Re: [Maxima-discuss] "distrib" package

[Gunter K. <gu...@pe...>]

I'm no expert in these matters so I could be completely wrong but... ... Have you tried the integrate function instead of the combination of Laplace and ilt? 
I assume that this function knows about additional magic. It will return an ilt, though, if it cannot get farther than that.

Kind regards,

Gunter.

On 3. September 2014 20:23:19 MESZ, Henry Baker <hb...@pi...> wrote:
>Since I'm so dense, what would be the probability when the group has
>size _one_;
>i.e., choose a from the top 1% of A and choose b from the top 1% of B;
>what is
>the probability that a beats b ?
>
>BTW, I tried "laplace" and "ilt", but they didn't work.  More
>precisely, "laplace"
>seemed to work ok, but "ilt" failed miserably.
>
>I also noticed that integrate(foo(x)*unit_step(x),x,minf,inf) isn't
>smart enough
>to simplify to integrate(foo(x),x,0,inf).
>
>At 11:00 AM 9/3/2014, Robert Dodier wrote:
>>On 2014-09-03, Henry Baker <hb...@pi...> wrote:
>>
>>> On a particular Olympic sport, the abilities of any individual
>>> in a population is normally distributed.
>>>
>>> Thus, for country A, with population Ap, mean Am, variance Av,
>>> the abilities of the individuals follow a normal distribution.
>>>
>>> Clearly, each country will choose from the upper tail of the
>>> distribution -- its highest 1%, for example.
>>>
>>> What is the probability that a 1% athlete from A will beat a 1%
>>> athlete from B, given the population, mean and variance of each
>country ?
>>
>>We are looking for P(ability(A) - ability(B) > 0) where ability(A)
>>and ability(B) are Gaussian tail distributions. That is, not the
>>entire bump (i.e. national population) but just the 1% who
>>are sent to the games. I think Maxima can figure out the density of
>>ability(A) - ability(B) exactly, but one must be careful with the
>>limits of integration in the convolution since we are working with
>>just the tails. Note sure if Maxima can then compute P(diff > 0)
>>since that requires another integration.
>>
>>I worked on a related problem recently. For the record:
>>http://maxima-solved.blogspot.com/2014/06/probability-density-of-sum-of-gamma-and.html
>>
>>> Now, suppose that we have a _group sport_ which requires a small
>>> number (k) athletes, and that the performance of each country is
>>> additive -- e.g., the gymnastics "team" medal, where the team is
>>> of size k.
>>>
>>> Now, what is the probability that country A will beat country B ?
>>
>>Well, for k larger than a few, the group ability is nearly Gaussian
>>even though the individual abilities are very non-Gaussian (via
>>central limit theorem). So one can come up with an approximation
>>more easily in the group case.
>>
>>Sounds like fun -- good luck.
>>
>>Robert Dodier
>
>
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