how to normalize histogram

Question

I ma creating the exponential distribution using inverse method. I want to normalize histogram. How can I do it?

This is my code

N=100;
Lambda=2;
r=rand(N,1);
X=-log(1-r)/Lambda;
hist(X), colormap(bone);

t = 0:0.01:5;
pdf=Lambda*exp(-Lambda*t);
hold on, plot(t,pdf,'LineWidth',2)

Answer 1

The histogram should be normalized to unit area so that it can be compared with the theoretical pdf. To normalize to unit area you need to divide by the number of samples and by the bin width:

N = 100;
Lambda=2;
r = rand(N,1);
X = -log(1-r)/Lambda;
[hy, hx] = hist(X); %/ get histogram values
hy = hy/numel(X)/(hx(2)-hx(1)); %//normalize histogram
bar(hx, hy) %// plot histogram
t = 0:0.01:5;
pdf = Lambda*exp(-Lambda*t);
hold on, plot(t,pdf,'LineWidth',2) %// plot pdf

Or use the new histogram function (introduced in R2014b), which automatically normalizes according to the specified normalization option:

N = 100;
Lambda=2;
r = rand(N,1);
X = -log(1-r)/Lambda;
histogram(X, 'Normalization', 'pdf') %// plot normalized histogram
t = 0:0.01:5;
pdf = Lambda*exp(-Lambda*t);
hold on, plot(t,pdf,'LineWidth',2) %// plot pdf