/usr/include/openturns/swig/Multinomial_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 | %feature("docstring") OT::Multinomial
"Multinomial distribution.
Available constructors:
Multinomial(*N=1, P=[0.5]*)
Parameters
----------
N : int, :math:`\\\\sum_{i = 1}^n x_i \\\\leq N`
Number of experiments.
P : sequence of float, :math:`p_i \\\\geq 0, i = 1, \\\\ldots, n` and :math:`\\\\sum_{i = 1}^n p_i \\\\leq 1`
Component probabilities (all positive with sum less than unity).
Notes
-----
Its probability density function is defined as:
.. math::
\\\\Prob{\\\\vect{X} = \\\\vect{x}} = \\\\frac{N!}{x_1! \\\\ldots x_n! (N - s)!}
p_1^{x_1} \\\\ldots p_n^{x_n} (1 - q)^{N - s},
\\\\quad \\\\forall \\\\vect{x} \\\\in \\\\Nset^n:
s = \\\\sum_{i = 1}^n x_i \\\\leq N
with :math:`N \\\\in \\\\Nset^*`, :math:`p_i \\\\geq 0, i = 1, \\\\ldots, n` and
:math:`\\\\sum_{i = 1}^n p_i \\\\leq 1`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{X_i} & = & N p_i, \\\\quad i = 1, \\\\ldots, n \\\\\\\\
\\\\Var{X_i} & = & N p_i (1 - p_i), \\\\quad i = 1, \\\\ldots, n \\\\\\\\
\\\\Cov{X_i, X_j} & = & - N p_i p_j, \\\\quad i, j = 1, \\\\ldots, n, i \\\\neq j
\\\\end{eqnarray*}
See Also
--------
Dirichlet
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> distribution = ot.Multinomial(1, [0.5])
Draw a sample:
>>> sample = distribution.getSample(5)"
// ---------------------------------------------------------------------
%feature("docstring") OT::Multinomial::getN
"Accessor to the number of experiments parameter :math:`N`.
Returns
-------
N : int
Number of experiments :math:`N`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Multinomial::getP
"Accessor to the component probabilities parameter :math:`\\\\vect{p}`.
Returns
-------
P : :class:`~openturns.Point`
Component probabilities :math:`\\\\vect{p}`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Multinomial::setN
"Accessor to the number of experiments parameter :math:`N`.
Parameters
----------
N : int, :math:`\\\\sum_{i = 1}^n x_i \\\\leq N`
Number of experiments :math:`N`."
// ---------------------------------------------------------------------
%feature("docstring") OT::Multinomial::setP
"Accessor to the component probabilities parameter :math:`\\\\vect{p}`.
Parameters
----------
P : sequence of float, :math:`0 \\\\leq p_i, i = 1, \\\\ldots, n` and :math:`\\\\sum_{i = 1}^n p_i \\\\leq 1`
Component probabilities (all positive with sum less than unity)."
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