Distributions

distributions ¶

Core functions for distributions module.

Functions¶

broken_power_law_log_normalization_constant ¶

broken_power_law_log_normalization_constant(x_min: float, x_max: float, transition: float, alpha_1: float, alpha_2: float) -> jax.Array

Log normalization constant of a broken power law distribution.

References: - GWTC-4.0: Population Properties of Merging Compact Binaries: https://arxiv.org/abs/2508.18083

Parameters:

Name	Type	Description	Default
`x_min`	`float`	The minimum value of the distribution.	required
`x_max`	`float`	The maximum value of the distribution.	required
`transition`	`float`	The transition point where the power law changes.	required
`alpha_1`	`float`	The power law index for x < transition.	required
`alpha_2`	`float`	The power law index for x >= transition.	required

Returns:

Type	Description
`Array`	The log normalization constant of the distribution.

broken_power_law_logpdf ¶

broken_power_law_logpdf(x: Array, x_min: float, x_max: float, transition: float, alpha_1: float, alpha_2: float) -> jax.Array

Log probability density function of a broken power law distribution.

References: - GWTC-4.0: Population Properties of Merging Compact Binaries: https://arxiv.org/abs/2508.18083

Parameters:

Name	Type	Description	Default
`x`	`Array`	The input value.	required
`x_min`	`float`	The minimum value of the distribution.	required
`x_max`	`float`	The maximum value of the distribution.	required
`transition`	`float`	The transition point where the power law changes.	required
`alpha_1`	`float`	The power law index for x < transition.	required
`alpha_2`	`float`	The power law index for x >= transition.	required

Returns:

Type	Description
`Array`	An array with the log probability density at x.

broken_power_law_unnormalized_logpdf ¶

broken_power_law_unnormalized_logpdf(x: Array, x_min: float, x_max: float, transition: float, alpha_1: float, alpha_2: float) -> jax.Array

Unnormalized log probability density function of a broken power law distribution.

References: - GWTC-4.0: Population Properties of Merging Compact Binaries: https://arxiv.org/abs/2508.18083

Parameters:

Name	Type	Description	Default
`x`	`Array`	The input value.	required
`x_min`	`float`	The minimum value of the distribution.	required
`x_max`	`float`	The maximum value of the distribution.	required
`transition`	`float`	The transition point where the power law changes.	required
`alpha_1`	`float`	The power law index for x < transition.	required
`alpha_2`	`float`	The power law index for x >= transition.	required

Returns:

Type	Description
`Array`	An array with the unnormalized log probability density at x.

mass_ratio_pairing_cdf ¶

mass_ratio_pairing_cdf(mass_ratio: Array, primary_mass: Array, beta: float, secondary_minimum: float, minimum: float = 0.0) -> Array

Return the normalized conditional pairing CDF P(q' <= q | m1).

mass_ratio_pairing_pdf ¶

mass_ratio_pairing_pdf(mass_ratio: Array, primary_mass: Array, beta: float, secondary_minimum: float, minimum: float = 0.0) -> Array

Return the normalized conditional pairing density p(q | m1).

power_law_plus_peak_cdf ¶

power_law_plus_peak_cdf(mass: Array, alpha: float, minimum: float, maximum: float, lambda_peak: float, peak_mean: float, peak_sigma: float, peak_maximum: float) -> Array

Return the normalized Talbot-Thrane-style power-law-plus-peak CDF.

power_law_plus_peak_pdf ¶

power_law_plus_peak_pdf(mass: Array, alpha: float, minimum: float, maximum: float, lambda_peak: float, peak_mean: float, peak_sigma: float, peak_maximum: float) -> Array

Return the normalized Talbot-Thrane-style power-law-plus-peak density.

planck_tapering_function ¶

planck_tapering_function(x: Array, x_min: float, delta: float) -> Array

Planck tapering function to smoothly transition between 0 and 1.

References: - GWTC-4.0: Population Properties of Merging Compact Binaries: https://arxiv.org/abs/2508.18083

Parameters:

Name	Type	Description	Default
`x`	`Array`	The input value.	required
`x_min`	`float`	The minimum value of the transition region.	required
`delta`	`float`	The width of the transition region.	required

Returns:

Type	Description
`Array`	An array with the value of the tapering function at x.