/usr/include/openturns/swig/Gamma_doc.i is in libopenturns-dev 1.9-5.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 | %feature("docstring") OT::Gamma
"Gamma distribution.
Available constructors:
Gamma(*k=1.0, lambda=1.0, gamma=0.0*)
Parameters
----------
k : float
shape parameter :math:`k > 0` with :math:`k = (\\\\mu - \\\\gamma)^2 / \\\\sigma^2`.
lambda : float
scale parameter :math:`\\\\lambda > 0` with :math:`\\\\lambda = (\\\\mu - \\\\gamma) / \\\\sigma^2`.
gamma : float, optional
Shift parameter :math:`\\\\gamma`.
Notes
-----
Its probability density function is defined as:
.. math::
f_X(x) = \\\\frac{\\\\lambda}{\\\\Gamma(k)}
\\\\left(\\\\lambda (x - \\\\gamma)\\\\right)^{k - 1}
\\\\exp\\\\left(- \\\\lambda (x - \\\\gamma)\\\\right),
\\\\quad x \\\\in [\\\\gamma; +\\\\infty[
with :math:`k, \\\\lambda > 0` and :math:`\\\\gamma \\\\in \\\\Rset`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{X} & = & \\\\frac{k}{\\\\lambda} + \\\\gamma \\\\\\\\
\\\\Var{X} & = & \\\\frac{\\\\sqrt{k}}{\\\\lambda}
\\\\end{eqnarray*}
It is possible to create a Gamma distribution from the alternative parametrization :math:`(\\\\mu, \\\\sigma, \\\\gamma)`: see :class:`~openturns.GammaMuSigma`. In that case, all the results are presented in that new parametrization.
In order to use the alternative parametrization :math:`(\\\\mu, \\\\sigma, \\\\gamma)` only to create the distribution, see the example below: all the results will be presented in the native parametrization :math:`(k, \\\\lambda, \\\\gamma)`.
Examples
--------
Create a distribution from its native parameters :math:`(k, \\\\lambda, \\\\gamma)`:
>>> import openturns as ot
>>> myDist = ot.Gamma(1.0, 1.0, 0.0)
Create a it from the alternative parametrization :math:`(\\\\mu, \\\\lambda, \\\\gamma)`:
>>> myDist2 = ot.Gamma()
>>> myDist2.setParameter(ot.GammaMuSigma()([1.0, 1.0, 0.0]))
Create it from :math:`(\\\\mu, \\\\lambda, \\\\gamma)` and keep that parametrization for the remaining study:
>>> myParam = ot.GammaMuSigma(1.5, 2.5, -0.5)
>>> myDist3 = ot.ParametrizedDistribution(myParam)
Draw a sample:
>>> sample = myDist.getSample(5)"
// ---------------------------------------------------------------------
%feature("docstring") OT::Gamma::getK
"Accessor to the distribution's shape parameter :math:`k`.
Returns
-------
k : float
Shape parameter :math:`k`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gamma::getLambda
"Accessor to the distribution's scale parameter :math:`\\\\lambda`.
Returns
-------
lambda : float
Scale parameter :math:`\\\\lambda`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gamma::getGamma
"Accessor to the distribution's shift parameter :math:`\\\\gamma`.
Returns
-------
gamma : float
Shift parameter :math:`\\\\gamma`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gamma::getMu
"Accessor to the distribution's mean.
Returns
-------
mu : float
Mean."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gamma::getSigma
"Accessor to the distribution's standard deviation.
Returns
-------
sigma : float, :math:`\\\\sigma > 0`
Standard deviation."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gamma::setK
"Accessor to the distribution's shape parameter :math:`k`.
Parameters
----------
k : float, :math:`k > 0`
Shape parameter :math:`k`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gamma::setLambda
"Accessor to the distribution's scale parameter :math:`\\\\lambda`.
Parameters
----------
lambda : float, :math:`\\\\lambda > 0`
Scale parameter :math:`\\\\lambda`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gamma::setKLambda
"Set the distribution's parameters.
For scale parameter :math:`\\\\lambda` and shape parameter :math:`k`.
Parameters
----------
k : float, :math:`k > 0`
Shape parameter :math:`k`.
lambda : float, :math:`\\\\lambda > 0`
Scale parameter :math:`\\\\lambda`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gamma::setGamma
"Accessor to the distribution's shift parameter :math:`\\\\gamma`.
Parameters
----------
gamma : float, :math:`\\\\gamma \\\\in \\\\Rset`
Shift parameter :math:`\\\\gamma`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Gamma::setMuSigma
"Accessor to the distribution's mean and standard deviation.
Parameters
----------
mu : float, :math:`\\\\mu > \\\\gamma`
Mean.
sigma : float, :math:`\\\\sigma > 0`
Standard deviation."
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