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

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Kevin Nelson
Kevin Nelson el 20 de Sept. de 2022
Comentada: VBBV el 24 de Oct. de 2022
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)
  1 comentario
Kevin Nelson
Kevin Nelson el 20 de Sept. de 2022
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?

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Respuestas (2)

VBBV
VBBV el 20 de Sept. de 2022
Editada: VBBV el 20 de Sept. de 2022
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)
  5 comentarios
Kevin Nelson
Kevin Nelson el 20 de Sept. de 2022
okay thank you very much
VBBV
VBBV el 24 de Oct. de 2022
Please accept the answer if it worked for you

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Chunru
Chunru el 20 de Sept. de 2022
% 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')
  3 comentarios
Chunru
Chunru el 20 de Sept. de 2022
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
Kevin Nelson el 20 de Sept. de 2022
Okay, thank you very much

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