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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 | %feature("docstring") OT::WeibullMuSigma
"Weibull distribution parameters.
Available constructors:
WeibullMuSigma(*mu=1.0, sigma=1.0, gamma=0.*)
Parameters
----------
mu : float
Mean.
sigma : float
Standard deviation :math:`\\\\sigma > 0`.
gamma : float, optional
Shift parameter :math:`\\\\gamma > \\\\mu`.
Notes
-----
The native parameters :math:`\\\\alpha` and :math:`\\\\beta` are searched such as:
.. math::
\\\\alpha &= \\\\frac{\\\\mu - \\\\gamma}{\\\\Gamma(1+\\\\frac{1}{\\\\beta})} \\\\\\\\
\\\\sigma^2 &= \\\\alpha^2 \\\\Gamma\\\\left(1 + \\\\frac{2}{\\\\beta}\\\\right) -
\\\\Gamma^2 \\\\left(1 + \\\\frac{1}{\\\\beta}\\\\right)
See also
--------
Weibull
Examples
--------
Create the parameters of the Weibull distribution:
>>> import openturns as ot
>>> parameters = ot.WeibullMuSigma(1.3, 1.23, -0.5)
Convert parameters into the native parameters:
>>> print(parameters([1.3, 1.23, -0.5]))
[1.99222,1.48961,-0.5]
The gradient of the transformation of the native parameters into the new
parameters:
>>> print(parameters.gradient())
[[ 1.25624 0.897176 0 ]
[ -0.218715 -1.31294 0 ]
[ -1.25624 -0.897176 1 ]]"
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