...unbiased

The estimator 26#26 given Eq. (6 (click here)) is unbiased in the following sense. Suppose a sample of N galaxies homogeneously distributed in space and with the same measured m and p. For N large enough, the distances average on the sample 29#29 will coincide with the estimator 26#26 (i.e. 30#30 where 31#31 is the mathematical expectancy of r, given m and p). The statistics of Eq. (6 (click here)) is generally used for inferring the distance of individual galaxies. It amounts to apply the above statistical formalism on a sample containing only one object, which cannot be done without ambiguousness.

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...correct

Note however that the converse does not hold since the Hubble constant H₀, DTF zero-point b^D and intrinsic DTF dispersion 12#12 degenerate into a single parameter 169#169.

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...approach

It can be proven similarly that 173#173 .

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...result

It can be proven similarly that 193#193 .

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...R(r^*)=0.25)

The standard deviation 262#262 is proportional to R(r^*)^-1/2, as expected.

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...flow

Since the real distance of MAT galaxies are not known, the contribution of the radial peculiar velocity inferred by GA flow model to observed redshift has been added under the approximation that galaxies distances are given by their observed redshifts.

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...catalog

Since the subsampling procedure in distance estimate depends on the values of 257#257 and 258#258, few iterations were performed in order to achieve the stable situation presented in Fig. 7.

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...)

Independently to these velocity bias problems, relative "zero-point" estimator always suffer from an additional bias inherited from the statistical uncertainties on the slope estimate (i.e. 309#309.

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