Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Peculiar Motions of Early-Type Galaxies in Two Distant Regions VI:
  The Maximum Likelihood Gaussian Algorithm   The EFAR project is designed to measure the properties and peculiar motions
of early-type galaxies in two distant regions. Here we describe the maximum
likelihood algorithm we developed to investigate the correlations between the
parameters of the EFAR database. One-, two-, and three-dimensional gaussian
models are constructed to determine the mean value and intrinsic spread of the
parameters, and the slopes and intrinsic parallel and orthogonal spread of the
Mgb'-Mg2, Mg2-sigma, Mgb'-sigma relations, and the Fundamental Plane. In the
latter case, the cluster peculiar velocities are also determined. We show that
this method is superior to ``canonical'' approaches of least-squares type,
which give biased slopes and biased peculiar velocities. We test the algorithm
with Monte Carlo simulations of mock EFAR catalogues and derive the systematic
and random errors on the estimated parameters. We find that random errors are
always dominant. We estimate the influence of systematic errors due to the way
clusters were selected and the hard limits and uncertainties in the selection
function parameters for the galaxies. We explore the influence of uniform
distributions in the Fundamental Plane parameters and the errors. We conclude
that the mean peculiar motions of the EFAR clusters can be determined reliably.
In particular, the placement of the two EFAR sample regions relative to the
Lauer and Postman dipole allows us to strongly constrain the amplitude of the
bulk motion in this direction.

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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: eess