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Fixed-Point Algorithms for Solving the Critical Value and Upper Tail Quantile of Kuiper's Statistics

Authors :
Zhang, Hong-Yan
Sun, Wei
Chen, Xiao
Lin, Rui-Jia
Zhou, Yu
Source :
Heliyon, 10(7): e28274, April 15, 2024
Publication Year :
2023

Abstract

Kuiper's statistic is a good measure for the difference of ideal distribution and empirical distribution in the goodness-of-fit test. However, it is a challenging problem to solve the critical value and upper tail quantile, or simply Kuiper pair, of Kuiper's statistics due to the difficulties of solving the nonlinear equation and reasonable approximation of infinite series. In this work, the contributions lie in three perspectives: firstly, the second order approximation for the infinite series of the cumulative distribution of the critical value is used to achieve higher precision; secondly, the principles and fixed-point algorithms for solving the Kuiper pair are presented with details; finally, finally, a mistake about the critical value $c^\alpha_n$ for $(\alpha, n)=(0.01,30)$ in Kuiper's distribution table has been labeled and corrected where $n$ is the sample capacity and $\alpha$ is the upper tail quantile. The algorithms are verified and validated by comparing with the table provided by Kuiper. The methods and algorithms proposed are enlightening and worth of introducing to the college students, computer programmers, engineers, experimental psychologists and so on.<br />Comment: 20 pages, 6 figures, 5 tables, code available on GitHub

Subjects

Subjects :
Statistics - Computation

Details

Database :
arXiv
Journal :
Heliyon, 10(7): e28274, April 15, 2024
Publication Type :
Report
Accession number :
edsarx.2308.09463
Document Type :
Working Paper
Full Text :
https://doi.org/10.1016/j.heliyon.2024.e28274