[R] distribution of second order statistic

Eugene Salinas (R) r-eugenesalinas at comcast.net
Mon Dec 15 18:51:41 CET 2003


Hi,

I am getting some weird results here and I think I am missing something. 
I am trying to program a function that for a set of random variables 
drawn from uniform distributions plots that distribution of the second 
order statistic of the ordered variables. (ie I have n uniform 
distributions on [0, w_i] for w_i different w_j and i=1..n. I want to 
plot the distribution of the second order statistic ie one less the 
maximum.

I thought that the way to do this is to calculate:
F=  Sum over i { (1-Fi) * Product of all j different i of Fj} + Product 
over all i of Fi

where Fi are just the respective uniform cdf for variable i.

The problem is that when I do this and plot F over the range from 0 to 
the highest of the w_i I don't get a cdf but something that slopes down 
at some point again. What is going on?????

Any help is greately appreciated....

Thanks, eugene.




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