How to calculate real probability of data

Hello, I have a slight question which maybe really simple but am getting stack somehow. Suppose we have a measured data say A=5*rand(1000,1). Suppose am to find the probability distribution of the data, I assume I would easily do this via histogram plot as the one inserted below. Which woul give probabilty distribution of the data in an histogram plot. My question is, is there a way I can get the probability values in a matrix of the same dimenions as A. I mean the vallues that were used to plot the histogram, is there a way I can extract this information?

histogram(A,'Normalization','probability')

Answer 1

[Paul]

"is there a way I can get the probability values in a matrix of the same dimenions as A."

The number of bins in the histogram will always, or very nearly always, be less than number of elements in A. So I don't think this will be possible.

"I mean the vallues that were used to plot the histogram, is there a way I can extract this information?"

histogram returns an object from which the properties of the the histogram can be obtained via dot indexing:

rng(100);
A = 5*rand(1000,1);
h = histogram(A,'Normalization','probability');

h.Values  % values of the bin heights

ans = 1×10

0.0980 0.1010 0.1060 0.0940 0.1000 0.1160 0.0920 0.0980 0.0930 0.1020

If the elements of A are supposed to be samples from a continuous distribution, then it may be better to use the pdf normalization of histogram. I guess it depends on how the histogram is going to be used.

Answer 2

[Torsten]

Usually, one assumes that the underlying distribution for the realizations in A is continuous. This implies that each element in A has probability 0. You could extract probabilities for an element to be in a certain interval, e.g. In the following example, if you take as interval [x(i),x(i+1)], then the probability that the random variable gets a value within this interval is approximately f(i+1)-f(i).

A = 5*rand(1000,1);
[f,x] = ecdf(A);
plot(x,f)