Chains of Truncated Beta Distributions and Benford’s Law

It was proved by Jang et al. that various chains of one-parameter distributions converge to Benford’s law. We study chains of truncated distributions and propose another approach, using a recent convergence result of the Lerch transcendent function, to proving that they converge to Benford’s law for initial Beta distributions with parameters α and 1.

Comparison of the Goodness-of-Fit Tests for Truncated Distributions

The aim of this paper is to investigate the finite sample behavior of seven goodness-of-fit tests for left truncated distributions of Chernobai et al. (2015) in terms of size and power. Simulation experiments are based on artificial data generated from the distributions that were used in the past or are used nowadays to describe the tails of asset returns. The study was conducted for different tail thickness and for changing truncation point. Simulation results indicate that the testing procedures do not work equally well under finite samples, and some of them require quite large number of observations to perform satisfactorily.

Generalized truncated distributions with N intervals deleted: Mathematical definition

The distributions obtained by N intervals truncations are characterized by its high sensitivity for stochastic volatility data. In stable intervals, we use this method to delete some certain range of data values from a domain of the random variable. A comprehensive treatment of the statistical properties of this distribution is presented. We assume Normal and Log-Lindley distributions to apply the obtained results.