Thread: Joint distributions for Order Statistics

1. Joint distributions for Order Statistics

I have a problem with part b of this question. I found the joint distribution and seem to have problem integrating it. I seem to have gotten a double integral that I cannot integrate. It appears I need part b for part c and d of this question.

So any help with the integration would be appreciated.

Thanks.

2. Re: Joint distributions for Order Statistics

When you're about to integrate, be careful how you set the values which you are going to integrate over. E.g. order statistic j goes from order statistic i to 1.

3. Re: Joint distributions for Order Statistics

can someone give me a hint on evaluating the integral. I tried converting factorials to gamma functions and can't seem to do anything either.

4. Re: Joint distributions for Order Statistics

As what Englund mentioned, when you obtain the joint pdf in part a) you should be aware and state the support accordingly:

as

http://en.wikipedia.org/wiki/Order_s...m_distribution

Do you mean you want to verify the normalizing constant ,
i.e. the usual identity for a joint pdf

This one will not be hard; you can try the substitution in the inner integral and you should figure out the beta integral.

For part b) you just need to apply this identity again to evaluate the cross moments

5. The Following User Says Thank You to BGM For This Useful Post:

bk123 (04-28-2013)

6. Re: Joint distributions for Order Statistics

Thanks. It came out very easily.

7. Re: Joint distributions for Order Statistics

Can someone give me a hint on part ii? I tried using the same substitution on the integral, but it doesn't seem to fall out as expected.

8. Re: Joint distributions for Order Statistics

f(yi|yj)=f(yi, yj)/f(yj)

9. Re: Joint distributions for Order Statistics

@BGM can you please make it more specific for the inner integral part. thx

10. Re: Joint distributions for Order Statistics

Sorry can you ask your question again, more precisely? Not exactly sure which part is not clear.

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