symmetry

CRAN: symmetry citation info Ivanović B, Milošević B, Obradović M (2023). symmetry: Testing for Symmetry of Data and Model Residuals . R package version 0.2.3, https://CRAN.R-project.org/package=symmetry . Corresponding BibTeX entry: @Manual{, title = {symmetry: Testing for Symmetry of Data and Model Residuals}, author = {Blagoje Ivanović and Bojana Milošević and Marko Obradović}, year = {2023}, note = {R package version 0.2.3}, url = {https://CRAN.R-project.org/package=symmetry}, }

NEWS code{white-space: pre-wrap;} span.smallcaps{font-variant: small-caps;} span.underline{text-decoration: underline;} div.column{display: inline-block; vertical-align: top; width: 50%;} div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;} ul.task-list{list-style: none;} Version 0.2.3 Fixed “sign” bootstrap method to work around a non-zero known mean. Version 0.2.2 Minor fixes for CRAN Version 0.2.1 Changed codenames of statistics to more sensible ones, like in the paper Added Rothman-Woodroofe and Baringhaus-Henze test statistics

Help for package symmetry const macros = { "\\R": "\\textsf{R}", "\\mbox": "\\text", "\\code": "\\texttt"}; function processMathHTML() { var l = document.getElementsByClassName('reqn'); for (let e of l) { katex.render(e.textContent, e, { throwOnError: false, macros }); } return; } Package {symmetry} Contents TestStatistics rmixnorm rsl symmetry symmetry_test Title: Testing for Symmetry of Data and Model Residuals Version: 0.2.3 Author: Blagoje Ivanović [aut, cre] Bojana Milošević [aut] Marko Obradović [aut] Date: 2023-03-10 Maintainer: Blagoje Ivanović <blagoje.ivanovic@matf.bg.ac.rs> Description: Implementations of a large number of tests for symmetry and their bootstrap variants, which can be used for testing the symmetry of random samples around a known or unknown mean. Functions are also there for testing the symmetry of model residuals around zero. Currently, the supported models are linear models and generalized autoregressive conditional heteroskedasticity (GARCH) models (fitted with the 'fGarch' package). All tests are implemented using the 'Rcpp' package which ensures great performance of the code. Depends: R (≥ 3.1.0) License: MIT + file LICENSE Encoding: UTF-8 Imports: Rcpp, Rdpack RdMacros: Rdpack LinkingTo: Rcpp, RcppArmadillo RoxygenNote: 7.2.2 Suggests: knitr, rmarkdown, sn, fGarch, testthat NeedsCompilation: yes Packaged: 2023-03-10 15:45:56 UTC; blaza Repository: CRAN Date/Publication: 2023-03-10 17:00:02 UTC Available test statistics for symmetry tests Description The list of implemented test statistics and their functions Usage B1(X) BH2(X) BHC1(X, k) BHC2(X, k) BHI(X) BHK(X) CM(X) FM(X) HM(X, k) K2U(X) K2(X) KS(X) SGN(X) WCX(X) MGG(X) MI(X) MOI(X, k) MOK(X, k) NAC1(X, k) NAC2(X, k) NAI(X, k) NAK(X, k) RW(X) Arguments X the numeric vector for which to calculate the test statistic k the 'k' parameter in the formula (if applicable) Details Below is a list of the implemented test statistics in the package. Each statistic is listed by it's name, a code string (e.g. 'B1', CM','MOI') and the formula of the statistic which is evaluated. The code string is used as an argument to the symmetry_test function. Some statistics depend on a parameter 'k' which can be seen from the formulas and is also passed as an argument. Each statistic is implemented as a function with the same name as the code string, so the name of the function is passed as the argument "stat" to the symmetry_test function Value The value of the test statistic. Test statistics The list of available statitics in the format "code(s) : name (reference)" MI : The Mira test statistic (see (Mira 1999)) CM : The Cabilio–Masaro test statistic (see (Cabilio and Masaro 1996)) MGG : The Miao, Gel and Gastwirth test statistic (see (Miao et al. 2006)) B1 : The \sqrt{b_1} test statistic (see (Milošević and Obradović 2019)) KS : The Kolmogorov–Smirnov test statistic (see (Milošević and Obradović 2019)) SGN : The Sign test statistic (see (Milošević and Obradović 2019)) KS : The Wilcoxon test statistic (see (Milošević and Obradović 2019)) FM : The characterization based test statistic (see (Feuerverger et al. 1977)) RW : The Rothman-Woodroofe test statistic (see (Gaigall 2019)) BHI : The Litvinova test statistic (see (Litvinova 2001)) BHK : The Baringhaus and Henze supremum-type test statistic (see (Baringhaus and Henze 1992)) BH2 : The Baringhaus-Henze test statistic (see (Baringhaus and Henze 