R help - Dec 2003 - distribution of second order statistic

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.

The order statistics have a beta distribution, so pbeta is all you need.

On Mon, 15 Dec 2003, Eugene Salinas (R) wrote:
> 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?????
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
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