LogNormalMuSigma

class LogNormalMuSigma(*args)

LogNormal distribution parameters.

Parameters
mufloat

The mean of the log-normal random variable.

sigmafloat

The standard deviation of the log-normal random variable, with:math:sigma > 0.

gammafloat, optional

Location parameter.

See also

LogNormal

Notes

The \mu (resp. \sigma) parameter is the mean (resp. the standard deviation) of the log-normal random variable, i.e.

\Expect{X} &= \mu \\
\Var{X} &= \sigma^2

where X is the log-normal random variable.

The native parameters are \mu_\ell and \sigma_\ell, which are the mean and standard deviation of the logarithm of the log-normal variable, i.e. the parameters of the associated normal variable. They are defined as follows:

\sigma_\ell &= \sqrt{\log{ \left( 1+\frac{\sigma^2}{(\mu-\gamma)^2} \right) }} \\
\mu_\ell &= \log{(\mu-\gamma)} - \frac{\sigma_\ell^2}{2}

Examples

Create the parameters of the LogNormal distribution:

>>> import openturns as ot
>>> parameters = ot.LogNormalMuSigma(0.63, 3.3, -0.5)

Convert parameters into the native parameters:

>>> print(parameters.evaluate())
[-1.00492,1.50143,-0.5]

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

>>> print(parameters.gradient())
[[  1.67704  -0.527552  0        ]
 [ -0.271228  0.180647  0        ]
 [ -1.67704   0.527552  1        ]]

Methods

__call__(self, inP)

Call self as a function.

evaluate(self)

Compute native parameters values.

getClassName(self)

Accessor to the object’s name.

getDescription(self)

Get the description of the parameters.

getDistribution(self)

Build a distribution based on a set of native parameters.

getId(self)

Accessor to the object’s id.

getName(self)

Accessor to the object’s name.

getShadowedId(self)

Accessor to the object’s shadowed id.

getValues(self)

Accessor to the parameters values.

getVisibility(self)

Accessor to the object’s visibility state.

gradient(self)

Get the gradient.

hasName(self)

Test if the object is named.

hasVisibleName(self)

Test if the object has a distinguishable name.

inverse(self, inP)

Convert to native parameters.

setName(self, name)

Accessor to the object’s name.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

setValues(self, values)

Accessor to the parameters values.

setVisibility(self, visible)

Accessor to the object’s visibility state.

__init__(self, *args)

Initialize self. See help(type(self)) for accurate signature.

evaluate(self)

Compute native parameters values.

Returns
valuesPoint

The native parameter values.

getClassName(self)

Accessor to the object’s name.

Returns
class_namestr

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

getDescription(self)

Get the description of the parameters.

Returns
collectionDescription

List of parameters names.

getDistribution(self)

Build a distribution based on a set of native parameters.

Returns
distributionDistribution

Distribution built with the native parameters.

getId(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getName(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

getShadowedId(self)

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getValues(self)

Accessor to the parameters values.

Returns
valuesPoint

List of parameters values.

getVisibility(self)

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

gradient(self)

Get the gradient.

Returns
gradientMatrix

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(self)

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasVisibleName(self)

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

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

inverse(self, inP)

Convert to native parameters.

Parameters
inPsequence of float

The non-native parameters.

Returns
outPPoint

The native parameters.

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setValues(self, values)

Accessor to the parameters values.

Parameters
valuessequence of float

List of parameters values.

setVisibility(self, visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.