How to get the probability value (y) for a given (x) from a probability normalised histogram?

Hello all,

Need some help with a prediction experiment I'm trying to run. I have some live-feed values, which I take in chunks and turn into histograms with probability normalisation. I need some way of getting the probability of a given value, based on that histogram. Basically I need the invert of a quantile function. The quantile gives me what the value is, given a probability. So if you imagine the histogram as a X, Y plot, the quantile is fed an Y value and it gives the associated X, I need something that I can feed an X value, and gives me the Y (which is the probability in the histogram). I hope my explanation makes sense.

[Alexander Grantcharov]

Just to clarify... Let's suggest we have this sample data in the X array.

X=[1 1 1 2 2 3 3 3 4 4 ];
h=histogram(X,4,'Normalization','probability');

If we build a histogram for the probabilities of the entries in the array we get this histogram:

Then I want to say what is the probability of getting 2 and I want the function to result in 0.2, or might ask what is the probability of getting a 5 and the function will give me a result of 0. Mind that I don't know the distribution or want to do fitting.

Answer 1

[dpb]

If you fit a functional to the distribution, then use icdf (inverse cdf) with those parameters; if empirical only then it's a lookup to the empirical data or a fit thereof.

ADDENDUM

For that, there is a function...

[N,edges] = histcounts(X,5);   % return the edges vector for lookup later
P=N/sum(N);                    % the normalized P values per bin

fnInvP=@(x) P(discretize(x,edges));

This will need to ensure that x is within range of X, however; wrap in a try...catch block would be one way; have to decide how to handle the error case of course.

[Alexander Grantcharov]

The distribution of my live feed could be completely random, so fitting a specific distribution function will not do. Anyways, I found a workaround. It is not particularly elegant one, but it works:

X=[1 1 1 2 2 3 3 3 4 4 ];
h=histogram(X,5,'Normalization','probability');
[N,edges] = histcounts(X,5);
T_Count = sumabs(N);
All_P = N/T_Count;

CheckValue = input('Enter a value to check its probability: ');

if CheckValue > edges(1,1) && CheckValue <= edges(1,2)
   P = All_P(1,1);
elseif CheckValue > edges(1,2) && CheckValue <= edges(1,3)
   P = All_P(1,2);
elseif CheckValue > edges(1,3) && CheckValue <= edges(1,4)
   P = All_P(1,3);
elseif CheckValue > edges(1,4) && CheckValue <= edges(1,5)
   P = All_P(1,4);
elseif CheckValue > edges(1,5) && CheckValue <= edges(1,6)
   P = All_P(1,5);
else
   P = 0;
end

disp(P);

Basically I construct two arrays containing the probability values and the edges of the bins. Then I check which bin the entered value corresponds to, and then address the necessary probability that corresponds to it. If the value is outside of the scope (has not occurred) it gets a probability of 0. Choppy, but it works. Was just hoping there is a function available to do this :)

Cheers!