I'm definitely doing the exponential distribution wrong, am I?

N = 1e4;

a=0; b=1;

x = a+(b-a)*rand([N,1]);

lambda = 1;

Y = -log(x)/lambda;

figure(1); clf

histogram(x,20,'Normalization','pdf');

hold on;

histogram(Y,20,'Normalization' , 'pdf')

hold off

xlabel('random variable $x$','Interpreter','latex','FontSize',20)

ylabel('Probability density','Interpreter','latex','FontSize',20)

title('Continuous uniform PDF','Interpreter','latex','FontSize',20)

[Kevin Nelson]

I'm trying to superimpose an exponential distribution to a uniform distribution, and it's not coming out right. Why? I was told I can transform from uniform to exponential by using the equation Y = − ln X/λ. Am I doing it wrong?

Answer 1

[VBBV]

N = 1e4;
a=0; b=1;
x = (a+(b-a)*rand([N,1]));
lambda = 11;   % try with different lambda values 
Y = -log(x)/lambda;
figure(1); clf
histogram(x,20,'Normalization','pdf');
hold on;
histogram(Y,20,'Normalization' , 'pdf')
hold off
xlabel('random variable $x$','Interpreter','latex','FontSize',20)
ylabel('Probability density','Interpreter','latex','FontSize',20)
title('Continuous uniform PDF','Interpreter','latex','FontSize',20)

[VBBV]

try with different lambda values

[Kevin Nelson]

Is that how it's supposed to look? Looks odd. I tried 10 and got something similar but it looked odd to me

[VBBV]

yes, it looks correct. A continuous uniform distribution looks flatter compared to exponential one, Refer or search any literature for further info

[Kevin Nelson]

okay thank you very much

[VBBV]

Please accept the answer if it worked for you

Answer 2

[Chunru]

% if X is uniform on [0,1] then −loge(X) follows an exponential distribution with parameter 1

N = 1e5;
a=0; b=1;
x = a+(b-a)*rand([N,1]);
lambda = 1;
Y = -log(x)/lambda;
figure(1); clf

histogram(x,100,'Normalization','pdf');
hold on;
histogram(Y,100,'Normalization' , 'pdf')

xx = 0:0.1:10;
plot(xx, pdf('Uniform', xx, 0, 1), 'r--', 'Linewidth', 2);
plot(xx, pdf('Exponential', xx, 1), 'b--', 'Linewidth', 2);

xlim([0 10])
hold off
xlabel('random variable $x$','Interpreter','latex','FontSize',20)
ylabel('Probability density','Interpreter','latex','FontSize',20)
title('Continuous uniform PDF','Interpreter','latex','FontSize',20)
legend('Hist-unif', 'Hist-exp', 'Unif', 'Exp')

[Kevin Nelson]

I'm confused. Are you saying my code is right? Because it initially came out to something similar with 20 bins as opposed to your 100 bins

[Chunru]

Yes. Your code is correct. I just change the number of samples and bin number to make the hist closer to the ideal pdf.

[Kevin Nelson]

Okay, thank you very much