Statistical Astronomy

Trumpler, Robert J.; Weaver, Harold F.

doi:10.1525/9780520347533

Cited by 200 publications

(102 citation statements)

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“…Finally, we also adopt the distance to the young, compact nebula K 3-35 (Tafoya et al 2011), determined using VLBI Exploration of Radio Astrometry (VERA) array observations of a bright water maser in the nebula 2 . Note that the trigonometric method is susceptible to the socalled Lutz-Kelker (L-K) bias (Lutz & Kelker 1973;Smith 2003Smith , 2006Francis 2014) which causes measured parallaxes to be systematically greater than their actual values in a statistical sense, and is broadly related to the Trumpler-Weaver bias (Trumpler & Weaver 1953). As emphasised by van Leeuwen (2007) and Francis (2014), the L-K bias is a sample statistical correction, and has not been applied to individual distances.…”

Section: Trigonometric Distancesmentioning

confidence: 99%

The Hα surface brightness - radius relation: a robust statistical distance indicator for planetary nebulae

Frew,

Parker,

Bojicic

2015

Preprint

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Measuring the distances to Galactic planetary nebulae (PNe) has been an intractable problem for many decades. We have now established a robust optical statistical distance indicator, the Hα surface brightness -radius or S Hα -r relation, which addresses this problem. We developed this relation from a critically evaluated sample of primary calibrating PNe. The robust nature of the method results from our revised calibrating distances with significantly reduced systematic uncertainties, and the recent availability of high-quality data, including updated nebular diameters and integrated Hα fluxes. The S Hα -r technique is simple in its application, requiring only an angular size, an integrated Hα flux, and the reddening to the PN. From these quantities, an intrinsic radius is calculated, which when combined with the angular size, yields the distance directly. Furthermore, we have found that optically thick PNe tend to populate the upper bound of the trend, while optically-thin PNe fall along the lower boundary in the S Hα -r plane. This enables sub-trends to be developed which offer even better precision in the determination of distances, as good as 18 per cent in the case of optically-thin, high-excitation PNe. This is significantly better than any previous statistical indicator. We use this technique to create a catalogue of statistical distances for over 1100 Galactic PNe, the largest such compilation in the literature to date. Finally, in an appendix, we investigate both a set of transitional PNe and a range of PN mimics in the S Hα -r plane, to demonstrate its use as a diagnostic tool. Interestingly, stellar ejecta around massive stars plot on a tight locus in S Hα -r space with the potential to act as a separate distance indicator for these objects.

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Section: Trigonometric Distancesmentioning

confidence: 99%

The Hα surface brightness - radius relation: a robust statistical distance indicator for planetary nebulae

Frew,

Parker,

Bojicic

2015

Preprint

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“…The answer for the first question seems to be quite clear: var M /n seems to be identical to the χ 2 value for M − 1 degree of freedom ( [Trumpler & Weaver 1953]; [Kendall & Stuart 1969]; [Press et al 1992]; the mean is obtained from the sample itself, and therefore the degree of freedom is M − 1). Nevertheless, the situation is not so obvious, because the χ 2 test needs n > 5 ( [Trumpler & Weaver 1953]; [Kendall & Stuart 1969]; [Press et al 1992]). In addition, some statistical text-books propose to use "quadratic" cells only ( [Diggle 1983], Chapt.…”

Section: The Testmentioning

confidence: 99%

“…There is no commonly accepted confidence level in statistics, above which the null-hypothesis should already be rejected ( [Trumpler & Weaver 1953]; [Kendall & Stuart 1969]). It is only a general agreement that confidence levels smaller than 95% should not be considered.…”

Section: The Testmentioning

confidence: 99%

A Remarkable Angular Distribution of the Intermediate Subclass of Gamma‐Ray Bursts

Mészáros

Bagoly

Horváth³

et al. 2000

ApJ

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In the article a test is developed, which allows to test the null-hypothesis of the intrinsic randomness in the angular distribution of gamma-ray bursts collected at the Current BATSE Catalog. The method is a modified version of the well-known counts-in-cells test, and fully eliminates the non-uniform skyexposure function of BATSE instrument. Applying this method to the case of 1 all gamma-ray bursts no intrinsic non-randomness was found. The test also did not find intrinsic non-randomnesses for the short and long gamma-ray bursts, respectively. On the other hand, using the method to the new intermediate subclass of gamma-ray bursts, the null-hypothesis of the intrinsic randomness for 181 intermediate gamma-ray bursts is rejected on the 96.4% confidence level. Taking 92 dimmer bursts from this subclass itself, we obtain the surprising result: This "dim" subclass of the intermediate subclass has an intrinsic non-randomness on the 99.3% confidence level. On the other hand, the 89 "bright" GRBs show no intrinsic non-randomness.

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“…This means that -at the begining -it is simply assumed that the Friedmannian model (either with Ω M > 1 or with with Ω M = 1 or with 0 < Ω M < 1) with zero cosmological constant is the correct model. Then it is asked that the observational data are in accordance with this model or not (for more details concerning this statistical approach see any standard text-book of Statistics (Trumpler & Weaver 1953;Kendall & Stuart 1976); from newer publications see, e.g., Feldman & Cousins (1998) and references therein).…”

Section: General Considerationsmentioning

confidence: 99%

“…Press et al (1992), Chapt.6.2) for ν = 58 degrees of freedom. Add here that fast approximate probability of the goodness-of-fit is obtainable also without the calculation of this function directly from the table of χ 2 distribution (see Trumpler & Weaver (1953), Table A5). One may use the fact that roughly for ν > 20 degrees of freedom the reduced χ 2 /ν distribution is practically not changing.…”

Section: The χ 2 Testmentioning

confidence: 99%

On the Reality of the Accelerating Universe

Mészáros

2002

ApJ

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Two groups recently deduced the positive value for the cosmological constant, concluding at a high (>= 99%) confidence level that the Universe should be accelerating. This conclusion followed from the statistical analysis of dozens of high-redshift supernovae. In this paper this conclusion is discussed. From the conservative frequentist's point of view the validity of null hypothesis of the zero cosmological constant is tested by the classical statistical chi^2 test for the 60 supernovae listed in Perlmutter et al. 1999 (ApJ, 517, 565). This sample contains 42 objects discovered in the frame of Supernova Cosmology Project and 18 low-redshift object detected earlier. Excluding the event SN1997O, which is doubtlessly an outlier, one obtains the result: The probability for seeing a worse chi^2 - if the null hypothesis is true - is in the 5% to 8% range, a value that does not indicate significant evidence againts the null. If one excludes further five possible outliers, proposed to be done by Perlmutter et al. 1999, then the sample of 54 supernovae is in an excellent accordance with the null hypothesis. It also seems that upernovae from the High-z Supernova Search Team does not change the acceptance of null hypothesis. This means that the rejection of the Einstein equations with zero cosmological constant - based on the supernova data alone - is still premature.Comment: 11 pages, no figures, accepted for publication in Ap

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Statistical Astronomy

Cited by 200 publications

References 0 publications

The Hα surface brightness - radius relation: a robust statistical distance indicator for planetary nebulae

The Hα surface brightness - radius relation: a robust statistical distance indicator for planetary nebulae

A Remarkable Angular Distribution of the Intermediate Subclass of Gamma‐Ray Bursts

On the Reality of the Accelerating Universe

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