popsynth.distributions.bpl_distribution module

class popsynth.distributions.bpl_distribution.BPLDistribution(seed: int = 1234, name: str = 'bpl')

Bases: popsynth.distribution.LuminosityDistribution

Lbreak

Lmax

Lmin

__init__(seed: int = 1234, name: str = 'bpl')

A broken power law luminosity distribution.

L ~ L^``alpha`` for L <= Lbreak L ~ L^``beta`` for L > Lbreak

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• Lmin (DistributionParameter) – Minimum value of the luminosity
• alpha (DistributionParameter) – Index of the lower power law
• Lbreak (DistributionParameter) – Luminosity of the power law break
• beta (DistributionParameter) – Index of the upper power law
• Lmax (DistributionParameter) – Maximum value of the luminosity

alpha

beta

draw_luminosity(size=1)

function to draw the luminosity via an alternative method must be implemented in child class

Parameters:size – Returns:

phi(L)

The functional form of the distribution. not required for sampling :param luminosity: Luminosity

popsynth.distributions.bpl_distribution.bpl(x, x0, x1, x2, a1, a2)

Broken power law between bounds.

Parameters:

• x – The domain of the function
• x0 – Lower bound
• x1 – Break point
• x2 – Upper bound
• a1 – Lower power law index
• a2 – Upper power low index

popsynth.distributions.bpl_distribution.integrate_pl(x0, x1, x2, a1, a2)

Integrate a broken power law between bounds.

Parameters:

• x0 – Lower bound
• x1 – Break point
• x2 – Upper bound
• a1 – Lower power law index
• a2 – Upper power low index

popsynth.distributions.bpl_distribution.sample_bpl(u, x0, x1, x2, a1, a2)

Sample from a broken power law between bounds.

Parameters:

• u – Uniform random number on {0,1}
• x0 – Lower bound
• x1 – Break point
• x2 – Upper bound
• a1 – Lower power law index
• a2 – Upper power low index