/usr/include/openturns/swig/Histogram_doc.i is in libopenturns-dev 1.7-3.
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 93 94 95 96 | %feature("docstring") OT::Histogram
"Histogram distribution.
Available constructors:
Histogram(*first=0., coll=ot.HistogramPairCollection(1)*)
Parameters
----------
first : float
Lower bound.
coll : :class:`~openturns.HistogramPairCollection`
Collection of :math:`(l_i, h_i)` where :math:`h_i` is the frequency of the
class :math:`i` and :math:`l_i` its width.
Notes
-----
Its probability density function is defined as:
.. math::
f_X(x) = \\\\sum_{i=1}^{n}H_i\\\\;\\\\boldsymbol{1}_{[x_i,x_{i+1}]}(x)
where :math:`H_i=h_i/S` is the relative frequency,
with :math:`S=\\\\sum_{i=1}^n h_i\\\\,l_i` the total frequency of data.
:math:`l_i = x_{i+1} - x_i , 1\\\\leq i \\\\leq n` and :math:`n` is the size of the
`ot.HistogramPairCollection`.
Its first moments are:
.. math::
:nowrap:
\\\\begin{eqnarray*}
\\\\Expect{X} & = & \\\\frac{1}{2 \\\\sum_{i=1}^n h_i\\\\,l_i}
\\\\sum_{i=1}^n h_i\\\\,l_i (x_{i+1} + x_i)\\\\\\\\
\\\\Var{X} & = & \\\\frac{1}{3 \\\\sum_{i=1}^n h_i\\\\,l_i}
\\\\sum_{i=1}^n h_i\\\\,l_i (x_{i+1}^2 + x_i\\\\,x_{i+1} + x_i^2)
\\\\end{eqnarray*}
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> collection = HistogramPairCollection(4)
>>> collection[0] = HistogramPair(1.0, 0.5)
>>> collection[1] = HistogramPair(0.7, 1.5)
>>> collection[2] = HistogramPair(1.2, 3.5)
>>> collection[3] = HistogramPair(0.9, 2.5)
>>> distribution = Histogram(-1.5, collection)
Draw a sample:
>>> sample = distribution.getSample(10)"
// ---------------------------------------------------------------------
%feature("docstring") OT::Histogram::getFirst
"Accessor to the distribution's lower bound.
Returns
-------
first : float
Lower bound."
// ---------------------------------------------------------------------
%feature("docstring") OT::Histogram::getPairCollection
"Accessor to the distribution's collection.
Returns
-------
coll : :class:`~openturns.HistogramPairCollection`
The collection of :math:`(l_i, h_i)` where :math:`h_i` is the frequency of
the class `i` and :math:`l_i` its width."
// ---------------------------------------------------------------------
%feature("docstring") OT::Histogram::setFirst
"Accessor to the distribution's lower bound.
Parameters
----------
first : float
Lower bound."
// ---------------------------------------------------------------------
%feature("docstring") OT::Histogram::setPairCollection
"Accessor to the distribution's collection.
Parameters
----------
coll : :class:`~openturns.HistogramPairCollection`
The collection of :math:`(l_i, h_i)` where :math:`h_i` is the frequency of
the class `i` and :math:`l_i` its width."
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