1%feature("docstring") OT::MaximumDistribution
2"Maximum distribution.
3
4Available constructors:
5    MaximumDistribution(*distribution*)
6
7    MaximumDistribution(*collection*)
8
9    MaximumDistribution(*distribution, size*)
10
11Parameters
12----------
13distribution : :class:`~openturns.Distribution`
14    The underlying distribution.
15collection : sequence of :class:`~openturns.Distribution`
16    A collection of pdfs.
17size : int
18    Number of instances of distribution.
19
20Notes
21-----
22The maximum distribution of F is the distribution of :math:`X = max(X_1, ... , X_n)`
23where :math:`(X_1, ... , X_n) \sim F`
24
25.. math::
26
27    \Prob{X\leq x}=\Prob{X_1\leq x,\dots,X_n\leq x}
28
29This simplifies to :math:`\Prob{X\leq x}=\prod_{i=1}^n F_i(x)`
30when :math:`X_1,\dots,X_n` are independent (second constructor) and finally
31it simplifies into :math:`F^n(x)` when the random variables are iid (third
32constructor).
33
34Examples
35--------
36Create a distribution:
37
38>>> import openturns as ot
39>>> coll = [ot.Uniform(2.5, 3.5), ot.LogUniform(1.0, 1.2), ot.Triangular(2.0, 3.0, 4.0)]
40>>> distribution = ot.MaximumDistribution(coll)
41
42Draw a sample:
43
44>>> sample = distribution.getSample(5)"
45
46// ---------------------------------------------------------------------
47
48%feature("docstring") OT::MaximumDistribution::getDistribution
49"Accessor to the underlying distribution.
50
51Returns
52-------
53distribution : :class:`~openturns.Distribution`
54    The underlying distribution."
55
56// ---------------------------------------------------------------------
57
58%feature("docstring") OT::MaximumDistribution::setDistribution
59"Accessor to the underlying distribution.
60
61Parameters
62----------
63distribution : :class:`~openturns.Distribution`
64    The underlying distribution."
65
66// ---------------------------------------------------------------------
67
68