1. Discrete Truncated Power‐Law Distributions
- Author
-
Maochao Xu, Hong Zhu, and Yingchao Xie
- Subjects
Statistics and Probability ,Mathematical optimization ,Monte Carlo method ,Order statistic ,Sample (statistics) ,010103 numerical & computational mathematics ,01 natural sciences ,Power law ,Upper and lower bounds ,010104 statistics & probability ,symbols.namesake ,Heavy-tailed distribution ,symbols ,Pareto distribution ,Statistical physics ,0101 mathematics ,Statistics, Probability and Uncertainty ,Intensity (heat transfer) ,Mathematics - Abstract
Summary Discrete power-law distributions have significant consequences for understanding many phenomena in practice, and have attracted much attention in recent decades. However, in many practical applications, there exists a natural upper bound for the probability tail. In this paper, we develop maximum likelihood estimates for truncated discrete power-law distributions based on the upper order statistics, and large sample properties are mentioned as well. Monte Carlo simulation is carried out to examine the finite sample performance of the estimates. Applications in real cyber attack data and peak gamma-ray intensity of solar flares are highlighted.
- Published
- 2016