A sufficient normality condition for Turing's formula

摘要

This paper establishes a previously unknown sufficient condition for the asymptotic normality of the non-parametric sample coverage estimate based on Good under a fixed underlying probability distribution {pk;k = 1,...} where all pk > 0. The sufficient condition of this paper supports a non-empty class of distributions and excludes the condition of Esty as a marginal case in which it is shown that the n~(1/2)-normalised sample coverage estimate proposed by Esty necessarily degenerates under a fixed {pk}. The convergent statistic in the newly established normality law and the resulting relevant confidence intervals are all of new forms, and specifically are different from those suggested by Esty.