TL;DR
This paper investigates the maximum possible variance of the missing mass in samples, providing insights into its concentration properties across different sample and alphabet sizes.
Contribution
It determines the maximal variance of the missing mass for any sample and alphabet sizes, advancing understanding of its concentration behavior.
Findings
Derived the maximal variance bounds for missing mass
Enhanced understanding of missing mass concentration properties
Applicable to diverse fields like ecology, linguistics, and information theory
Abstract
The missing mass refers to the probability of elements not observed in a sample, and since the work of Good and Turing during WWII, has been studied extensively in many areas including ecology, linguistic, networks and information theory. This work determines what is the \emph{maximal variance of the missing mass}, for any sample and alphabet sizes. The result helps in understanding the missing mass concentration properties.
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Taxonomy
TopicsAlgorithms and Data Compression · Bayesian Methods and Mixture Models · DNA and Biological Computing