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I have to get an integral in a previous post Help on an integral.. Some guru gave me hints of how to approximate its value, but I need approximation with largely varying $a$ and $b$.

I realized that it's indeed about a random variable with CDF of $$F(x) = (1-e^{-\frac{x}{2}})^b$$

So my question, is there any known random distribution have a similar CDF as above?

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could you maybe give a bit of an insight into where it arises? It resembles some modified exponential decay functions. –  Alex Jun 18 '13 at 13:54
    
In fact, the CDF $F(x)$ is CDF of the maximum of $b$ exponential distributed random variables. –  parfois Jun 19 '13 at 0:47
    
Did you try this list? en.wikipedia.org/wiki/… –  Alex Jun 19 '13 at 2:31
    
thanks, Alex, Weibull is somewhat similar to my CDF. But when used for this integration, the error is still large. –  parfois Jun 19 '13 at 5:31
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