popsynth.distributions.bpl_distribution module

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

Bases: LuminosityDistribution

Lmin

alpha

Lbreak

beta

Lmax

__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

phi(L)

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

draw_luminosity(size=1)

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

Parameters

size –

Returns

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.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.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