Broken Power Law
Broken power law distribution implementation.
Functions¶
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. |
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(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. |