pyhs3.distributions.AsymmetricCrystalBallDist

class pyhs3.distributions.AsymmetricCrystalBallDist(**data)

Crystal Ball distribution implementation.

Implements the generalized asymmetrical double-sided Crystal Ball line shape as defined in ROOT’s RooCrystalBall.

The probability density function is defined as:

\[\begin{split}f(m; m_0, \sigma_L, \sigma_R, \alpha_L, \alpha_R, n_L, n_R) = \begin{cases} A_L \cdot \left(B_L - \frac{m - m_0}{\sigma_L}\right)^{-n_L}, & \text{for } \frac{m - m_0}{\sigma_L} < -\alpha_L \\ \exp\left(-\frac{1}{2} \cdot \left[\frac{m - m_0}{\sigma_L}\right]^2\right), & \text{for } \frac{m - m_0}{\sigma_L} \leq 0 \\ \exp\left(-\frac{1}{2} \cdot \left[\frac{m - m_0}{\sigma_R}\right]^2\right), & \text{for } \frac{m - m_0}{\sigma_R} \leq \alpha_R \\ A_R \cdot \left(B_R + \frac{m - m_0}{\sigma_R}\right)^{-n_R}, & \text{otherwise} \end{cases}\end{split}\]

where:

\[\begin{split}\begin{align} A_i &= \left(\frac{n_i}{\alpha_i}\right)^{n_i} \cdot \exp\left(-\frac{\alpha_i^2}{2}\right) \\ B_i &= \frac{n_i}{\alpha_i} - \alpha_i \end{align}\end{split}\]

Parameters:

• m – Observable variable

• m0 – Peak position (mean)

• sigma_L – Left-side width parameter (must be > 0)

• sigma_R – Right-side width parameter (must be > 0)

• alpha_L – Left-side transition point (must be > 0)

• alpha_R – Right-side transition point (must be > 0)

• n_L – Left-side power law exponent (must be > 0)

• n_R – Right-side power law exponent (must be > 0)

Note

All parameters except m and m0 must be positive. The distribution reduces to a single-sided Crystal Ball when one of the alpha parameters is set to zero.

Parameters:

data (Any)

__init__(**data)

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

Parameters:

data (Any)

Methods

__init__(**data)	Create a new model by parsing and validating input data from keyword arguments.
construct([_fields_set])
copy(*[, include, exclude, update, deep])	Returns a copy of the model.
dict(*[, include, exclude, by_alias, ...])
expression(context)	Evaluate the Crystal Ball distribution.
from_orm(obj)
get_parameter_list(context, param_key)	Reconstruct a parameter list from flattened indexed keys.
json(*[, include, exclude, by_alias, ...])
model_construct([_fields_set])	Creates a new instance of the Model class with validated data.
model_copy(*[, update, deep])	!!! abstract "Usage Documentation"
model_dump(*[, mode, include, exclude, ...])	!!! abstract "Usage Documentation"
model_dump_json(*[, indent, include, ...])	!!! abstract "Usage Documentation"
model_json_schema([by_alias, ref_template, ...])	Generates a JSON schema for a model class.
model_parametrized_name(params)	Compute the class name for parametrizations of generic classes.
model_post_init(context, /)	This function is meant to behave like a BaseModel method to initialise private attributes.
model_rebuild(*[, force, raise_errors, ...])	Try to rebuild the pydantic-core schema for the model.
model_validate(obj, *[, strict, ...])	Validate a pydantic model instance.
model_validate_json(json_data, *[, strict, ...])	!!! abstract "Usage Documentation"
model_validate_strings(obj, *[, strict, ...])	Validate the given object with string data against the Pydantic model.
parse_file(path, *[, content_type, ...])
parse_obj(obj)
parse_raw(b, *[, content_type, encoding, ...])
process_parameter(param_key)	Process a single parameter that can be either a string reference or numeric value.
process_parameter_list(param_key)	Process a list parameter containing mixed string references and numeric values.
schema([by_alias, ref_template])
schema_json(*[, by_alias, ref_template])
update_forward_refs(**localns)
validate(value)

Attributes

constants	Dictionary of PyTensor constants generated from numeric field values.
model_computed_fields
model_config	Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].
model_extra	Get extra fields set during validation.
model_fields
model_fields_set	Returns the set of fields that have been explicitly set on this model instance.
parameters	Set of parameter names this component depends on.
type
alpha_L
alpha_R
m
m0
n_L
n_R
sigma_R
sigma_L
name