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Fixed-point algorithms for solving the critical value and upper tail quantile of Kuiper's statistics
Hong-Yan Zhang1, Wei Sun1, Xiao Chen1,2
1School of Information Science and Technology, Hainan Normal University, No. 99, Rd. LongKun South, Haikou 571158, China.
Heliyon
|April 1, 2024
Summary
This study improves calculations for Kuiper
Area of Science:
- Statistics
- Goodness-of-fit testing
Background:
- Kuiper's statistic is valuable for comparing empirical and ideal distributions.
- Calculating critical values and quantiles for Kuiper's statistic is computationally challenging.
Purpose of the Study:
- To develop a more precise method for calculating Kuiper's statistic critical values and quantiles.
- To present detailed algorithms for solving the Kuiper pair.
- To correct an error in existing Kuiper distribution tables.
Main Methods:
- Utilized a second-order approximation for the infinite series of the cumulative distribution.
- Developed and detailed fixed-point algorithms for solving the Kuiper pair.
- Validated algorithms against Kuiper's original table.
Main Results:
- Achieved higher precision in critical value calculations.
- Provided a corrected critical value for a specific sample size and quantile.
- Demonstrated the efficacy of the proposed algorithms.
Conclusions:
- The developed methods offer a more accurate approach to Kuiper's statistic analysis.
- The corrected table and algorithms are valuable resources for researchers and practitioners.
- The findings are applicable to various fields requiring goodness-of-fit assessments.
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