Re: [Maxima-discuss] "distrib" package

[Henry B. <hb...@pi...>]

Thanks for your reply, Michael.

That's the trouble with math; almost every question is still being worked on!

I'm primarily interested in the tails of the distributions, as I'm trying to approximate the following "Olympic athlete" problem.

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 ?

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 ?

I'm generally interested in asymptotics, so while an exact expression would be fun, my main interest is in the first-order approximations to the probabilities.

I thought that Maxima might be able to help me formulate and/or solve this problem.

At 08:17 AM 9/3/2014, you wrote:
>Dear Henry,
>
>this is called the Behrens Fischer problem. As far as I know there are no exact solutions to it, just various approximations. The most common approximation is from Welch. 
>
>See http://en.wikipedia.org/wiki/Behrens%E2%80%93Fisher_problem.
>
>Best regards,
>
>Michael
>
>-----Original Message-----
>From: Henry Baker [mailto:hb...@pi...] 
>Sent: Wednesday, September 03, 2014 4:23 PM
>To: max...@li...
>Subject: [Maxima-discuss] "distrib" package
>
>I am just starting to play with the "distrib" package, and it looks to be very cool!
>
>I'm extremely rusty on my probability, so I'd like to ask an extremely simple question:
>
>Suppose I take 8 samples from normal distribution A and 8 samples from normal distribution B, each with its own mean and variance.
>
>What is the probability that the sum of the 8 A-samples will exceed the sum of the 8 B-samples ?
>
>Of course, "8" might also be some other number, like 5.
>
>Thanks for any help.