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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | %feature("docstring") OT::Epanechnikov
"Epanechnikov distribution.
Available constructor:
Epanechnikov()
Notes
-----
Its probability density function is defined as:
.. math::
f_X(x) = \\\\frac{3}{4}\\\\,(1 - x^2), \\\\quad x \\\\in [-1; 1]
It has no parameters and is intended to be used as a kernel within a
:class:`~openturns.KernelSmoothing`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{X} & = & 0 \\\\\\\\
\\\\Var{X} & = & \\\\frac{1}{5}
\\\\end{eqnarray*}
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> distribution = ot.Epanechnikov()
Draw a sample:
>>> sample = distribution.getSample(10)"
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