0
$\begingroup$

I understand that the p.d.f of order statistics for Independent Non-Identical Distributions are given by the Bapat-Beg theorem as previously explained in another question. As explained in the article, the formula quickly becomes an intractable expression as the number of statistics goes up. I was wondering if the expression simplifies a little bit for the ordered cumulative distribution function. In particular what would it be for the number of non-identical distributions $n=3$ and the order statistics is the middle value $k=2.$

$\endgroup$
1
$\begingroup$

It seems the correct formula is the following (the three cumulative probability distributions are named $c_1, c_2,\text{ and } c_3$).

$$C_\text{order 2} = c_1 c_2 + c_1 c_3 + c_2 c_3 -2 c_1 c_2 c_3$$

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.