/usr/include/openturns/swig/BetaMuSigma_doc.i is in libopenturns-dev 1.7-3.
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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 | %feature("docstring") OT::BetaMuSigma
"Beta distribution parameters.
Available constructors:
BetaMuSigma(*mu=0.5, sigma=* :math:`1/(2\\\\sqrt{5})` *, a=0., b=1.0*)
Parameters
----------
mu : float
Mean.
sigma : float
Standard deviation :math:`\\\\sigma > 0`.
a : float
Lower bound.
b : float, :math:`b > a`
Upper bound.
Notes
-----
The native parameters are defined as follows:
.. math::
t &= \\\\frac{(b - \\\\mu) (\\\\mu - a)}{\\\\sigma^2} - 1.0 \\\\\\\\
r &= \\\\frac{\\\\mu - a}{b - a} t
See also
--------
Beta
Examples
--------
Create the parameters of the Beta distribution:
>>> import openturns as ot
>>> parameters = ot.BetaMuSigma(0.2, 0.6, -1, 2)
Convert parameters into the native parameters:
>>> print(parameters([0.2, 0.6, -1, 2]))
[2,5,-1,2]
The gradient of the transformation of the native parameters into the new
parameters:
>>> print(parameters.gradient())
[[ 2.33333 1.66667 0 0 ]
[ -8 -20 0 0 ]
[ -3 -5 1 0 ]
[ 0.666667 3.33333 0 1 ]]"
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