1%feature("docstring") OT::MeixnerDistribution
2"Meixner distribution.
3
4Parameters
5----------
6beta : float, :math:`\beta > 0`
7    Scale parameter.
8alpha : float, :math:`\alpha \in [-\pi; \pi]`
9    Skewness parameter.
10delta : float, :math:`\delta > 0`
11    Shape parameter.
12gamma : float
13    Position parameter :math:`\gamma`.
14
15Notes
16-----
17Its probability density function is defined as:
18
19.. math::
20
21    f_X(x) = \frac{\left(2 \cos(\alpha / 2)\right)^{2 \delta}}
22                  {2 \beta \pi \Gamma(2 \delta)}
23             \exp\left(\frac{\alpha (x - \gamma)}{\beta}\right)
24             \left|\Gamma\left(\delta + i \frac{x - \gamma}{\beta}
25                               \right)\right|^2,
26             \quad x \in \Rset
27
28with :math:`\beta, \delta > 0`, :math:`\alpha \in [-\pi; \pi]`,
29:math:`\gamma \in \Rset` and where :math:`i^2 = -1`.
30
31Its first moments are:
32
33.. math::
34    :nowrap:
35
36    \begin{eqnarray*}
37        \Expect{X} & = & \beta \delta \tan(\alpha / 2) + \gamma \\
38        \Var{X} & = & \frac{\beta^2 \delta}{1 + \cos(\alpha)}
39    \end{eqnarray*}
40
41Examples
42--------
43Create a distribution:
44
45>>> import openturns as ot
46>>> distribution = ot.MeixnerDistribution(1.0, 0.0, 1.0, 0.0)
47
48Draw a sample:
49
50>>> sample = distribution.getSample(5)"
51
52// ---------------------------------------------------------------------
53
54%feature("docstring") OT::MeixnerDistribution::getBeta
55"Accessor to the distribution's scale parameter :math:`\beta`.
56
57Returns
58-------
59beta : float
60    Scale parameter :math:`\beta`."
61
62// ---------------------------------------------------------------------
63
64%feature("docstring") OT::MeixnerDistribution::getAlpha
65"Accessor to the distribution's skewness parameter :math:`\alpha`.
66
67Returns
68-------
69alpha : float
70    Skewness parameter :math:`\alpha`."
71
72// ---------------------------------------------------------------------
73
74%feature("docstring") OT::MeixnerDistribution::getDelta
75"Accessor to the distribution's shape parameter :math:`\delta`.
76
77Returns
78-------
79delta : float
80    Shape parameter :math:`\delta`."
81
82// ---------------------------------------------------------------------
83
84%feature("docstring") OT::MeixnerDistribution::getGamma
85"Accessor to the distribution's position parameter :math:`\gamma`.
86
87Returns
88-------
89gamma : float
90    Position parameter :math:`\gamma`."
91
92// ---------------------------------------------------------------------
93
94%feature("docstring") OT::MeixnerDistribution::setBeta
95"Accessor to the distribution's scale parameter :math:`\beta`.
96
97Parameters
98----------
99beta : float, :math:`\beta > 0`
100    Scale parameter :math:`\beta`."
101
102// ---------------------------------------------------------------------
103
104%feature("docstring") OT::MeixnerDistribution::setAlpha
105"Accessor to the distribution's skewness parameter :math:`\alpha`.
106
107Parameters
108----------
109alpha : float, :math:`\alpha \in [-\pi; \pi]`
110    Skewness parameter :math:`\alpha`."
111
112// ---------------------------------------------------------------------
113
114%feature("docstring") OT::MeixnerDistribution::setDelta
115"Accessor to the distribution's shape parameter :math:`\delta`.
116
117Parameters
118----------
119delta : float, :math:`\delta > 0`
120    Shape parameter :math:`\delta`."
121
122// ---------------------------------------------------------------------
123
124%feature("docstring") OT::MeixnerDistribution::setGamma
125"Accessor to the distribution's position parameter :math:`\gamma`.
126
127Parameters
128----------
129gamma : float, :math:`\gamma \in \Rset`
130    Position parameter :math:`\gamma`."
131