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Fixed-point algorithms for solving the critical value and upper tail quantile of Kuiper's statistics

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KuiperVnStatistic

BibTeX Item for Citation with LaTeX: @article{ZHANG2024e28274, title = {Fixed-point algorithms for solving the critical value and upper tail quantile of Kuiper's statistics}, journal = {Heliyon}, volume = {10}, number = {7}, pages = {e28274}, year = {2024}, issn = {2405-8440}, doi = {https://doi.org/10.1016/j.heliyon.2024.e28274}, url = {https://www.sciencedirect.com/science/article/pii/S2405844024043056}, author = {Hong-Yan Zhang and Wei Sun and Xiao Chen and Rui-Jia Lin and Yu Zhou}, keywords = {Kuiper's statistic, Upper tail quantile, Fixed-point algorithm, Numerical approximation, Algorithm design, STEM education}, }

Code for Kuiper's Vn statistic in the Goodness-of-fit Test in Mathematical Statistics

/*********** Compile+Link+Run at Unix/Linux terminal *****************

  • Compile+Link: $ gcc KuiperPairSolver.c main.c -o Kuiper -lm
  •       or    $ g++ KuiperPairSolver.c main.c -o Kuiper
    
  • Run: $ ./Kuiper 0.05 100 1 1 2.45
  •             $ ./Kuiper 0.05 100  1  2  2.45 
    
  •             $ ./Kuiper 0.05 100  2  1  2.45 >> test.txt
    
  •             $ ./Kuiper 0.05 100  2  2  2.45 >> test.txt
    
  • Note that the initial value is important for the iteration and our
  • suggestions are as follows:
  • V_n test, direct iterative method, guess in (0.5, 2.5)
  • V_n test, Newton iterative method, guess in (1.1, 2.5)
  • V_{n,n} test, direct iterative method, guess in (2.4, 2.6)
  • V_{n,n} test, direct iterative method, guess in (2.2, 2.6)
  • optional guess for all of most applications, guess = 2.45
  • Newton iterative method works well for both V_n and V_{n,n} test
  • *******************************************************************/

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Fixed-point algorithms for solving the critical value and upper tail quantile of Kuiper's statistics

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