Measurement of Hubble constant: non-Gaussian errors in HST Key Project data

Singh, Meghendra; Gupta, Shashikant; Pandey, A. K.; Sharma, Satendra

doi:10.1088/1475-7516/2016/08/026

Cited by 6 publications

(6 citation statements)

References 11 publications

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“…For example, the observed data may not be a random sample of independent, identically distributed variables (need to test the critical linear combinations of variables), or the observed distribution of data may be heavy-tailed. Apparently, there is no guarantee that the Gaussian feature is invariant for the astronomical data (Chen et al 2003;Crandall et al 2015;Singh et al 2016;Zhang 2017). Similarly, for simple linear regression, one of model assumptions explicitly indicate that the probability distribution of the random component is normal (Mendenhall & JSincich 2011).…”

Section: Analysis Of Methodologymentioning

confidence: 99%

“…In observed astrophysical fields, Gaussian statistics has been an important point followed by astronomers with great interests for quite a long time. However, Chen et al (2003), Singh et al (2016) and Bailey (2017) have demonstrated that the prior assumptions can not arbitrarily depend on the normality. Clearly, other more robust approaches are needed.…”

Section: Confidence Intervals and Bootstrap Methodsmentioning

confidence: 99%

“…However, the astrophysical fact is that non-Normality might be more prevailing in measurements than once thought (Chen et al 2003;Crandall et al 2015;Das & Imon 2016). For instance, Singh et al (2016) used Kolmogorov-Smirnov (K-S) test and pointed out that measurements of Hubble constant show non-Gaussian error distribution in HST Key project Data. There are several tests for normality, such as graphical method, analytical test procedures, supernormality and rescaled moments test (Das & Imon 2016).…”

Section: Non-normality Of Error Distributionmentioning

confidence: 99%

“…where F n (X) depends on the observed sample and denotes the empirical distribution function. F(X) is the theoretical cumulative distribution function of the Gaussian distribution (Singh et al 2016). Note that our goal in this subsection is only to test normality of one-dimension data set instead of estimating the parameters, and applying the K-S test needs to be cautious due to inapplicability in some situations (Feigelson & Babu 2012).…”

Section: Non-normality Of Error Distributionmentioning

confidence: 99%

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Most Frequent Value Statistics and the Hubble Constant

Zhang

2018

PASP

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The measurement of Hubble constant (H 0 ) is clearly a very important task in astrophysics and cosmology. Based on the principle of minimization of the information loss, we propose a robust most frequent value (MFV) procedure to determine H 0 , regardless of the Gaussian or non-Gaussian distributions. The updated data set of H 0 contains the 591 measurements including the extensive compilations of Huchra and other researchers. The calculated result of the MFV is H 0 =67.498 km s −1 Mpc −1 , which is very close to the average value of recent Planck H 0 value (67.81±0.92 km s −1 Mpc −1 and 66.93±0.62 km s −1 Mpc −1 ) and Dark Energy Survey Year 1 Results. Furthermore, we apply the bootstrap method to estimate the uncertainty of the MFV of H 0 under different conditions, and find that the 95% confidence interval for the MFV of H 0 measurements is [66.319, 68.690] associated with statistical bootstrap errors, while a systematically larger estimate is H 67.498 0 3.278 7.970 = -+ (systematic uncertainty). Especially, the non-Normality of error distribution is again verified via the empirical distribution function test including Shapiro-Wilk test and Anderson-Darling test. These results illustrate that the MFV algorithm has many advantages in the analysis of such statistical problems, no matter what the distributions of the original measurements are.

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Section: Analysis Of Methodologymentioning

confidence: 99%

Section: Confidence Intervals and Bootstrap Methodsmentioning

confidence: 99%

Section: Non-normality Of Error Distributionmentioning

confidence: 99%

Section: Non-normality Of Error Distributionmentioning

confidence: 99%

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Most Frequent Value Statistics and the Hubble Constant

Zhang

2018

PASP

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“…Another non-negligible point is the heavytailed problem of the observed distribution. Essentially, no one can be accurately aware whether or not the normality feature is intrinsic for the measurement data [12,16,55,57,58].…”

Section: Discussionmentioning

confidence: 99%

MFV approach to robust estimate of neutron lifetime

Zhang

et al. 2022

Eur. Phys. J. C

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Aiming at evaluating the lifetime of the neutron, we introduce a novel statistical method to analyse the updated compilation of precise measurements including the 2022 dataset of Particle Data Group (PDG). Based on the minimization for the information loss principle, unlike the median statistics method, we apply the most frequent value (MFV) procedure to estimate the neutron lifetime, irrespective of the Gaussian or non-Gaussian distributions. Providing a more robust way, the calculated result of the MFV is $$\tau _n=881.16^{+2.25}_{-2.35}$$ τ n = 881 . 16 - 2.35 + 2.25 s with statistical bootstrap errors, while the result of median statistics is $$\tau _n=881.5^{+5.5}_{-3}$$ τ n = 881 . 5 - 3 + 5.5 s according to the binomial distribution. Using the different central estimates, we also construct the error distributions of neutron lifetime measurements and find the non-Gaussianity, which is still meaningful.

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