- #1

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- Thread starter dmatador
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- #1

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- #2

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Maximize/minimize = take the derivative and set it equal to zero

- #3

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Maybe you could elaborate on that? More specifically.

- #4

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But write down your binomial dist. It should be

neg_binomial = A * p^k * (1-p)^r

where A won't depend on p, but will be some combinatoric.

Now take the derivative with respect to p.

A*k*p^(k-1)*(1-p)^r + A*r*p^k*(1-p)^(r-1)

now set that equal to 0 and solve for p. It will be some explicit value depending on your parameters.

Sorry for skimping on the latex, if its too unclear I can re-write it for you.

edit: But the point is that whenever you want to find a max or min, that is an equivalent statement to saying that the slope of the function has to be zero (although a zero slope isn't always a max or min).

- #5

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I tried it for Y = 11, r = 5. I ended up getting p = -5, which is clearly wrong.

- #6

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I tried it for Y = 11, r = 5. I ended up getting p = -5, which is clearly wrong.

First off, one obvious mistake on what I wrote to you before.

The second term of the expression should be negative not positive (from the chain rule on the derivative of (1-p)). Maybe double check that the rest is right.

If it still doesn't give a sensible answer I'll work it out explicitly tomorrow.

Sorry about that.

- #7

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