A sufficient normality condition for Turing's formula

Abstract

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 {p k ; k=1, …} where all p k >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-normalised sample coverage estimate proposed by Esty necessarily degenerates under a fixed {p k }. 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.