distributions.local_pareto_to_piecewise()

Converts the local Pareto distribution with local alpha alpha(x)

Usage

distributions.local_pareto_to_piecewise(
    t, alpha, rel_tolerance=0.0001, stop_survival=1e-09, stop_at=Ellipsis
)

above t to a piecewise Pareto that matches its survival function exactly at the thresholds and within rel_tolerance between them.

Parameters

t: float

Threshold; P(X > x) = 1 below it.

alpha: callable

alpha(x) -> float, finite and non-negative, positive where the conversion stops.

rel_tolerance: float = 1e-4

stop_survival: float = 1e-9

Stop once the survival function falls below this.

stop_at: float = inf

Stop at this amount.

Returns

tuple of (PiecewisePareto, float, float)

The approximation, the largest relative error found, and where the approximated range ends (the last alpha continues above it).

Examples

>>> import math
>>> from prospicio.distributions import local_pareto_to_piecewise
>>> pp, err, end = local_pareto_to_piecewise(1000.0, lambda x: 1.5 + 0.3 * math.log(x / 1000.0))
>>> err <= 1e-4

True