The Rate of Convergence to the Limit of the Probability of Encountering an Accidental Similarity in the Presence of Counter Examples
Dmitriy V. Vinogradov · Automatic Documentation and Mathematical Linguistics · 2018
This paper refines the main result of [1], where the limit $$ - {e^{ - a}} - a{e^{ - a}}\left[ {1 - {e^{ - c\sqrt a }}} \right]$$ was proved for the probability of encountering an accidental similarity between two parent examples without $$m = c\sqrt n $$ counter examples if each parent example and counter example is described by a series of $$\sqrt n $$ independent Bernoulli trials with success probability $$p = \sqrt {a/n} $$ . In this paper, we prove that the rate of convergence to the limit is proportional to $${n^{\frac{1}{2}}}$$ .