Small Samples' Permille Cramér-Von Mises Statistic Critical Values for Continuous Distributions as Functions of Sample Size

Along with other order statistics, the Cramér–von Mises (CM) statistic can assess the goodness of fit. CM does not have an explicit formula for the cumulative distribution function and the alternate way is to obtain its critical value from a Monte Carlo (MC) experiment. A high resolution experiment was deployed to generate a large amount of data resembling CM. Twenty-one repetitions of the experiment were conducted, and in each case, critical values of the CM statistic were obtained for all permilles and sample sizes from 2 to 30. The raw data presented here can serve to interpolate and extract probabilities associated with CM statistic directly, or to obtain a mathematical model for the bivariate dependence.

• Publication year

  2025

• Venue

  International Conference on Data Technologies and Applications

• Publication date

  2025-11-05

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.3390/data10110181
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Type-I Heavy-Tailed Burr XII Distribution with Applications to Quality Control, Skewed Reliability Engineering Systems and Lifetime Data

  2025cited by this paper
• A Bayesian inference with Hamiltonian Monte Carlo (HMC) framework for a three-parameter model with reliability applications

  2025cited by this paper
• The Cramér-Von Mises Statistic for Continuous Distributions: A Monte Carlo Study for Calculating Its Associated Probability

  2025influential reference
• Improving inference in exponential logarithmic distribution

  2025cited by this paper
• Goodness-of-Fit Tests for COM-Poisson Distribution Using Stein's Characterization

  2025cited by this paper
• A robust and powerful metric for distributional homogeneity

  2025cited by this paper
• Pharmacometric and statistical considerations for dose optimization

  2024influential reference
• Detecting Extreme Values with Order Statistics in Samples from Continuous Distributions

  2020cited by this paper
• Cramér-von Mises and Anderson-Darling Goodness-of-Fit Tests for the Two-Parameter Kappa Distribution

  2013cited by this paper
• Two Nonparametric Control Charts for Detecting Arbitrary Distribution Changes

  2012cited by this paper
• Tests of Measurement Invariance Without Subgroups: A Generalization of Classical Methods

  2012cited by this paper
• A Quantitative Comparison of the Lee-Carter Model under Different Types of Non-Gaussian Innovations

  2011cited by this paper
• Alternatives to the Chi-Square Test for Evaluating Rank Histograms from Ensemble Forecasts

  2005influential reference
• A general best‐fit method for concentration‐response curves and the estimation of low‐effect concentrations

  2001cited by this paper
• On the composition of elementary errors

  1994cited by this paper
• EDF Statistics for Goodness of Fit and Some Comparisons

  1974cited by this paper
• Wahrscheinlichkeit, Statistik und Wahrheit

  1936cited by this paper
• Theory of Statistical Estimation

  1925cited by this paper
• On the Mathematical Foundations of Theoretical Statistics

  year unknowncited by this paper

• No citing papers are available for this paper.