.. _book_fig_chapter5_fig_malmquist_bias:


Malmquist Bias Example
----------------------
Figure 5.2

An illustration of the bias in a subsample selected using measurements with
finite errors, when the population distribution is a steep function. The
sample is drawn from the distribution :math:`p(x) \propto 10^{0.6x}`, shown
by the solid line in the left panel, and convolved with heteroscedastic errors
with widths in the range :math:`0.5 < \sigma < 1.5`. When a subsample is
selected using "measured" values, as illustrated in the left panel, the
distribution of differences between the "observed" and true values is biased,
as shown by the histogram in the right panel. The distribution is biased
because more objects with larger true x are scattered into the subsample
from the right side, than from the left side where the true x are smaller.



.. image:: ../images/chapter5/fig_malmquist_bias_1.png
    :scale: 100
    :align: center


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