How to estimate probabilities of an arbitrary range, based on the probability distribution of a given a data set of numbers?
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Clarisha Nijman
on 22 Oct 2018
Commented: Clarisha Nijman
on 23 Oct 2018
Hello,
Given a series of values x, I want to estimate the probabilities of a range of numbers U, in(using) the probability distribution of the given series x. My code works for one value, but I need probabilities of a range, Can somebody give me some feedback please?
Thank you in advance.
This is the code:
%%Generate some data/series
x=randi([-2 50],25,1);
%Values/ranges of interest
U=[-100:100];
%define histogram and probability distribution of x
h = histogram(x);
h.Normalization = 'probability';%Changing count in probabilities
h.Values(U); %finding probabilities of range U
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Accepted Answer
Bruno Luong
on 22 Oct 2018
Edited: Bruno Luong
on 22 Oct 2018
Use HISTCOUNTS then
N = histcounts(x, [-Inf, U, Inf]);
P = N(2:end) / sum(N)
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More Answers (2)
Torsten
on 22 Oct 2018
%%Generate some data/series
X=randi([-2 50],25,1);
%Values/ranges of interest
U=[-100:100];
X = sort(X)
[countsX, binsX] = hist(X)
cdfX = cumsum(countsX) / sum(countsX)
extrap_left = (min(U) > max(X));
extrap_right = (max(U) > max(X));
p_U_left = interp1(binsX,cdfX,min(U),'linear',extrap_left)
p_U_right = interp1(binsX,cdfX,max(U),'linear',extrap_right)
p_U = p_U_right - p_U_left
4 Comments
Torsten
on 22 Oct 2018
Edited: Torsten
on 22 Oct 2018
If you get discrete values from a random variable, say [ 1 2 4 5 6 ], how should it be possible to tell p({3}) ? (Hint: It's impossible).
In my opinion, the most reasonable estimate would be p=0 since it does not appear in the list.
If you know the distribution the values stem from, you can get a Maximum Likelihood Estimate (MLE) of the parameters describing the distribution. Having calculated these parameters, you can give estimates of probabilities for elements of your choice.
Bruno Luong
on 22 Oct 2018
Edited: Bruno Luong
on 22 Oct 2018
not sure, is it what you want?
x=randi([-2 50],10000,1);
U=[-100:100];
h = histogram(x, U);
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