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Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data. MATHEMATICS 2022. [DOI: 10.3390/math10081316] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
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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van Heerden CJL, Pretorius C. Tests for symmetry based on the integrated empirical process. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.1998832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
| | - Charl Pretorius
- North-West University, Potchefstroom, South Africa
- University of the Free State, Bloemfontein, South Africa
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Comparison of symmetry tests against some skew-symmetric alternatives in i.i.d. and non-i.i.d. setting. Comput Stat Data Anal 2020. [DOI: 10.1016/j.csda.2020.106991] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Niu C, Guo X, Li Y, Zhu L. Pairwise distance-based tests for conditional symmetry. Comput Stat Data Anal 2018. [DOI: 10.1016/j.csda.2018.06.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Nikitin YY. Local exact Bahadur efficiencies of two scale-free tests of normality based on a recent characterization. METRIKA 2018. [DOI: 10.1007/s00184-018-0673-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Affiliation(s)
- Jun Zhang
- College of Mathematics and Statistics, Shenzhen University, Shenzhen, People's Republic of China
- Institute of Statistical Sciences, Shenzhen-Hong Kong Joint Research Center for Applied Statistical Sciences, Shenzhen University, Shenzhen, People's Republic of China
| | - Jing Zhang
- College of Mathematics and Statistics, Shenzhen University, Shenzhen, People's Republic of China
| | - Xuehu Zhu
- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, People's Republic of China
| | - Tao Lu
- Department of Mathematics and Statistics, University of Nevada, Reno, NV, USA
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