This is a program to generate samples from a bivariate distribution defined only by the conditional distributions:

f1(x | y)=(1-y)-1

f2(y | x)=(3y2)/x3

where 0<y<x<1

Using Gibbs sampling, we sample repeatedly from the conditional distributions. At each iteration, one component is chosen at random for updating. f1 is sampled directly as a UNIF(y,1) random variable, and f2 is sampled using rejection sampling with 3*UNIF(0,x) as the enveloping function

You can specify the desired number of bivariate samples, and starting values for X and Y satisfying


If you submit invalid values, or leave the boxes blank, the program will choose the default sample size of 100 and randomly generate valid starting values for X and Y.

Please input desired sample size and starting values for X and Y:
Desired sample size:
Initial X:
Initial Y:

Here are the results:
Generated samples of (x, y):

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