/usr/include/openturns/swig/Gumbel_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 | %feature("docstring") OT::Gumbel
"Gumbel distribution.
Available constructors:
Gumbel(*alpha=1.0, beta=0.0*)
Parameters
----------
alpha : float
scale parameter :math:`\\\\alpha > 0`.
beta : float
location parameter :math:`\\\\beta`.
Notes
-----
Its probability density function is defined as:
.. math::
f_X(x) = \\\\alpha
\\\\exp\\\\left[- \\\\alpha (x - \\\\beta)
- \\\\exp\\\\left(- \\\\alpha (x - \\\\beta)\\\\right)\\\\right],
\\\\quad x \\\\in \\\\Rset
with :math:`\\\\alpha > 0` and :math:`\\\\beta \\\\in \\\\Rset`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{X} & = & \\\\beta + \\\\frac{\\\\gamma}{\\\\alpha} \\\\\\\\
\\\\Var{X} & = & \\\\frac{\\\\pi^2}{6 \\\\alpha^2}
\\\\end{eqnarray*}
where :math:`\\\\gamma` is the Euler-Mascheroni constant.
It is possible to create a Gumbel distribution from the alternative parametrizations :math:`(\\\\mu, \\\\sigma)`: see :class:`~openturns.GumbelMuSigma` or :math:`(a,b)`: see :class:`~openturns.GumbelAB`. In that case, all the results are presented in that new parametrization.
In order to use the alternative parametrization only to create the distribution, see the example below: all the results will be presented in the native parametrization :math:`(\\\\alpha, \\\\beta)`.
Examples
--------
Create a distribution in its native parameters :math:`(\\\\alpha, \\\\beta)`:
>>> import openturns as ot
>>> myDist = ot.Gumbel(1.0, 0.0)
Create a it with the alternative parametrization :math:`(\\\\mu, \\\\sigma)`:
>>> myDist2 = ot.Gumbel()
>>> myDist2.setParameter(ot.GumbelMuSigma()([0.58, 1.28]))
Create a it with the alternative parametrization :math:`(a,b)`:
>>> myDist3 = ot.Gumbel()
>>> myDist3.setParameter(ot.GumbelAB()([0.0, 1.0]))
Create it from :math:`(\\\\mu, \\\\sigma)` and keep that parametrization for the remaining study:
>>> myParam = ot.GumbelMuSigma(0.58, 1.28)
>>> myDist4 = ot.ParametrizedDistribution(myParam)
Create it from :math:`(a,b)` and keep that parametrization for the remaining study:
>>> myParam = ot.GumbelAB(0.0, 1.0)
>>> myDist5 = ot.ParametrizedDistribution(myParam)
Draw a sample:
>>> sample = myDist.getSample(5)"
// ---------------------------------------------------------------------
%feature("docstring") OT::Gumbel::getAlpha
"Accessor to the distribution's scale parameter :math:`\\\\alpha`.
Returns
-------
alpha : float
Scale parameter :math:`\\\\alpha`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gumbel::getBeta
"Accessor to the distribution's location parameter :math:`\\\\beta`.
Returns
-------
beta : float
Location parameter :math:`\\\\beta`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gumbel::getMu
"Accessor to the distribution's mean.
Returns
-------
mu : float
Mean."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gumbel::getSigma
"Accessor to the distribution's standard deviation.
Returns
-------
sigma : float, :math:`\\\\sigma > 0`
Standard deviation."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gumbel::setAlpha
"Accessor to the distribution's scale parameter :math:`\\\\alpha`.
Parameters
----------
alpha : float, :math:`\\\\alpha > 0`
Scale parameter :math:`\\\\alpha`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gumbel::setBeta
"Accessor to the distribution's scale parameter :math:`\\\\beta`.
Parameters
----------
beta : float, :math:`\\\\beta \\\\in \\\\Rset`
Location parameter :math:`\\\\beta`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gumbel::setMuSigma
"Accessor to the distribution's mean and standard deviation.
Parameters
----------
mu : float
Mean.
sigma : float, :math:`\\\\sigma > 0`
Standard deviation."
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