import numpy as np
from popsynth.distribution import DistributionParameter, LuminosityDistribution
[docs]class ParetoDistribution(LuminosityDistribution):
_distribution_name = "ParetoDistribution"
Lmin = DistributionParameter(default=1, vmin=0)
alpha = DistributionParameter(default=1)
[docs] def __init__(self, seed: int = 1234, name: str = "pareto"):
"""
A Pareto luminosity function.
``alpha``*``Lmin``^``alpha`` / L^(``alpha``+1)
:param seed: Random seed
:type seed: int
:param name: Name of the distribution
:type name: str
:param Lmin: Minimum value of the luminosity
:type Lmin: :class:`DistributionParameter`
:param alpha: Index of the pareto distribution
:type alpha: :class:`DistributionParameter`
"""
lf_form = r"\frac{\alpha L_{\rm min}^{\alpha}}{L^{\alpha+1}}"
super(ParetoDistribution, self).__init__(
seed=seed, name=name, form=lf_form
)
[docs] def phi(self, L):
out = np.zeros_like(L)
idx = L >= self.Lmin
out[idx] = (
self.alpha * self.Lmin**self.alpha / L[idx] ** (self.alpha + 1)
)
return out
[docs] def draw_luminosity(self, size: int = 1):
return (np.random.pareto(self.alpha, size) + 1) * self.Lmin