/usr/include/openturns/swig/Arcsine_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 | %feature("docstring") OT::Arcsine
"Arcsine distribution.
Available constructors:
Arcsine(*a=-1.0, b=1.0*)
Parameters
----------
a : float
lower bound.
b : float
upper bound, :math:`b > a`
Notes
-----
Its probability density function is defined as:
.. math::
f_X(x) = \\\\frac{1}{\\\\pi \\\\sqrt{(x - a)(b - x)}},
\\\\quad x \\\\in [a, b]
with :math:`a < b`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{X} & = & \\\\frac{a + b}{2} \\\\\\\\
\\\\Var{X} & = & \\\\frac{(b - a)^2}{8}
\\\\end{eqnarray*}
It is possible to create an Arcsine distribution from the alternative parametrization :math:`(\\\\mu, \\\\sigma)`: see :class:`~openturns.ArcsineMuSigma`. In that case, all the results are presented in that new parametrization.
In order to use the alternative parametrization :math:`(\\\\mu, \\\\sigma)` only to create the distribution, see the example below: all the results will be presented in the native parametrization :math:`(a, b)`
Examples
--------
Create a distribution from its native parameters :math:`(a, b)`:
>>> import openturns as ot
>>> myDist = ot.Arcsine(2.0, 3.0)
Create a it from the alternative parametrization :math:`(\\\\mu, \\\\sigma)`:
>>> myDist2 = ot.Arcsine()
>>> myDist2.setParameter(ot.ArcsineMuSigma()([2.5, 0.35]))
Create it from :math:`(\\\\mu, \\\\sigma)` and keep that parametrization for the remaining study:
>>> myParam = ot.ArcsineMuSigma(2.5, 0.35)
>>> myDist3 = ot.ParametrizedDistribution(myParam)
Draw a sample:
>>> sample = myDist.getSample(5)"
// ---------------------------------------------------------------------
%feature("docstring") OT::Arcsine::getA
"Accessor to the distribution's lower bound.
Returns
-------
a : float
Lower bound."
// ---------------------------------------------------------------------
%feature("docstring") OT::Arcsine::getB
"Accessor to the distribution's upper bound.
Returns
-------
b : float
Upper bound."
// ---------------------------------------------------------------------
%feature("docstring") OT::Arcsine::getMu
"Accessor to the distribution's mean.
Returns
-------
mu : float
Mean."
// ---------------------------------------------------------------------
%feature("docstring") OT::Arcsine::getSigma
"Accessor to the distribution's standard deviation.
Returns
-------
sigma : float
Standard deviation."
// ---------------------------------------------------------------------
%feature("docstring") OT::Arcsine::setA
"Accessor to the distribution's lower bound.
Parameters
----------
a : float, :math:`a < b`
Lower bound."
// ---------------------------------------------------------------------
%feature("docstring") OT::Arcsine::setB
"Accessor to the distribution's upper bound.
Parameters
----------
b : float, :math:`a < b`
Upper bound."
// ---------------------------------------------------------------------
%feature("docstring") OT::Arcsine::setMu
"Accessor to the distribution's mean.
Parameters
----------
mu : float
Mean."
// ---------------------------------------------------------------------
%feature("docstring") OT::Arcsine::setSigma
"Accessor to the distribution's standard deviation.
Parameters
----------
sigma : float, :math:`\\\\sigma > 0`
Standard deviation."
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