A Monte Carlo evaluation of the performance of two new tests for symmetry

Allison, James S.; Pretorius, Charl

doi:10.1007/s00180-016-0680-4

Cited by 10 publications

(3 citation statements)

References 32 publications

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“…Remark 1. The most commonly used choices for the weight function w a (•) are w a (t) = e −a|t| and w a (t) = e −at 2 (see, e.g., [18,19]). Due to the positive support of the Rayleigh distribution, we use w a (t) = e −a|t| = e −at , t ≥ 0.…”

Section: Test Statisticmentioning

confidence: 99%

Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data

2022

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We propose a new goodness-of-fit test for the Rayleigh distribution which is based on a distributional fixed-point property of the Stein characterization. The limiting null distribution of the test is derived and the consistency against fixed alternatives is also shown. The results of a finite-sample comparison is presented, where we compare the power performance of the new test to a variety of other tests. In addition to existing tests for the Rayleigh distribution we also exploit the link between the exponential and Rayleigh distributions. This allows us to include some powerful tests developed specifically for the exponential distribution in the comparison. It is found that the new test outperforms competing tests for many of the alternative distributions. Interestingly, the highest estimated power, against all alternative distributions considered, is obtained by one of the tests specifically developed for the Rayleigh distribution and not by any of the exponentiality tests based on the transformed data. The use of the new test is illustrated on a real-world COVID-19 data set.

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Section: Test Statisticmentioning

confidence: 99%

Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data

2022

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“…Fan, Li, and Wang (2017) claimed that the recently proposed penalized least-squares methods in high-dimensional settings are sensitive to the symmetry of the error distributions when selecting the non zero parameters in the mean regression, and these penalized methods usually need the assumption that the distribution of model error is symmetric about zero. To measure the symmetry or asymmetry for a continuous variable or the model error, there are amount of work in the literature, see for example, Ngatchouwandji (2009); Ngatchouwandji and Harel (2013); Allison and Pretorius (2017); Fan and Gencay (1995); Ahmad and Li (1997); Neumeyer, Dette, and Nagel (2005); Davis and Quade (1978); Harald (1928); Rothman and Woodroofe (1972); Srinivasan and Godio (1974); Butler (1969); Orlov (1972); Randles et al (1980); Gupta (1967); Csörgő and Heathcote (1987); Antille, Kersting, and Zucchini (1982); Hill and Rao (1977); Bhattacharya (2009); Li and Morris (1991); Gastwirth (1971). Recently, Patil, Patil, and Bagkavos (2012) proposed a measure of asymmetry by using the correlation coefficient of the density function and distribution function, and showed this correlation coefficient-based measure works well in capturing the visual impression of asymmetry in a given density curve.…”

Section: Introductionmentioning

confidence: 99%

Testing symmetry of model errors for non linear multiplicative distortion measurement error models

Zhang,

Feng,

Zhou

2023

Communications in Statistics - Theory and Methods

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To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibrationbased residuals, and the conditional absolute logarithmic calibrationbased residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage.

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“…becomes the Shannon's entropy as given in(4). There are also characterization results based on some information measures of order statistics and record values in the literature.…”

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confidence: 99%

Characterization of symmetric distributions based on concomitants of ordered variables from FGMs family of bivariate distributions

Ahmadi

Fashandi

2019

Filomat

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Several characterization results of a symmetric distribution based on concomitants of order statistics as well as k-records from Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions are established. These include characterizations of a symmetric distribution on the basis of equality in distribution, moments, Rényi and Tsallis entropies of concomitants of upper and lower order statistics, also in terms of the same properties of concomitants of upper and lower k-records.

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A Monte Carlo evaluation of the performance of two new tests for symmetry

Cited by 10 publications

References 32 publications

Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data

Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data

Testing symmetry of model errors for non linear multiplicative distortion measurement error models

Characterization of symmetric distributions based on concomitants of ordered variables from FGMs family of bivariate distributions

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