pystra.distributions.maximum.Maximum#

class Maximum(name, parent, N, input_type=None, startpoint=None)[source]#

Bases: Distribution

Distribution of maximima from the passed in parent distribution

Attributes:

name (str): Name of the random variable
mean (float): Mean
stdv (float): Standard deviation
parent (Distribution): Parent distribution object
N (float): Power to which distribution is raised
input_type (any): Change meaning of mean and stdv
startpoint (float): Start point for seach

Methods

`cdf`	Cumulative distribution function
`dF_dtheta`	Derivatives of the CDF w.r.t.
`getMean`
`getName`
`getStartPoint`
`getStdv`
`jacobian`	Compute the Jacobian (e.g. Lemaire, eq.
`pdf`	Probability density function
`plot`	Plot the probability density function.
`ppf`	inverse cumulative distribution function
`sample`	Draw random samples from the distribution.
`setStartPoint`
`set_location`	Updating the parent distribution location parameter.
`set_scale`	Updating the parent distribution scale parameter.
`u_to_x`	Transformation from u to x
`update_stats`	Updates the mean and stdv estimates - used for sensitivity analysis where the parent distribution params may change after instantiation
`x_to_u`	Transformation from x to u
`zero_distn`

pdf(x)[source]#: Probability density function

cdf(x)[source]#: Cumulative distribution function

ppf(p)[source]#: inverse cumulative distribution function

u_to_x(u)[source]#: Transformation from u to x

x_to_u(x)[source]#: Transformation from x to u

jacobian(u, x)[source]#: Compute the Jacobian (e.g. Lemaire, eq. 4.9)

set_location(loc=0)[source]#: Updating the parent distribution location parameter.

set_scale(scale=1)[source]#: Updating the parent distribution scale parameter.

update_stats()[source]#: Updates the mean and stdv estimates - used for sensitivity analysis where the parent distribution params may change after instantiation

dF_dtheta(x)#

Derivatives of the CDF w.r.t. each sensitivity parameter.

Returns ∂F_X(x)/∂θ for every parameter listed by sensitivity_params. The base-class implementation uses central finite differences on the CDF via _make_copy().

Before computing derivatives, a reconstruction sanity check verifies that _make_copy() (with no overrides) reproduces the current distribution. This catches both constructor failures (e.g. composite distributions) and silent mismatches (e.g. distributions whose extra constructor arguments are not stored in _ctor_kwargs).

Subclasses may override this with analytical expressions for better accuracy and performance (see Normal and Lognormal).

Parameters:: x (float) – Evaluation point in physical space.
Returns:: {param_name: ∂F/∂θ} for each parameter in sensitivity_params.
Return type:: dict
Raises:: ValueError – If the distribution cannot be faithfully reconstructed by _make_copy().

plot(ax=None, **kwargs)#

Plot the probability density function.

Parameters:

ax (matplotlib.axes.Axes, optional) – Axes to plot on. A new figure is created if None.
**kwargs – Additional keyword arguments forwarded to ax.plot().

Returns:

The axes containing the plot.

Return type:

matplotlib.axes.Axes

sample(n=1000)#

Draw random samples from the distribution.

Uses inverse-transform sampling via ppf.

Parameters:: n (int, optional) – Number of samples (default 1000).
Returns:: Array of shape (n,) with sampled values.
Return type:: ndarray

property sensitivity_params#

Distribution parameters for which sensitivities are computed.

Returns a dict {param_name: current_value} listing every parameter with respect to which \(\partial\beta/\partial\theta\) should be evaluated.

The default implementation returns {"mean": μ, "std": σ}, which is appropriate for most distributions. Distributions with additional parameters of interest (e.g. the GEV shape parameter) should override this property to include them.

Parameters listed in _ctor_kwargs but not in sensitivity_params are held fixed during sensitivity analysis — they are only used by _make_copy() to faithfully reconstruct the distribution.

Returns:: {param_name: current_value}
Return type:: dict