/usr/include/openturns/swig/Dirichlet_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 | %feature("docstring") OT::Dirichlet
"Dirichlet distribution.
Available constructors:
Dirichlet(*theta=[1.0, 1.0]*)
Parameters
----------
theta : sequence of float, :math:`\\\\theta_i > 0, i = 1, \\\\ldots, n+1`
theta must be at least bidimensional.
Notes
-----
Its probability density function is defined as:
.. math::
f_{\\\\vect{X}}(\\\\vect{x}) = \\\\frac{\\\\Gamma(|\\\\vect{\\\\theta}|_1)}
{\\\\prod_{j=1}^{n + 1} \\\\Gamma(\\\\theta_j)}
\\\\left[1 - \\\\sum_{j=1}^{n} x_j
\\\\right]^{\\\\theta_{n+1} - 1}
\\\\prod_{j=1}^n x_j^{\\\\theta_j - 1},
\\\\quad \\\\vect{x} \\\\in \\\\Delta(\\\\vect{X})
with :math:`\\\\Delta(\\\\vect{X}) = \\\\{ \\\\vect{x} \\\\in \\\\Rset^n : x_i \\\\geq 0, \\\\sum_{i=1}^n x_i \\\\leq 1, i = 1, \\\\ldots, n \\\\}`
and :math:`\\\\theta_i > 0, i = 1, \\\\ldots, n+1` and where :math:`|\\\\vect{\\\\theta}|_1 = \\\\sum_{i=1}^{n+1} \\\\theta_i`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{\\\\vect{X}} & = & \\\\Tr{(\\\\theta_i/|\\\\vect{\\\\theta}|_1,
\\\\quad i = 1, \\\\ldots, n)} \\\\\\\\
\\\\Cov{\\\\vect{X}} & = & \\\\left[- \\\\frac{\\\\theta_i \\\\theta_j}
{|\\\\vect{\\\\theta}|_1^2
(|\\\\vect{\\\\theta}|_1+1)},
\\\\quad i,j = 1, \\\\ldots, n \\\\right]
\\\\end{eqnarray*}
.. warning::
The present implementation does not model the :math:`n+1`-th component of
the Dirichlet distribution as it is fixed:
.. math::
X_{n + 1} = 1 - \\\\sum_{i=1}^{n} X_i
See Also
--------
Multinomial
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> distribution = ot.Dirichlet([1., 1., 1.])
Draw a sample:
>>> sample = distribution.getSample(10)"
// ---------------------------------------------------------------------
%feature("docstring") OT::Dirichlet::getTheta
"Accessor to the distribution's vector parameter.
Returns
-------
theta : float, :class:`~openturns.NumericalPoint`"
// ---------------------------------------------------------------------
%feature("docstring") OT::Dirichlet::setTheta
"Accessor to the distribution's vector parameter.
Parameters
----------
theta : float, sequence of float, :math:`\\\\theta_i > 0, i = 1, \\\\ldots, n+1`"
|