Math Is Fun Forum

alioumpa

Member

Registered: 2007-07-17

Posts: 3

ORDER Statistics (extremely difficult problem)

Hi all,

I would appreciate any help regarding the following problem:

Consider the ordered random variables (R.Vs) x1 > x2 >, ...> xn. Each R.V is distributed according to the probability density function (pdf) f(x).
The question is: What is the probability that a*min[ x1, x2,..., xn] > x1 + x2 +...+ xn ?, where a is a real number greater than 1.

Sakes

Last edited by alioumpa (2007-07-17 02:57:40)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: ORDER Statistics (extremely difficult problem)

When you say min[ , , ,], what does this mean in probability?
Also, what is your f(x), is it a normal curve.  I don't understand.

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igloo myrtilles fourmis

alioumpa

Member

Registered: 2007-07-17

Posts: 3

Re: ORDER Statistics (extremely difficult problem)

Thanks for your reply!

The problem is the calculation of the probability that

a*min[ x1, x2,..., xn] > x1 + x2 +...+ xn.

If we consider the RV g=min[ x1, x2,..., xn], then its pdf will be 

f_g(g)=n* f(g) (  1-F(g) )^(n-1)

and its cdf

F_g(g)=1- ( 1-F(g) )^n

where f(x) and F(x) are the pdf and cdf of the RV x1, x2,..., xn.

Also, assume that f(x) is the pdf of the normal distribution.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: ORDER Statistics (extremely difficult problem)

I will start reading on this subject, but I'm way behind you, so anything you wish to post to educate me would be appreciated, time permitting.  My first question is, is how complicated is it to integrate a pdf to create a cumulative cdf?

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igloo myrtilles fourmis

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: ORDER Statistics (extremely difficult problem)

It's like tossing n dices, and to get the chance of getting the sum of dice values
less than a(sounding ei) times of the least dice value.

But it's so hard !!!!!!!!!

Last edited by George,Y (2007-07-23 20:21:58)

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X'(y-Xβ)=0

alioumpa

Member

Registered: 2007-07-17

Posts: 3

Re: ORDER Statistics (extremely difficult problem)

After searching the net I found out that a solution to the problem is involved in the paper "Unified Analysis of Generalized Selection Combining with Normalized Threshold Test Per Branch", which deals with a telecommunication problem.
And it's not easy!!

Thanks for your replies!