Cramer–von Mises and Anderson‐Darling goodness of fit tests for extreme value distributions with unknown parameters

By Francesco Laio. 2004

231 citations recorded by the source corpus.

The use of goodness of fit tests based on Cramer–von Mises and Anderson‐Darling statistics is discussed, with reference to the composite hypothesis that a sample of observations comes from a distribution, FH, whose parameters are unspecified. When this is the case, the critical region of the test has to be redetermined for each hypothetical distribution FH. To avoid this difficulty, a transformation is proposed that produces a new test statistic which is independent of FH. This transformation involves three coefficients that are determined using the asymptotic theory of tests based on the empirical distribution function. A single table of coefficients is thus sufficient for carrying out the test with different hypothetical distributions; a set of probability models of common use in extreme value analysis is considered here, including the following: extreme value 1 and 2, normal and lognormal, generalized extreme value, three‐parameter gamma, and log‐Pearson type 3, in all cases with parameters estimated using maximum likelihood. Monte Carlo simulations are used to determine small sample corrections and to assess the power of the tests compared to alternative approaches.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/de228d0b024ca53cf1e617a0e0c9ea4ff42d0b71

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Citations in the corpus

A copula-based joint deficit index for droughts. (2010, methodology): “…the appropriateness of G2, Kolmogorov–Smirnov (KS) and Cramer-von Mises (CM) tests were applied for the goodness of fit at the 5% significance level in this study, with model parameters estimated by maximum likelihood (ML) method (see Rao and Hamed (2000) and Laio (2004) for mathematical details).”
Approximation of modified Anderson–Darling test statistics for extreme value distributions with unknown shape parameter (2013, background): “Thus this set of alternative distributions is appealing because the distributions should be able to mimic various flood like behaviors and to avoid the case when the applied distribution is equal to the assumed distribution (Laio, 2004).”
A comparison of homogeneity tests for regional frequency analysis (2007, methodology): “Laio, and P. Claps (2007), A comparison of homogeneity tests for regional frequency analysis, Water”
Threshold detection for the generalized Pareto distribution: Review of representative methods and application to the NOAA NCDC daily rainfall database (2016, background): “…departure between the empirical and fitted distributions [see e.g., Stephens, 1986; Ahmad et al., 1988; Dupuis, 1998; Choulakian and Stephens, 2001; Laio, 2004; Deidda and Puliga, 2006; Deidda 2007; Serinaldi and Kilsby, 2014], and (b) Hill-assumption-based methods, which detect the lowest…”
A study on selection of probability distributions for at-site flood frequency analysis in Australia (2013, background): “The Anderson–Darling statistic has shown good skills for small sample size and heavytailed distributions often encountered in flood frequency analysis (Onoz and Bayazit 1995; Laio 2004).”
Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia (2011, methodology): “The Anderson‐Darling Statistic has shown good skills for small sample size and heavy-tailed distributions, often encountered in flood frequency analysis (Onoz and Bayazit 1995 and Laio 2004 ).”
Sensitivity of goodness-of-fit statistics to rainfall data rounding off (2006, background): “On the contrary, shape of skewed distributions was explicitly accounted in expressions provided by Laio (2004) .”
Irreversibility and complex network behavior of stream flow fluctuations (2016, methodology): “15 [49] J.R.M. Hosking, J.R. Wallis, Regional Frequency Analysis: An Approach Based on L-Moments, Cambridge University Press, New York, 1997.16 [50] F. Laio, Cramer–von Mises and Anderson–Darling goodness of fit tests for extreme value distributions with unknown parameters, Water Resour.”