LogNormalMuSigma¶

class LogNormalMuSigma(*args)¶

LogNormal distribution parameters.

Parameters:

mufloat

The mean of the LogNormal random variable.

Default value is $e^{0.5}$ .

sigmafloat

The standard deviation of the LogNormal random variable, with $\sigma > 0$ .

Default value is $\sqrt{e^{2}-e}$ .

gammafloat, optional

Location parameter.

Default value is 0.0.

See also

LogNormal

Notes

Let $X$ be a random variable that follows a LogNormal distribution such that:

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

The native parameters of $X$ are $\mu_\ell$ and $\sigma_\ell$ , which are such that $\log X$ follows a normal distribution whose mean is $\mu_\ell$ and whose variance is $\sigma_\ell^2$ . Then we have:

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

The default values of $(\mu, \sigma, \gamma)$ are defined so that the associated native parameters have the default values: $(\mu_\ell, \sigma_\ell, \gamma_\ell) = (0.0, 1.0, 0.0)$ .

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

`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.
`getName`()	Accessor to the object's name.
`getValues`()	Accessor to the parameters values.
`gradient`()	Get the gradient.
`hasName`()	Test if the object is named.
`inverse`(inP)	Convert to native parameters.
`setName`(name)	Accessor to the object's name.
`setValues`(values)	Accessor to the parameters values.

__init__(*args)¶

evaluate()¶

Compute native parameters values.

Returns:

valuesPoint: The native parameter values.

getClassName()¶

Accessor to the object’s name.

Returns:

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

getDescription()¶

Get the description of the parameters.

Returns:

collectionDescription: List of parameters names.

getDistribution()¶

Build a distribution based on a set of native parameters.

Returns:

distributionDistribution: Distribution built with the native parameters.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getValues()¶

Accessor to the parameters values.

Returns:

valuesPoint: List of parameters values.

gradient()¶

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()¶

Test if the object is named.

Returns: