Benfordness of the Generalized Gamma Distribution
Zelong Bi, Irfan Durmi\'c, Steven J. Miller
TL;DR
This paper provides a mathematical explanation for why the generalized gamma distribution often follows Benford's Law and introduces a measure to quantify its deviation from Benfordness.
Contribution
It offers a theoretical analysis of the generalized gamma distribution's Benfordness and proposes a new measure for its deviation from Benford's Law.
Findings
The generalized gamma distribution exhibits Benford-like behavior.
A new measure quantifies the deviation from Benford's Law.
Mathematical explanation supports empirical observations.
Abstract
The generalized gamma distribution shows up in many problems related to engineering, hydrology as well as survival analysis. Earlier work has been done that estimated the deviation of the exponential and the Weibull distribution from Benford's Law. We give a mathematical explanation for the Benfordness of the generalized gamma distribution and present a measure for the deviation of the generalized gamma distribution from the Benford distribution.
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Taxonomy
TopicsBenford’s Law and Fraud Detection