With independent negative binomial observations from a single group, find the likelihood equation and show that ????

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With independent negative binomial observations from a single group, find the likelihood equation and show that ̂???? = ȳ. (ML estimation for ???? requires iterative methods, as R. A. Fisher showed in an appendix to Bliss (1953). See also Anscombe (1950).) How does this generalize to the one-way layout?

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