/usr/include/openturns/swig/NonCentralStudent_doc.i is in libopenturns-dev 1.7-3.
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 | %feature("docstring") OT::NonCentralStudent
"NonCentralStudent distribution.
Available constructors:
NonCentralStudent(*nu=5.0, delta=0., gamma=0.*)
Parameters
----------
nu : float, :math:`\\\\nu > 0`
Generalised number degree of freedom.
delta : float
Non-centrality parameter :math:`\\\\delta`.
gamma : float
Shift parameter :math:`\\\\gamma`.
Notes
-----
Its probability density function is defined as:
.. math::
f_X(x) = \\\\frac{exp \\\\left(-\\\\delta^2 / 2 \\\\right)}
{\\\\sqrt{\\\\nu\\\\pi} \\\\Gamma \\\\left(\\\\frac{\\\\nu}{2} \\\\right)}
\\\\left(\\\\frac{\\\\nu}{\\\\nu + (x - \\\\gamma)^2}\\\\right) ^ {\\\\frac{\\\\nu + 1}{2}}
\\\\sum_{j=0}^{\\\\infty}
\\\\frac{\\\\Gamma \\\\left(\\\\frac{\\\\nu + j + 1}{2}\\\\right)}{\\\\Gamma(j + 1)}
\\\\left(\\\\delta(x - \\\\gamma)
\\\\sqrt{\\\\frac{2}{\\\\nu + (x - \\\\gamma)^2}}\\\\right) ^ j,
\\\\quad x \\\\in \\\\Rset
With :math:`\\\\Gamma` denotes Euler's Gamma function
:class:`~openturns.SpecFunc_Gamma`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{X} & = & \\\\gamma + \\\\delta sqrt{\\\\frac{\\\\nu}{2}}
\\\\frac{\\\\Gamma\\\\left(\\\\frac{\\\\nu - 1}{2}\\\\right)}
{\\\\Gamma \\\\left(\\\\frac{\\\\nu}{2}\\\\right)}
\\\\quad \\\\text{ if }\\\\nu > 1\\\\\\\\
\\\\Var{X} & = & \\\\frac{\\\\nu}{\\\\nu - 2} (1 + \\\\delta^2) -
\\\\left(\\\\frac{\\\\nu}{2}\\\\delta^2
\\\\frac{\\\\Gamma \\\\left(\\\\frac{\\\\nu - 1}{2}\\\\right)}
{\\\\Gamma \\\\left(\\\\frac{\\\\nu}{2}\\\\right)}
- \\\\gamma \\\\right)^2
\\\\quad \\\\text{ if }\\\\nu>2
\\\\end{eqnarray*}
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> distribution = ot.NonCentralStudent(6.)
Draw a sample:
>>> sample = distribution.getSample(10)"
// ---------------------------------------------------------------------
%feature("docstring") OT::NonCentralStudent::getNu
"Accessor to the distribution's generalised number degrees of freedom.
Returns
-------
nu : float
Generalised number degrees of freedom :math:`\\\\nu`."
// ---------------------------------------------------------------------
%feature("docstring") OT::NonCentralStudent::getDelta
"Accessor to the distribution's non-centrality parameter.
Returns
-------
delta : float
Non-centrality parameter :math:`\\\\delta`."
// ---------------------------------------------------------------------
%feature("docstring") OT::NonCentralStudent::getGamma
"Accessor to the distribution's shift from the origin.
Returns
-------
gamma : float
Shift parameter :math:`\\\\gamma`."
// ---------------------------------------------------------------------
%feature("docstring") OT::NonCentralStudent::setNu
"Accessor to the distribution's generalised number degrees of freedom.
Parameters
----------
nu : float, :math:`\\\\nu > 0`
Generalised number degrees of freedom :math:`\\\\nu`."
// ---------------------------------------------------------------------
%feature("docstring") OT::NonCentralStudent::setDelta
"Accessor to the distribution's non-centrality parameter.
Parameters
----------
delta : float
Non-centrality parameter :math:`\\\\delta`."
// ---------------------------------------------------------------------
%feature("docstring") OT::NonCentralStudent::setGamma
"Accessor to the distribution's shift from the origin.
Parameters
----------
gamma : float
Shift parameter :math:`\\\\gamma`."
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