/usr/include/openturns/swig/MeixnerDistribution_doc.i is in libopenturns-dev 1.7-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 | %feature("docstring") OT::MeixnerDistribution
"Meixner distribution.
Available constructors:
MeixnerDistribution(*alpha=1.0, beta=0., delta=1.0, mu=0.*)
Parameters
----------
alpha : float, :math:`\\\\alpha > 0`
Scale parameter.
beta : float, :math:`\\\\beta \\\\in [-\\\\pi; \\\\pi]`
Skewness parameter.
delta : float, :math:`\\\\delta > 0`
Shape parameter.
mu : float
Location parameter :math:`\\\\mu`.
Notes
-----
Its probability density function is defined as:
.. math::
f_X(x) = \\\\frac{\\\\left(2 \\\\cos(\\\\beta / 2)\\\\right)^{2 \\\\delta}}
{2 \\\\alpha \\\\pi \\\\Gamma(2 \\\\delta)}
\\\\exp\\\\left(\\\\frac{\\\\beta (x - \\\\mu)}{\\\\alpha}\\\\right)
\\\\left|\\\\Gamma\\\\left(\\\\delta + i \\\\frac{x - \\\\mu}{\\\\alpha}
\\\\right)\\\\right|^2,
\\\\quad x \\\\in \\\\Rset
with :math:`\\\\alpha, \\\\delta > 0`, :math:`\\\\beta \\\\in [-\\\\pi; \\\\pi]`,
:math:`\\\\mu \\\\in \\\\Rset` and where :math:`i^2 = -1`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{X} & = & \\\\alpha \\\\delta \\\\tan(\\\\beta / 2) + \\\\mu \\\\\\\\
\\\\Var{X} & = & \\\\frac{\\\\alpha^2 \\\\delta}{1 + \\\\cos(\\\\beta)}
\\\\end{eqnarray*}
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> distribution = ot.MeixnerDistribution(1., 0., 1., 0.)
Draw a sample:
>>> sample = distribution.getSample(10)"
// ---------------------------------------------------------------------
%feature("docstring") OT::MeixnerDistribution::getAlpha
"Accessor to the distribution's scale parameter :math:`\\\\alpha`.
Returns
-------
alpha : float
Scale parameter :math:`\\\\alpha`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MeixnerDistribution::getBeta
"Accessor to the distribution's skewness parameter :math:`\\\\beta`.
Returns
-------
beta : float
Skewness parameter :math:`\\\\beta`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MeixnerDistribution::getDelta
"Accessor to the distribution's shape parameter :math:`\\\\delta`.
Returns
-------
delta : float
Shape parameter :math:`\\\\delta`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MeixnerDistribution::getMu
"Accessor to the distribution's location parameter :math:`\\\\mu`.
Returns
-------
mu : float
Location parameter :math:`\\\\mu`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MeixnerDistribution::setAlpha
"Accessor to the distribution's scale parameter :math:`\\\\alpha`.
Parameters
----------
alpha : float, :math:`\\\\alpha > 0`
Scale parameter :math:`\\\\alpha`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MeixnerDistribution::setBeta
"Accessor to the distribution's skewness parameter :math:`\\\\beta`.
Parameters
----------
beta : float, :math:`\\\\beta \\\\in [-\\\\pi; \\\\pi]`
Skewness parameter :math:`\\\\beta`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MeixnerDistribution::setDelta
"Accessor to the distribution's shape parameter :math:`\\\\delta`.
Parameters
----------
delta : float, :math:`\\\\delta > 0`
Shape parameter :math:`\\\\delta`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MeixnerDistribution::setMu
"Accessor to the distribution's location parameter :math:`\\\\mu`.
Parameters
----------
mu : float, :math:`\\\\mu \\\\in \\\\Rset`
Location parameter :math:`\\\\mu`."
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