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- W2079665817 abstract "Summary In a paper in Biometrika, Anscombe (1950) considered the question of solving the equation with respect to x. Here “Log” denotes the natural logarithm, while N s , where N k >0 and N s =0 for s>k, denotes the number of items ⩾s in a sample of independent observations from a population with the negative binomial distribution and m denotes the sampling mean: it can in the case k ⩾ 2 be shown that the equation (*) has at least one root. In vain search for “Gegenbeispiele”, Anscombe was led to the conjecture (l.c., 367) that (*) has no solution, if m 2 > 2S, and a unique solution, if k ⩾ 2 and m 2 < 2S. In the latter case, x equals the maximum-likelihood estimate of the parameter ϰ. In the present paper it will, after some preliminaries, be shown that the equation (*) has no solution, if k=l, or if k⩾2 and m 2 ⩾ 2S, whereas (*) has a unique solution, if k ⩾ 2 and m 2 < 2S." @default.
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- W2079665817 date "1976-10-01" @default.
- W2079665817 modified "2023-09-25" @default.
- W2079665817 title "On the solution of a maximum-likelihood equation of the negative binomial distribution" @default.
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- W2079665817 doi "https://doi.org/10.1080/03461238.1976.10405618" @default.
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