Maximum of two correlated random variables

[touqeerazam]

Hi all,

I want to find maximum of two random variables which are correlated and are non gaussian too. Baiscally I need an analytical orr approximate solution to their bivaraite distribution with means and varaince of resulting distribution. There is some work by Clark 'The greatest of finite set of random variables' but that assumes gaussian correlated variables.

so if A & B are two correlated random varaibles. I need C=Max(A,B)?

one other method is to use quadratic taylor polynomial for A & B. and use Max (A,B)=(A+B+abs(A-B))/2. But I don't know can i approximate abs(A-B) by quadratic polynomial (without regression). In other words, if I can get any method to approximate abs(A-B) by analytical expression. This will also give me Max operation (what I really need).

Sorry for long question

I will be very grateful to you if anyone could figure out solution or any directions

cheers
Touqeer

 

[Pere Callahan]

Are you given the joint distribution f of Aand B? then you could try and compute the distribution of C=max(A,B) as

$$\mathbb{P}(C\leq c)=\int_{-\infty}^c{da\,\int_{-\infty}^a{db\,f(a,b)}}+\int_{-\infty}^c{db\,\int_{-\infty}^b{da\,f(a,b)}}.$$

 

[touqeerazam]

Hi,

Thanks Pere. I don't have their joint dis 'f'. Its difficult to get JPDF of correlated non gaussian variables (not sure how to get). What all I have is varaible A & B given as,

A=a0+a1x+a2x^2+a3y+a4y^2
B=b0+b1x+b2x^2+b3y+b4y^2

where x & y are two parameters which are correlated non gaussian, and I have their PDFs. ai's and bi's are just coefficients.

Can you please point out any solution?

Thanks
Touqeer