import numpy as np
from popsynth.distribution import DistributionParameter, LuminosityDistribution
[docs]class Log10NormalDistribution(LuminosityDistribution):
_distribution_name = "Log10NormalDistribution"
mu = DistributionParameter()
tau = DistributionParameter(vmin=0)
[docs] def __init__(self, seed: int = 1234, name: str = "log10norm"):
"""
A log10-normal luminosity function
Log10Normal(``mu``, ``tau``)
:param seed: Random seed
:type seed: int
:param name: Name of the distribution
:type name: str
:param mu: Mean of the log10 normal
:type mu: :class:`DistributionParameter`
:param tau: Standard deviation of the log10 normal
:type tau: :class:`DistributionParameter`
"""
lf_form = r"\mathrm{Log_{10}Normal(\mu, \tau)}"
super(Log10NormalDistribution, self).__init__(
name=name, seed=seed, form=lf_form
)
[docs] def phi(self, L):
return (1.0 / (self.tau * L * np.sqrt(2 * np.pi))) * np.exp(
-((np.log10(L) - self.mu) ** 2) / (2 * self.tau**2)
)
[docs] def draw_luminosity(self, size=1):
x = np.random.normal(loc=self.mu, scale=self.tau, size=size)
return np.power(10.0, x)