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Binomial-proportion Fisher scoring

For

Y = n^{- 1} Bin (n, p)

, the score and information are

S (p) = \frac{n ( Y - p )}{p ( 1 - p )}, I (p) = \frac{n}{p ( 1 - p )} .

Consequently one Fisher-scoring step sends every interior starting value directly to the MLE

p = Y

.

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