Analytical Confidence Intervals for the Number of Different Objects in Data Streams

This paper develops a new mathematical-statistical approach to analyze class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 distinct elements in stream, based on Chernoff bounds. The FMa has reached significant popularity bigdata stream learning, attention literature mainly been algorithmic aspects, basically complexity optimality, while statistical analysis these often faced heuristically. provided here shows deep connections with mathematical special functions extreme value theory. latter connection may help explaining heuristic considerations, first opens many numerical issues, at end present paper. Finally, are tested an anonymized real data MonteCarlo simulations support our choice this context.