Gamma#

class zfit.prior.Gamma(alpha, beta, mu=0, name=None)[source]#

Bases: BasePrior

Gamma prior distribution.

The Gamma distribution is a flexible family of continuous probability distributions for positive values. Its shape can range from exponential-like (alpha=1) to bell-shaped (larger alpha values). The distribution is commonly used in Bayesian inference due to its conjugacy properties with certain likelihoods.

This prior is suitable for: - Rate parameters and inverse scales - Precision parameters (inverse of variance) - Waiting times and lifetimes - Any positive parameter with flexibility in shape

The parameterization used here: - Mean = alpha/beta (when mu=0) - Variance = alpha/beta²

Example

>>> # Gamma prior with shape=2, rate=1
>>> prior = Gamma(alpha=2.0, beta=1.0)
>>>
>>> # Shifted Gamma starting at 0.5
>>> prior = Gamma(alpha=2.0, beta=1.0, mu=0.5)

Initialize a Gamma prior.

Parameters:

  • alpha (float) – Shape parameter controlling the form of the distribution. Must be positive. Larger values make the distribution more bell-shaped.

  • beta (float) – Rate parameter (inverse scale). Must be positive. Larger values shift the distribution toward zero.

  • mu (float) – Location parameter that shifts the entire distribution. Defaults to 0 for a standard Gamma. The distribution has support on [mu, ∞).

  • name (str | None) – Optional name for the prior

__eq__(other)#

Compare two priors for equality.

Parameters:

other – Another ZfitPrior instance to compare with

Returns:

True if the priors are equal

Return type:

bool

__hash__()#

Return hash of the prior based on pdf and name.

Returns:

Hash value for the prior

Return type:

int

log_pdf(value=None)#

Return the log probability of the prior at the given value(s).

Parameters:

value – The parameter value(s) to evaluate the log probability at

Returns:

The log probability

sample(n)#

Sample n values from the prior distribution.

Parameters:

n – Number of samples to draw

Returns:

An array of samples