On the performance of Turing's formula: A simulation study

ABSTRACT

Turing's formula is an amazing result that allows one to estimate the probability of observing something that has not been observed before. After a brief review of the literature, we perform a simulation study to better understand how well this formula works in a variety of situations. We also compare the performance of Turing's formula with several modifications that have appeared in the literature. We find that these modifications tend to outperform Turing's formula, but usually not by very much. We further find that Turing's formula and its modifications tend to work better for heavy-tailed distributions than for light-tailed ones.

KEYWORDS:

• Good-Turing estimation
• Simulation study
• Turing's formula

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05
• 62G32

Acknowledgments

The authors wish to thank the two anonymous referees, whose comments led to a great improvement in the presentation of this article.