{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T14:23:04Z","timestamp":1762352584198,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T00:00:00Z","timestamp":1762300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Data"],"abstract":"<jats:p>Along with other order statistics, the Cram\u00e9r\u2013von 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.<\/jats:p>","DOI":"10.3390\/data10110181","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T13:19:29Z","timestamp":1762348769000},"page":"181","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Small Samples\u2019 Permille Cram\u00e9r\u2013Von Mises Statistic Critical Values for Continuous Distributions as Functions of Sample Size"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8524-743X","authenticated-orcid":false,"given":"Lorentz","family":"J\u00e4ntschi","sequence":"first","affiliation":[{"name":"Department of Physics and Chemistry, Technical University of Cluj-Napoca, 103-105 Muncii Blvd., 400641 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1080\/00224065.2012.11917887","article-title":"Two nonparametric control charts for detecting arbitrary distribution changes","volume":"44","author":"Ross","year":"2012","journal-title":"J. Qual. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Qiu, X., Xiao, Y., Gordon, A., and Yakovlev, A. (2006). Assessing stability of gene selection in microarray data analysis. BMC Bioinform., 7.","DOI":"10.1186\/1471-2105-7-50"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s11336-012-9302-4","article-title":"Tests of measurement invariance without subgroups: A generalization of classical methods","volume":"78","author":"Merkle","year":"2013","journal-title":"Psychometrika"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1061\/(ASCE)HE.1943-5584.0000723","article-title":"Cram\u00e9r-von Mises and Anderson-Darling goodness-of-fit tests for the two-parameter kappa distribution","volume":"18","author":"Ashkar","year":"2013","journal-title":"J. Hydrol. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1002\/psp4.13271","article-title":"Pharmacometric and statistical considerations for dose optimization","volume":"2025","author":"Chotsiri","year":"2025","journal-title":"CPT Pharmacometrics Syst. Pharmacol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1057\/gpp.2011.20","article-title":"A quantitative comparison of the Lee-Carter model under different types of non-Gaussian innovations","volume":"36","author":"Wang","year":"2011","journal-title":"Geneva Pap. Risk Insur.-Issues Pract."},{"key":"ref_7","first-page":"2991","article-title":"Type-I Heavy-Tailed Burr XII Distribution with Applications to Quality Control, Skewed Reliability Engineering Systems and Lifetime Data","volume":"144","author":"Obulezi","year":"2025","journal-title":"Comput. Model. Eng. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"J\u00e4ntschi, L. (2025). The Cram\u00e9r\u2013Von Mises Statistic for Continuous Distributions: A Monte Carlo Study for Calculating Its Associated Probability. Symmetry, 17.","DOI":"10.3390\/sym17091542"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1002\/etc.5620200228","article-title":"A general best-fit method for concentration-response curves and the estimation of low-effect concentrations","volume":"20","author":"Scholze","year":"2001","journal-title":"Environ. Toxicol. Chem."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"J\u00e4ntschi, L. (2020). Detecting extreme values with order statistics in samples from continuous distributions. Mathematics, 8.","DOI":"10.3390\/math8020216"},{"key":"ref_11","first-page":"13","article-title":"On the composition of elementary errors","volume":"1","year":"1928","journal-title":"Scand. Actuar. J."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Von Mises, R. (1928). Wahrscheinlichkeit, Statistik und Wahrheit, Springer.","DOI":"10.1007\/978-3-662-36230-3"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"85","DOI":"10.17713\/ajs.v54i2.1906","article-title":"Goodness-of-Fit Tests for COM-Poisson Distribution Using Stein\u2019s Characterization","volume":"54","author":"Traison","year":"2025","journal-title":"Austrian J. Stat."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"100365","DOI":"10.1016\/j.kjs.2025.100365","article-title":"A Bayesian inference with Hamiltonian Monte Carlo (HMC) framework for a three-parameter model with reliability applications","volume":"52","author":"Muhammad","year":"2025","journal-title":"Kuwait J. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Singh Nayal, A., Ramos, P.L., Tyagi, A., and Singh, B. (2024). Improving inference in exponential logarithmic distribution. Commun.-Stat.-Simul. Comput., 1\u201325.","DOI":"10.1080\/03610918.2024.2446346"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"e12370","DOI":"10.1111\/stan.12370","article-title":"A robust and powerful metric for distributional homogeneity","volume":"79","author":"Chen","year":"2025","journal-title":"Stat. Neerl."},{"key":"ref_17","first-page":"309","article-title":"On the mathematical foundations of theoretical statistics","volume":"222","author":"Fisher","year":"1922","journal-title":"Philos. Trans. R. Soc. London. Ser. A Contain. Pap. A Math. Phys. Character"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1017\/S0305004100009580","article-title":"Theory of statistical estimation","volume":"Volume 22","author":"Fisher","year":"1925","journal-title":"Mathematical Proceedings of the Cambridge Philosophical Society"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1175\/WAF884.1","article-title":"Alternatives to the chi-square test for evaluating rank histograms from ensemble forecasts","volume":"20","author":"Elmore","year":"2005","journal-title":"Weather Forecast."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1080\/01621459.1974.10480196","article-title":"EDF statistics for goodness of fit and some comparisons","volume":"69","author":"Stephens","year":"1974","journal-title":"J. Am. Stat. Assoc."}],"container-title":["Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2306-5729\/10\/11\/181\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T14:11:14Z","timestamp":1762351874000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2306-5729\/10\/11\/181"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,5]]},"references-count":20,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["data10110181"],"URL":"https:\/\/doi.org\/10.3390\/data10110181","relation":{},"ISSN":["2306-5729"],"issn-type":[{"value":"2306-5729","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,5]]}}}