1992)) MOI and MOK : The Milošević and Obradović test statistics (see (Milošević and Obradović 2016)) NAI and NAK : The Nikitin and Ahsanullah test statistics (see (Nikitin and Ahsanullah 2015)) K2 and K2U : The Božin, Milošević, Nikitin and Obradović Kolmogorov type statistics based on V- and U- statistics respectively (see (Božin et al. 2018)) NAC1, NAC2, BHC1 and BHC2 : The Allison and Pretorius test statistics (see (Allison and Pretorius 2017)) References Allison JS, Pretorius C (2017). “A Monte Carlo evaluation of the performance of two new tests for symmetry.” Computational Statistics , 32 (4), 1323–1338. doi:10.1007/s00180-016-0680-4 . Baringhaus L, Henze N (1992). “A characterization of and new consistent tests for symmetry.” Communications in statistics-theory and methods , 21 (6), 1555–1566. doi:10.1080/03610929208830863 . Božin V, Milošević B, Nikitin Y, Obradović M (2018). “New Characterization-Based Symmetry Tests.” Bulletin of the Malaysian Mathematical Sciences Society , 10–1007. doi:10.1007/s40840-018-0680-3 . Cabilio P, Masaro J (1996). “A simple test of symmetry about an unknown median.” Canadian Journal of Statistics , 24 (3), 349–361. doi:10.2307/3315744 . Feuerverger A, Mureika RA, others (1977). “The empirical characteristic function and its applications.” The Annals of Statistics , 5 (1), 88–97. doi:10.1214/aos/1176343742 . Gaigall D (2019). “Rothman-Woodroofe symmetry test statistic revisited.” Computational Statistics & Data Analysis , 106837. Litvinova VV (2001). “New nonparametric test for symmetry and its asymptotic efficiency.” Vestnik St. Petersburg University Mathematics , 34 (4), 12–14. Miao W, Gel YR, Gastwirth JL (2006). “A new test of symmetry about an unknown median.” In Random Walk, Sequential Analysis And Related Topics: A Festschrift in Honor of Yuan-Shih Chow , 199–214. World Scientific. Milošević B, Obradović M (2016). “Characterization based symmetry tests and their asymptotic efficiencies.” Statistics & Probability Letters , 119 , 155–162. Milošević B, Obradović M (2019). “Comparison of efficiencies of some symmetry tests around an unknown centre.” Statistics , 53 (1), 43–57. Mira A (1999). “Distribution-free test for symmetry based on Bonferroni's measure.” Journal of Applied Statistics , 26 (8), 959–972. doi:10.1080/02664769921963 . Nikitin Y, Ahsanullah M (2015). “New U-empirical Tests of Symmetry Based on Extremal Order Statistics, and their Efficiencies.” In Mathematical Statistics and Limit Theorems , 231–248. Springer. doi:10.1007/978-3-319-12442-1_13 . Mixture of 2 normal distributions Description Generates random numbers from a mixture of 2 normal distributions Usage rmixnorm(n, mean1 = 0, sd1 = 1, mean2 = 0, sd2 = 1, p = 0.5) Arguments n number of observations mean1 mean of the first normal sd1 standard deviation of the first normal mean2 mean of the second normal sd2 standard deviation of the second normal p probability of the first normal Value Vector of random numbers from the specified mixture of normals. Azzalini skew logistic distribution Description Generates random numbers from the skew logistic distribution Usage rsl(n = 1, xi = 0, omega = 1, alpha = 0, dp = NULL) Arguments n sample size. xi vector of location parameters. omega vector of (positive) scale parameters. alpha vector of slant parameters. dp a vector of length 3 whose elements represent the parameters described above. If dp is specified, the individual parameters cannot be set. Value Vector of random numbers from Azzalini skew logistic distribution. symmetry: A package which implements tests for symmetry of random samples, linear models and generalized autoregressive conditional heteroskedasticity (GARCH) models Description The package contains a large number of tests for symmetry (and their bootstrap variants), which can be used to test the symmetry of random samples or of model residuals. Currently, the supported models are linear models and generalized autoregressive conditional heteroskedasticity (GARCH) models (fitted with the 'fGarch' package). The tests are implemented using the 'Rcpp' package which ensures great performance. Details To see the available tests, see TestStatistics For documentation on how to perform the tests, see symmetry_test Perform symmetry tests Description This is a generic function used to perform symmetry tests on numeric vectors or objects of class lm (linear models) and objects of class fGARCH (GARCH mdels fitted with the fGarch pack