/usr/include/openturns/swig/InverseGamma_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 | %feature("docstring") OT::InverseGamma
"InverseGamma distribution.
Helper class for defining the Inverse Gamma distribution which is the inverse of a :math:`\\\\Gamma` distribution.
Available constructors:
InverseGamma(*k, lambda*)
Parameters
----------
k : float, :math:`k > 0`,
Shape parameter. By default, :math:`k=1`.
lambda : float, :math:`\\\\lambda > 0`.
Scale parameter. By default, :math:`\\\\lambda=1`.
Notes
-----
:math:`X` follows an Inverse Gamma distribution of parameters :math:`(k, \\\\lambda)` means that :math:`\\\\dfrac{1}{X}` follows the :math:`\\\\Gamma(k, \\\\dfrac{1}{\\\\lambda})` distribution, with :math:`k>0` and :math:`\\\\lambda>0`.
Its probability density function is defined as:
.. math::
f_X(x) = \\\\dfrac{\\\\exp \\\\left( -\\\\dfrac{1}{\\\\lambda x}\\\\right)}{\\\\Gamma(k)\\\\lambda^kx^{k+1}}, \\\\quad x \\\\in [0; +\\\\infty[
with :math:`k >0 , \\\\lambda > 0`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{X} & = & \\\\dfrac{1}{\\\\lambda(k-1)} \\\\quad \\\\text{if } k>1 \\\\\\\\
\\\\Var{X} & = &\\\\dfrac{1}{\\\\lambda^2(k-1)^2(k-2)} \\\\quad \\\\text{if } k>2
\\\\end{eqnarray*}
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> distribution = ot.InverseGamma(1., 1.)
Draw a sample:
>>> sample = distribution.getSample(10)"
// ---------------------------------------------------------------------
%feature("docstring") OT::InverseGamma::getK
"Accessor to the parameter :math:`k`.
Returns
-------
k : float
Shape parameter :math:`k`."
// ---------------------------------------------------------------------
%feature("docstring") OT::InverseGamma::getLambda
"Accessor to the parameter :math:`\\\\lambda`.
Returns
-------
lambda : float
Scale parameter :math:`\\\\lambda`."
// ---------------------------------------------------------------------
%feature("docstring") OT::InverseGamma::setK
"Accessor to the distribution's shape parameter :math:`k`.
Parameters
----------
k : float, :math:`k > 0`
Parameter :math:`k`."
// ---------------------------------------------------------------------
%feature("docstring") OT::InverseGamma::setLambda
"Accessor to the distribution's scale parameter :math:`\\\\lambda`.
Parameters
----------
lambda : float, :math:`\\\\lambda > 0`
Parameter :math:`\\\\lambda`."
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