{"title":"A Brief Study about Nonparametric Adherence Tests","authors":"Vinicius R. Domingues, Luan C. S. M. Ozelim","volume":107,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":699,"pagesEnd":703,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10003242","abstract":"The statistical study has become indispensable for various fields of knowledge. Not any different, in Geotechnics the study of probabilistic and statistical methods has gained power considering its use in characterizing the uncertainties inherent in soil properties. One of the situations where engineers are constantly faced is the definition of a probability distribution that represents significantly the sampled data. To be able to discard bad distributions, goodness-of-fit tests are necessary. In this paper, three non-parametric goodness-of-fit tests are applied to a data set computationally generated to test the goodness-of-fit of them to a series of known distributions. It is shown that the use of normal distribution does not always provide satisfactory results regarding physical and behavioral representation of the modeled parameters.","references":"[1] Torman, V. B. L.; Coster, R.; Riboldi, J. 2012. Normalidade de\r\nvari\u00e1veis: m\u00e9todos de verifca\u00e7\u00e3o e compara\u00e7\u00e3o de alguns testes n\u00e3o\r\nparam\u00e9tricos por simula\u00e7\u00e3o, Rev. HCPA, Porto Alegre, v.32, n.2, p.227-\r\n234.\r\n[2] Anderson, T. W. and Darling, D. A. 1954. A Test of Goodness-of-Fit.\r\nJournal of the American Statistical Association, 49: 765\u2013769.\r\n[3] Gassem, A. 2011. On Cram\u00e9r\u2013von Mises type test based on local time of\r\nswitching diffusion process. Journal of Statistical Planning and\r\nInference, Vol 141(4), P. 1355\u20131361.\r\n[4] Inglot, T. and Ledwina, T. 2004. On consistent minimax\r\ndistinguishability and intermediate efficiency of Cram\u00e9r\u2013von Mises test.\r\nJournal of Statistical Planning and Inference, Vol. 124 (2), P. 453\u2013474.\r\n[5] D'Agostino, R. B. and Stephens, M. A.. 1986. Goodness-of-Fit\r\nTechniques. New York: Marcel Dekker. ISBN 0-8247-7487-6, 1986.\r\n[6] Coronel-Brizio, H. F. and Hern\u00e1ndez-Montoya, A. R. 2010. The\r\nAnderson\u2013Darling test of fit for the power-law distribution from leftcensored\r\nsamples. Physica A: Statistical Mechanics and its Applications,\r\nVol. 389 (17), P. 3508\u20133515.\r\n[7] Heo, J-H., Shin, H., Nam, W., Om, J., Jeong, C. 2013. Approximation of\r\nmodified Anderson\u2013Darling test statistics for extreme value distributions\r\nwith unknown shape parameter. Journal of Hydrology, Vol. 499 (30), P.\r\n41\u201349.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 107, 2015"}