A Cumulative Residual Entropy Characterization of the Rayleigh Distribution and Related Goodness-of-Fit Test

Baratpour, S.; Khodadadi, F.

doi:10.18869/acadpub.jsri.9.2.115

Cited by 8 publications

(6 citation statements)

References 28 publications

(19 reference statements)

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“…certainty). This theoretical LoS probability curve across the centre of the galaxy is broadly in agreement with the observational velocity probability curve presented by McNamara et al ( 2004), and has similarities to a Rayleigh distribution, suggesting the distribution has a maximum Cumulative Residual Entropy (Baratpour & Khodadadi 2012). More realistic curves to match observational values would introduce a mass distribution function for the stars, but although more complex, the fundamental dynamics would not be changed.…”

Section: Time-distance and Velocity-radius Curves For M15supporting

confidence: 88%

The Dynamics of Globular Clusters and Elliptical Galaxies

Marr¹

2020

Preprint

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Equations of motion are generated for an idealised model spherical galaxy or globular cluster evolving from the epoch of galactic separation until it attains a semi-equilibrium state through gravitational collapse. The theoretical radial surface density is computed and compared with two globular clusters, M15 and M80, and shows a good fit to observational data. The model is contrasted with King's model, and mean cycle time and velocity are computed. The velocity-radius curve is developed, and Gaussian RMS values derived from which half-light radius vs. mass are plotted for 735 spherical objects, including 544 normal ellipticals and compact, massive, and intermediate mass objects. These latter show a linear mean log-log R − M vir slope of 0.604 ± 0.003, equivalent to a Faber-Jackson slope of γ = 3.66±0.009 over a mass range of 7 decades. and a slope of 0.0045 ± 0.0001 on a semi-log plot of R 1/2 − σ. Globular clusters, dwarf elliptical and dwarf spherical galaxies show a distinct anomaly on these plots, consistent with the ellipticals containing a supermassive black hole (SMBH) whose mass increases as the velocity dispersion increases, compared with the remaining types of spherical or irregular galaxies without a massive core.

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Section: Time-distance and Velocity-radius Curves For M15supporting

confidence: 88%

The Dynamics of Globular Clusters and Elliptical Galaxies

Marr¹

2020

Preprint

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“…, can be constructed, where X = 1 n n i=1 X i . Rao et al (2004) proved the consistency of the CRE and Baratpour and Khodadadi (2012) extended the proof to the test statistic CK n .…”

Section: Tests Based On Entropymentioning

confidence: 89%

A Review of Goodness-of-Fit Tests for the Rayleigh Distribution

Liebenberg

Allison²

2023

AJS

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The Rayleigh distribution has recently become popular as a model for a range of phenomena. As a result, a number of goodness-of-fit tests have been developed for this distribution. In this paper, we provide the first overview of goodness-of-fit tests for the Rayleigh distribution and compare these tests in a Monte-Carlo study to identify the tests that provide the highest powers against a wide range of alternatives. Our findings suggest that two recently developed tests as well as a test based on the Laplace transform and a test based on the Hellinger distance are the better performing tests.

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“…However, even though the applications of the Rayleigh distribution increased significantly over the past few decades, literature on tests specifically developed for the Rayleigh distribution is relatively scarce. Some of these include a test proposed by [10] based on the empirical Laplace transform, a test based on entropy suggested by [11] as well as [12] and an empirical likelihood based test by [13]. It has become a common approach to use distributional characterizations to propose goodness-of-fit testing procedures, see, e.g., Ref.…”

Section: Introductionmentioning

confidence: 99%

“…The traditional Kolmogorov-Smirnov (KS n ), Cramér-von Mises (CM n ) and Anderson-Darling (AD n ) tests; • A test based on the empirical Laplace transform proposed by [10], EL n,a ; • A test based on the cumulative residual entropy proposed by [11], CR n , and • A test based on an estimator of the Kullback-Leibler divergence proposed by [12], KL n,a .…”

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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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A Cumulative Residual Entropy Characterization of the Rayleigh Distribution and Related Goodness-of-Fit Test

Cited by 8 publications

References 28 publications

The Dynamics of Globular Clusters and Elliptical Galaxies

The Dynamics of Globular Clusters and Elliptical Galaxies

A Review of Goodness-of-Fit Tests for the Rayleigh Distribution

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

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