Theoretical Foundations of Applied Discrete Mathematics

Compound Poisson approximation for the distribution of the number of monotone tuples in random sequence

A. A. Minakov

Moscow State Institute of Radio-Engineering, Electronics and Automation, Moscow

Abstract: The distribution of the number of monotone tuples in the sequence of independent uniformly distributed random variables taking values in the set $\{0,\dots ,N-1\}$ is considered. By means of the Stein method, an estimate for the variation distance between the distribution of the number of monotone tuples and compound Poisson distribution are constructed. As a corollary of this result, the limit theorem for the number of monotone tuples is proved. The approximating distribution in it is the distribution of the sum of Poisson number of independent random variables with geometric distribution.

Keywords: monotone tuples, estimate for the variation distance of the compound Poisson approximation, compound Poisson distribution, Stein method.

UDC: 519.214