arXiv subjects
Publications and source records attributed to Sergej V. Aksenov.
We extend the definition of the Lerch distribution to the set of nonnegative integers for greater applicability to modeling count data. We express its properties in terms of Lerch's transcendent, and study its unimodality, hazard function and variance-to-mean ratio.
We consider the problem of statistical inference for the S distribution and introduce new minimum distance estimators for the four parameters of the S distribution using Kolmogorov-Smirnov, Cramer-von Mises and related distance metrics. Approximate goodness-of-fit and confidence intervals for parameters are calculated using bootstrap methods. We discuss further how the S distribution can be used to solve various problems of statistical modeling associated with parameter inference, including goodness-of-fit tests, Monte Carlo simulations and modeling trends in the distributions.