/usr/include/openturns/swig/GeneralizedExtremeValue_doc.i is in libopenturns-dev 1.9-5.
This file is owned by root:root, with mode 0o644.
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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 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 | %feature("docstring") OT::GeneralizedExtremeValue
"Generalized ExtremeValue distribution.
Available constructors:
GeneralizedExtremeValue(*mu=0.0, sigma=1.0, xi=0.0*)
Parameters
----------
mu : float
Location parameter :math:`\\\\sigma`.
sigma : float, :math:`\\\\sigma > 0`
Scale parameter :math:`\\\\sigma`.
xi : float
Shape parameter :math:`\\\\xi`.
Notes
-----
Its cumulative distribution function is defined as:
.. math::
F_X(x) = \\\\left\\\\{\\\\begin{array}{ll}
\\\\displaystyle \\\\exp\\\\left\\\\{-\\\\left[1+\\\\xi\\\\left(\\\\dfrac{x-\\\\mu}{\\\\sigma}\\\\right)\\\\right]^{-1/\\\\xi}\\\\right\\\\}
& \\\\text{ if } \\\\xi \\\\neq 0 \\\\\\\\
\\\\displaystyle \\\\exp\\\\left\\\\{-\\\\left(\\\\dfrac{x-\\\\mu}{\\\\sigma}\\\\right)\\\\right\\\\}
& \\\\text{ if } \\\\xi = 0
\\\\end{array}\\\\right.
for :math:`\\\\quad x \\\\in [\\\\mu-\\\\sigma/\\\\xi, +\\\\infty) \\\\text{ if } \\\\xi>0, x \\\\in \\\\Rset \\\\text{ if } \\\\xi=0, x \\\\in (-\\\\infty,\\\\mu-\\\\sigma/\\\\xi] \\\\text{ if } \\\\xi<0.`, with :math:`\\\\sigma > 0` and :math:`\\\\xi \\\\in \\\\Rset`.
:math:`F_X` is zero for :math:`x` less than the lower bound of the support and one for :math:`x` greater than the upper bound of the support.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{X} & = & \\\\left\\\\{\\\\begin{array}{ll}
\\\\mu+\\\\sigma\\\\dfrac{\\\\Gamma(1-\\\\xi)-1}{\\\\xi} & \\\\text{ if } \\\\xi < 1, \\\\xi\\\\neq 0 \\\\\\\\
\\\\mu + \\\\sigma\\\\gamma & \\\\text{ if } \\\\xi= 0 \\\\\\\\
\\\\infty & \\\\text{ if } \\\\xi \\\\geq 1
\\\\end{array}
\\\\right.\\\\\\\\
\\\\Var{X} & = & \\\\left\\\\{\\\\begin{array}{ll}
\\\\sigma^2\\\\dfrac{\\\\Gamma(1-2\\\\xi)-\\\\Gamma^2(1-\\\\xi)}{\\\\xi^2} & \\\\text{ if } \\\\xi < 1/2, \\\\xi\\\\neq 0 \\\\\\\\
\\\\sigma^2\\\\dfrac{\\\\pi^2}{6} & \\\\text{ if } \\\\xi= 0 \\\\\\\\
\\\\infty & \\\\text{ if } \\\\xi \\\\geq 1/2
\\\\end{array}
\\\\right.
\\\\end{eqnarray*}
where :math:`\\\\gamma` is Euler's constant.
Link with other distributions: if :math:`X\\\\sim`:class:`~openturns.GeneralizedExtremeValue`:math:`(\\\\mu, \\\\sigma, \\\\xi)`, then :math:`X\\\\sim`:class:`~openturns.Frechet`:math:`(1/\\\\xi, \\\\sigma/\\\\xi, \\\\mu-\\\\sigma/\\\\xi)` if :math:`\\\\xi>0`, :math:`-X\\\\sim`:class:`~openturns.Weibull`:math:`(sigma/\\\\xi, -1/\\\\xi, \\\\sigma/\\\\xi-\\\\mu)` if :math:`\\\\xi<0` (note the minus sign) and :math:`X\\\\sim`:class:`~openturns.Gumbel`:math:`(1/\\\\sigma, \\\\mu)` if :math:`\\\\xi=0`.
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> distribution = ot.GeneralizedExtremeValue(1.0, 2.0, -0.2)
Draw a sample:
>>> sample = distribution.getSample(5)"
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralizedExtremeValue::getActualDistribution
"Accessor to the internal distribution.
Returns
-------
distribution : :class:`~openturns.Distribution`
The actual distribution in charge of the computation (:class:`~openturns.Weibull`, :class:`~openturns.Frechet`, :class:`~openturns.Gumbel`)."
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralizedExtremeValue::getMu
"Accessor to the distribution's location parameter :math:`\\\\mu`.
Returns
-------
mu : float
Location parameter :math:`\\\\mu`."
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralizedExtremeValue::getSigma
"Accessor to the distribution's scale parameter :math:`\\\\sigma`.
Returns
-------
sigma : float
Scale parameter :math:`\\\\sigma`."
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralizedExtremeValue::getXi
"Accessor to the distribution's shape parameter :math:`\\\\xi`.
Returns
-------
xi : float
Shape parameter :math:`\\\\xi`."
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralizedExtremeValue::setActualDistribution
"Accessor to the internal distribution.
Parameters
----------
distribution : :class:`~openturns.Distribution`
The actual distribution in charge of the computation (:class:`~openturns.Weibull`, :class:`~openturns.Frechet`, :class:`~openturns.Gumbel`)."
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralizedExtremeValue::setMu
"Accessor to the distribution's location parameter :math:`\\\\mu`.
Parameters
----------
mu : float
Location parameter :math:`\\\\mu`."
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralizedExtremeValue::setSigma
"Accessor to the distribution's scale parameter :math:`\\\\sigma`.
Parameters
----------
sigma : float, :math:`\\\\sigma > 0`
Scale parameter :math:`\\\\sigma`."
// ---------------------------------------------------------------------
%feature("docstring") OT::GeneralizedExtremeValue::setXi
"Accessor to the distribution's shape parameter :math:`\\\\xi`.
Parameters
----------
xi : float, :math:`\\\\xi \\\\in \\\\Rset`
Shape parameter :math:`\\\\xi`."
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