How to find PDF, CDF and the probability at a certain point from histogram ?

Suppose that I have an array of random numbers, e.g.

X=randn(1,1000);
hist(X,100);

Using the histogram ,I want to find and plot the PDF and CDF of X, and for a constant value a, I also want to find the probabilities P(X=a) and P(X<=a).

Any help would be appreciated. Thank you.

Answer 1

[Image Analyst]

Is this homework? Hint: just take the counts return argument from hist() and normalize the counts array by the total number of counts. Then get cdf by using cumsum() on the normalized counts.

[may]

No it is not a homework. Thanks.

[may]

Is the following correct?

%for PDF 
a=hist(X,100);
plot(a./sum(a));

%for CDF 
plot(cumsum(a./sum(a)))

but how can I use the same X-axis values?

[Image Analyst]

Looks pretty close to me. This is how I'd do it.

[counts, binCenters] = hist(X, 100);
pdf = counts ./ sum(counts(:));
cdf = cumsum(pdf);
subplot(1,2,1);
plot(binCenters, pdf, 'b-', 'LineWidth', 3);
title('PDF', 'FontSize', 25);
xlabel('X Value', 'FontSize', 25);
yxlabel('PDF Percentage', 'FontSize', 25);
grid on;
subplot(1,2,2);
plot(binCenters, cdf, 'r-', 'LineWidth', 3);
title('CDF', 'FontSize', 25);
xlabel('X Value', 'FontSize', 25);
yxlabel('CDF Percentage', 'FontSize', 25);
grid on;

[may]

Thanks a lot. just a question; let say I want to know the probability P(X=1.2) or P(X<1.2), how can I find these probabilities?

[Image Analyst]

P(X=1.2) = 0 because chances are it will never be exactly 1.2

P(X<1.2) = cdf(1.2) so you need to find the index that corresponds to 1.2

index = find(binCenters<1.2, 1, 'last');
p = cdf(index);

[may]

thanks a lot!

[may]

just a question; when I change the number of bins in hist function, I get different PDF's, the shape is the same but the numbers on Y axis are different! any help would be appreciated.