WeibullMuSigma

class WeibullMuSigma(*args)

Weibull distribution parameters.

Available constructors:
WeibullMuSigma(mu=1.0, sigma=1.0, gamma=0.)
Parameters:

mu : float

Mean.

sigma : float

Standard deviation \sigma > 0.

gamma : float, optional

Shift parameter \gamma > \mu.

See also

Weibull

Notes

The native parameters \alpha and \beta are searched such as:

\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)

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.evaluate())
[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        ]]

Methods

__call__(inP)
evaluate() Compute native parameters values.
getClassName() Accessor to the object’s name.
getDescription() Get the description of the parameters.
getDistribution() Build a distribution based on a set of native parameters.
getId() Accessor to the object’s id.
getName() Accessor to the object’s name.
getShadowedId() Accessor to the object’s shadowed id.
getValues() Accessor to the parameters values.
getVisibility() Accessor to the object’s visibility state.
gradient() Get the gradient.
hasName() Test if the object is named.
hasVisibleName() Test if the object has a distinguishable name.
inverse(inP) Convert to native parameters.
setName(name) Accessor to the object’s name.
setShadowedId(id) Accessor to the object’s shadowed id.
setValues(values) Accessor to the parameters values.
setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)
evaluate()

Compute native parameters values.

Returns:

values : Point

The native parameter values.

getClassName()

Accessor to the object’s name.

Returns:

class_name : str

The object class name (object.__class__.__name__).

getDescription()

Get the description of the parameters.

Returns:

collection : Description

List of parameters names.

getDistribution()

Build a distribution based on a set of native parameters.

Returns:

distribution : Distribution

Distribution built with the native parameters.

getId()

Accessor to the object’s id.

Returns:

id : int

Internal unique identifier.

getName()

Accessor to the object’s name.

Returns:

name : str

The name of the object.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:

id : int

Internal unique identifier.

getValues()

Accessor to the parameters values.

Returns:

values : Point

List of parameters values.

getVisibility()

Accessor to the object’s visibility state.

Returns:

visible : bool

Visibility flag.

gradient()

Get the gradient.

Returns:

gradient : Matrix

The gradient of the transformation of the native parameters into the new parameters.

Notes

If we note (p_1, \dots, p_q) the native parameters and (p'_1, \dots, p'_q) the new ones, then the gradient matrix is \left( \dfrac{\partial p'_i}{\partial p_j} \right)_{1 \leq i,j \leq  q}.

hasName()

Test if the object is named.

Returns:

hasName : bool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:

hasVisibleName : bool

True if the name is not empty and not the default one.

inverse(inP)

Convert to native parameters.

Parameters:

inP : sequence of float

The non-native parameters.

Returns:

outP : Point

The native parameters.

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:

id : int

Internal unique identifier.

setValues(values)

Accessor to the parameters values.

Parameters:

values : sequence of float

List of parameters values.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:

visible : bool

Visibility flag.