The Anderson-Darling test of fit for the power law distribution from left censored samples

TL;DR

This paper develops a maximum likelihood estimation and Anderson-Darling goodness-of-fit test for power law distributions using left-censored data, with practical applications demonstrated on financial index data.

Contribution

It introduces a novel approach for fitting and testing power law models with censored samples, including explicit estimators and critical value tables.

Findings

Effective fit testing for power law distributions with censored data

Application to Dow Jones index data demonstrates practical utility

Provides asymptotic critical values for the Anderson-Darling statistic

Abstract

Maximum likelihood estimation and a test of fit based on the Anderson-Darling statistic is presented for the case of the power law distribution when the parameters are estimated from a left-censored sample. Expressions for the maximum likelihood estimators and tables of asymptotic percentage points for the A^2 statistic are given. The technique is illustrated for data from the Dow Jones Industrial Average index, an example of high theoretical and practical importance in Econophysics, Finance, Physics, Biology and, in general, in other related Sciences such as Complexity Sciences.