/usr/include/openturns/swig/Student_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 | %feature("docstring") OT::Student
"Student distribution.
Available constructors:
Student(*nu=3.0, d=1*)
Student(*nu, mu, sigma=1.0*)
Student(*nu, mu, sigma, R*)
Parameters
----------
d : int, :math:`d \\\\geq 1`
Dimension.
nu : float, :math:`\\\\nu > 0`
Generalised number degrees of freedom.
mu : float :math:`\\\\mu`, sequence of float, :math:`\\\\vect{\\\\mu} \\\\in \\\\Rset^d`, optional
If :math:`\\\\nu > 1`: mean.
If :math:`\\\\nu = 1`: location parameter.
Default is :math:`\\\\vect{\\\\mu} = (0, \\\\dots, 0) \\\\in \\\\Rset^d`.
sigma : float :math:`\\\\sigma`, sequence of float, :math:`\\\\vect{\\\\sigma} \\\\in \\\\Rset^{*d}_+`, optional
Scale parameter.
Default is :math:`\\\\vect{\\\\sigma} = (1, \\\\dots, 1) \\\\in \\\\Rset^d`.
R : :class:`~openturns.CorrelationMatrix` :math:`\\\\mat{R} \\\\in \\\\Rset^d \\\\times \\\\Rset^d`, optional
If :math:`\\\\nu > 2`: correlation matrix.
If :math:`\\\\nu \\\\leq 2`: generalized correlation matrix.
Default is :math:`\\\\mat{R} = I_d \\\\in \\\\Rset^d \\\\times \\\\Rset^d`.
Notes
-----
Its probability density function is defined as:
.. math::
f_X(x) = \\\\frac{\\\\Gamma \\\\left(\\\\frac{\\\\nu + d}{2}\\\\right)}
{(\\\\pi \\\\nu) ^ {\\\\frac{d}{2}} \\\\Gamma \\\\left(\\\\frac{\\\\nu}{2}\\\\right)}
\\\\frac{\\\\left| \\\\mathrm{det}(\\\\mat{R}) \\\\right| ^ {-1/2}}
{\\\\prod_{k = 1} ^ d \\\\sigma_k}
\\\\left(1 + \\\\frac{\\\\vect{z} ^ t \\\\mat{R} ^ {-1} \\\\vect{z}}{\\\\nu}
\\\\right) ^ {-\\\\frac{\\\\nu + d}{2}}, \\\\quad x \\\\in \\\\Rset
with :math:`\\\\nu > 0, d \\\\geq 1, \\\\mat{R} \\\\in \\\\Rset^d \\\\times \\\\Rset^d,
\\\\sigma_k > 0, k=1, \\\\dots, d` .
where :math:`\\\\vect{z}=\\\\mat{\\\\Delta}^{-1}\\\\left(\\\\vect{x}-\\\\vect{\\\\mu}\\\\right)`,
:math:`\\\\mat{\\\\Delta} = \\\\mat{\\\\mathrm{diag}}(\\\\vect{\\\\sigma})` and :math:`\\\\Gamma`
denotes Euler's Gamma function :class:`~openturns.SpecFunc_Gamma`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\vect{\\\\Expect{X}} & = & \\\\vect{\\\\mu} \\\\quad \\\\text{ if }\\\\nu>1\\\\\\\\
\\\\mat{\\\\Cov{X}} & = & \\\\displaystyle \\\\frac{\\\\nu}{\\\\nu-2}
\\\\Tr{\\\\mat{\\\\Delta}}\\\\,\\\\mat{R}\\\\,\\\\mat{\\\\Delta}
\\\\quad \\\\text{ if }\\\\nu>2
\\\\end{eqnarray*}
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> distribution = ot.Student(5.0, -0.5, 2.0)
Draw a sample:
>>> sample = distribution.getSample(10)"
// ---------------------------------------------------------------------
%feature("docstring") OT::Student::getMu
"Accessor to the distribution's mean.
Returns
-------
mu : float
Mean.
Only defined when the dimension is 1
(else, use the :func:`getMean()` method inherited from the
EllipticalDistribution class)."
// ---------------------------------------------------------------------
%feature("docstring") OT::Student::getNu
"Accessor to the distribution's generalised number degrees of freedom.
Returns
-------
nu : float
Generalised number degrees of freedom."
// ---------------------------------------------------------------------
%feature("docstring") OT::Student::setMu
"Accessor to the distribution's mean.
Parameters
----------
mu : float
Mean."
// ---------------------------------------------------------------------
%feature("docstring") OT::Student::setNu
"Accessor to the distribution's generalised number degrees of freedom.
Parameters
----------
nu : float, :math:`\\\\nu > 0`
Generalised number degrees of freedom."
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