Astron. Astrophys. 340, L35-L38 (1998)
5. Conclusions
Among the two methods presented in this paper to represent the pdf
of the distance determined from the parallax
has two disavantages.
-
The distribution is strongly asymmetrical and can be used only
numerically in later computations.
-
In deriving the rms from the variances, the unprobable large values
of x play a major role, increasing the rms in a way that can be
considered as unrealistic.
The Gaussian representation of
has the advantage of being usable as such in
further evaluations of uncertainties of quantities depending among
others on the observed parallaxes. One may remark from Table 2
that the quality of fit worsens rather quickly when k
increases. For this reason, our suggestion is to use the solution with
k=2.5 which encompasses 98.64% of the probability distributions
and formulae (13) and (15). One may remark also that with this
Gaussian pdf, the position of the maximum correspond closely to the
mean between the maximum given by and
. It is however to be noted that its derivation
used the true rather than the observed value of the parallax. This may
introduce an additional uncertainty, particularly for large
.
Finally, the tables presented show that the solutions degrade for
large values of . It is not reasonnable to use
any pdf for . Then, the determination of the
distance from parallaxes looses its physical significance, and
photometric determinations are definitely better. In any case, cutting
a sample at some value of may introduce a bias,
so that users are invited to ascertain that the sample satisfies the
conditions of applicability of the method.
© European Southern Observatory (ESO) 1998
Online publication: November 9, 1998
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