/usr/include/openturns/swig/DistFunc_doc.i is in libopenturns-dev 1.9-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 | %feature("docstring") OT::DistFunc::pNormal
"CDF of an unit-variance centered Normal distribution.
Parameters
----------
x : float
Location
tail : bool, default=False
Tail flag
Returns
-------
cdf : float
Examples
--------
>>> import openturns as ot
>>> cdf = ot.DistFunc.pNormal(0.9)"
// ---------------------------------------------------------------------
%feature("docstring") OT::DistFunc::qNormal
"Quantile of an unit-variance centered Normal distribution.
Parameters
----------
prob : float
Returns
-------
q : float
Examples
--------
>>> import openturns as ot
>>> q = ot.DistFunc.qNormal(0.95)"
// ---------------------------------------------------------------------
%feature("docstring") OT::DistFunc::rNormal
"Realization of an unit-variance centered Normal distribution.
Returns
-------
realization : float
Examples
--------
>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> r = ot.DistFunc.rNormal()"
// ---------------------------------------------------------------------
%feature("docstring") OT::DistFunc::kFactorPooled
"Exact margin factor for bilateral covering interval of pooled Normal populations.
Parameters
----------
n : int
The size of the population
m : int
The size of the pool
p : float :math:`0<p<1`
The probability level of the covering interval
alpha : float :math:`0<\\\\alpha<1`
The confidence level of the covering interval
Returns
-------
k : float
The margin factor
Notes
-----
This method allows to compute the *exact* margin factor :math:`k` of a
pool of :math:`m` Normal populations of size :math:`n` with unknown
means :math:`\\\\mu_i` and unknown common variance :math:`\\\\sigma^2`.
Let :math:`m_i=\\\\dfrac{1}{n}\\\\sum_{j=1}^nX_{ij}` be the empirical mean
of the ith population :math:`(X_{i1},\\\\dots,X_{in})` and
:math:`\\\\sigma^2_{mn}=\\\\dfrac{}{}\\\\sum_{i=1}^m\\\\sum_{j=1}^n(X_{ij}-m_i)^2`
the empirical *pooled* variance. The covering factor :math:`k` is such
that the intervals :math:`[m_i-k\\\\sigma_{mn},m_i+k\\\\sigma_{mn}]` satisfy:
.. math::
\\\\Prob{\\\\Prob{X_i\\\\in[m_i-k\\\\sigma_{mn},m_i+k\\\\sigma_{mn}]}\\\\geq p}=\\\\alpha
for :math:`i\\\\in\\\\{1,\\\\dots,m\\\\}`. It reduces to find :math:`k` such that:
.. math::
\\\\int_{\\\\Rset}F(x,k;\\\\nu_{m,n},p)\\\\phi_{0,1/\\\\sqrt{n}}(x)\\\\,\\\\di x = \\\\alpha
where :math:`phi_{0,1/\\\\sqrt{n}}` is the density function of the normal
distribution with a mean equals to 0 and a variance equals to
:math:`1/n`, :math:`\\\\nu_{m,n}=m(n-1)` and :math:`F(x,k;\\\\nu_{m,n},p)`
the function defined by:
.. math::
F(x,k;\\\\nu_{m,n},p)=\\\\bar{F}_{\\\\chi^2_{\\\\nu_{m,n}}}(\\\\nu_{m,n} R^2(x;p)/k^2)
where :math:`\\\\bar{F}_{\\\\chi^2_{\\\\nu_{m,n}}}` is the complementary distribution
function of a chi-square distribution with :math:`\\\\nu_{m,n}` degrees
of freedom and :math:`R(x;p)` the solution of:
.. math::
\\\\Phi(x + R) - \\\\Phi(x - R) = p
Examples
--------
>>> import openturns as ot
>>> k = ot.DistFunc.kFactorPooled(5, 3, 0.95, 0.9)"
// ---------------------------------------------------------------------
%feature("docstring") OT::DistFunc::kFactor
"Exact margin factor for bilateral covering interval of a Normal population.
Parameters
----------
n : int
The size of the population
p : float :math:`0<p<1`
The probability level of the covering interval
alpha : float :math:`0<\\\\alpha<1`
The confidence level of the covering interval
Returns
-------
k : float
The margin factor
Notes
-----
This method allows to compute the *exact* margin factor :math:`k` of a
Normal population of size :math:`n` with unknown
means :math:`\\\\mu_i` and unknown common variance :math:`\\\\sigma^2`. It
is equivalent to the pooled version with :math:`m=1`.
Examples
--------
>>> import openturns as ot
>>> k = ot.DistFunc.kFactor(5, 0.95, 0.9)"
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