1. ## Finding P(X-Y=0)

Hi,

I have several distributions which I want to compare. They include the Burr distribution, Johnson SB, logistic and a few others. They are all independent. And the range for all data is between 0 and 20

I want to find the probability that the difference in the distributions is 0. What is the best way to go about doing this? I realise I have to double integrate the functions but am not sure how to get the probability for the difference distribution.

Hope this is clear. Thanks

2. ## Re: Finding P(X-Y=0)

Technically speaking if are independent continuous random variables, then

And it holds even when have the identical distribution.

There are some measures for the differences between distributions. See e.g.

http://en.wikipedia.org/wiki/Divergence_(statistics)

3. ## Re: Finding P(X-Y=0)

Originally Posted by BGM
Technically speaking if are independent continuous random variables, then

And it holds even when have the identical distribution.

There are some measures for the differences between distributions. See e.g.

http://en.wikipedia.org/wiki/Divergence_(statistics)
Thanks very much for your response.

Just to clarify, all the scores lie between 0 and 20. So we integrate f(X) over 0 to 20 but what do we integrate f(Y) over? I don't understand how Pr(X-Y=0) = 0 when Pr(X-Y=0) is what we want to find. How do we then go about the case where Pr(X>=Y)?

To give you some background I am looking a competitor scores in a game. I have mapped each competitors data to some distribution and want to find the probability of competitor A having a greater score than competitor B.

How do we go about the case if there are three competitors competing at once? ie: Pr(X>=Y, X>=Z), X has a greater score than both Y and Z.