1%feature("docstring") OT::MeixnerFactory
2"Meixner specific orthonormal univariate polynomial family.
3
4For the :class:`~openturns.NegativeBinomial` distribution.
5
6Available constructors:
7    MeixnerFactory(*r=1.0, p=0.5*)
8
9Parameters
10----------
11r : float, :math:`r > 0`
12    Number of failures parameter of the :class:`~openturns.NegativeBinomial`
13    distribution.
14p : float, :math:`0 < p < 1`
15    Success probability parameter of the :class:`~openturns.NegativeBinomial`
16    distribution.
17
18Notes
19-----
20Any sequence of orthogonal polynomials has a recurrence formula relating any
21three consecutive polynomials as follows:
22
23.. math::
24
25    P_{i + 1} = (a_i x + b_i) P_i + c_i P_{i - 1}, \quad 1 < i
26
27The recurrence coefficients for the Meixner polynomials come analytically
28and read:
29
30.. math::
31
32    \begin{array}{rcl}
33        a_i & = & \displaystyle \frac{p - 1}
34                                     {\sqrt{p (i + 1) (i + r)}} \\
35        b_i & = & \displaystyle \frac{p (i + r) + i}
36                                     {\sqrt{p (i + 1) (i + r)}} \\
37        c_i & = & \displaystyle - \frac{\sqrt{p i (i + r - 1)}}
38                                       {\sqrt{p (i + 1) (i + r)}} \\
39    \end{array}, \quad 1 < i
40
41where :math:`r` and :math:`p` are the parameters of the
42:class:`~openturns.NegativeBinomial` distribution.
43
44See also
45--------
46StandardDistributionPolynomialFactory
47
48Examples
49--------
50>>> import openturns as ot
51>>> polynomial_factory = ot.MeixnerFactory()
52>>> for i in range(3):
53...     print(polynomial_factory.build(i))
541
550.707107 - 0.707107 * X
560.5 - 1.25 * X + 0.25 * X^2"
57
58// ---------------------------------------------------------------------
59
60%feature("docstring") OT::MeixnerFactory::getP
61"Accessor to the success probability parameter :math:`p`.
62
63Of the :class:`~openturns.NegativeBinomial` distribution.
64
65Returns
66-------
67p : float
68    Success probability parameter of the :class:`~openturns.NegativeBinomial`
69    distribution."
70
71// ---------------------------------------------------------------------
72
73%feature("docstring") OT::MeixnerFactory::getR
74"Accessor to the number of failures parameter :math:`r`.
75
76Of the :class:`~openturns.NegativeBinomial` distribution.
77
78Returns
79-------
80r : int
81    Number of failures parameter of the :class:`~openturns.NegativeBinomial`
82    distribution."
83