = cumsum([0,heights.*dt]);
F = spline(t, [0, Fvals, 0]);
DF = fnder(F);
hold on
fnplt(DF, 'r', 2)
hold off
ylims = ylim;
ylim([0,ylims(2)]);
```

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