Partial case of multinomial

Markiyan Hirnyk — Fri, 08 Mar 2013 11:15:26 Z

A similar question was asked and answered here:
http://www.mapleprimes.com/questions/126141-Multinomial-Distribution-In-Maple.
A trinomial distribution can be created as a procedure

>Multinomial:=proc (n, k, x, p)
if nops(x) = k and nops(p) = k and sum(p[j], j = 1 .. k) = 1 and 0 < min(p) and sum(x[j], j = 1 .. k) = n
then factorial(n)*mul(p[j]^x[j], j = 1 .. k)/mul(factorial(x[j]), j = 1 .. k)
else 0
end if
end proc;
In your case n=3, k=3, p=[1/6, 1/2, 1/3], and x=[x1,x2,x3], where xj, j=1..3, are integers.
For example,
> Multinomial(3, 3, [1, 2, 0], [1/6, 1/2, 1/3]);
1/8
The values of the trinomial distribution are vectors. The mean of each component
can be found in such a way. The command
> add(add(add(x2*Multinomial(3, 3, [x1, x2, x3], [1/6, 1/2, 1/3]), x1 = 0 .. 3), x2 = 0 .. 3), x3 = 0 .. 3);
3/2
produces the one for the second component.
The command
>add(add(add(x2^2*Multinomial(3, 3, [x1, x2, x3], [1/6, 1/2, 1/3]), x1 = 0 .. 3), x2 = 0 .. 3), x3 = 0 .. 3)-
add(add(add(x2*Multinomial(3, 3, [x1, x2, x3], [1/6, 1/2, 1/3]), x1 = 0 .. 3), x2 = 0 .. 3), x3 = 0 .. 3)^2;
3/4
produces its variance.
In order to define the two random trinomial distributions X and Y and to calculate Cov(X,Y), their joint probability distribution (PS. as a sevenfour-dimensional Array) should be given .

Edit. Multinomial(n,k,x,p) replaced by Multinomial.

Not working

knovick — Sat, 09 Mar 2013 04:29:35 Z

This answer isn't working. I am getting unable to match errors with no help on this error available when I click through Maple. Are there any other suggestions available?

Working

Markiyan Hirnyk — Sun, 10 Mar 2013 10:53:19 Z

@knovick See trinomial.mw and screen10.03.13.docx . I am waiting for your feedback.

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Partial case of multinomial

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