B. A. Rogozin, “Compactness and the concentration functions of the convolutions of a distribution”, Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 1,Pages <nobr>81

Compactness and the concentration functions of the convolutions of a distribution

B. A. Rogozin

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science

Abstract: A relationship is investigated between the compactness conditions of the distributions of sums of independent identically distributed random variables under an appropriate scaling and the behavior of the sequence of concentration functions of these sums.

Keywords: independent identically distributed random variables, sum, convolution, median, quantile, compactness, finite noncompactness, Levy concentration function, censored variance, majorizied varying function, unimodal distribution.

Received: 15.06.2001

DOI: 10.4213/tvp159