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

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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)

### Answers (2)

VBBV
on 20 Sep 2022

Edited: VBBV
on 20 Sep 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 Comments

Chunru
on 20 Sep 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 Comments

Chunru
on 20 Sep 2022

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