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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