Beta#

class cuqi.distribution.Beta(alpha=None, beta=None, is_symmetric=False, **kwargs)#

Multivariate beta distribution of independent random variables x_i. Each is distributed according to the PDF function

\[f(x) = x^{(\alpha-1)}(1-x)^{(\beta-1)}\Gamma(\alpha+\beta) / (\Gamma(\alpha)\Gamma(\beta))\]

where \(\Gamma\) is the Gamma function.

Parameters:

alpha (float or array_like) – The shape parameter \(\alpha\) of the beta distribution.
beta (float or array_like) – The shape parameter \(\beta\) of the beta distribution.

Example

# % Generate a beta distribution
import numpy as np
import cuqi
import matplotlib.pyplot as plt
alpha = 0.5
beta  = 0.5
rng = np.random.RandomState(1)
x = cuqi.distribution.Beta(alpha, beta)
samples = x.sample(1000, rng=rng)
samples.hist_chain(0, bins=70)

__init__(alpha=None, beta=None, is_symmetric=False, **kwargs)#

Initialize the core properties of the distribution.

Parameters:

name (str, default None) – Name of distribution.
geometry (Geometry, default _DefaultGeometry (or None)) – Geometry of distribution.
is_symmetric (bool, default None) – Indicator if distribution is symmetric.

Methods

`__init__`([alpha, beta, is_symmetric])	Initialize the core properties of the distribution.
`cdf`(x)
`disable_FD`()	Disable finite difference approximation for logd gradient.
`enable_FD`([epsilon])	Enable finite difference approximation for logd gradient.
`get_conditioning_variables`()	Return the conditioning variables of this distribution (if any).
`get_mutable_variables`()	Return any public variable that is mutable (attribute or property) except those in the ignore_vars list
`get_parameter_names`()	Returns the names of the parameters that the density can be evaluated at or conditioned on.
`gradient`(args, *kwargs)	Returns the gradient of the log density at x.
`logd`(args, *kwargs)	Evaluate the un-normalized log density function of the distribution.
`logpdf`(x)	Evaluate the log probability density function of the distribution.
`pdf`(x)	Evaluate the log probability density function of the distribution.
`sample`([N])	Sample from the distribution.
`to_likelihood`(data)	Convert conditional distribution to a likelihood function given observed data

Attributes

`FD_enabled`	Returns True if finite difference approximation of the logd gradient is enabled.
`FD_epsilon`	Spacing for the finite difference approximation of the logd gradient.
`dim`	Return the dimension of the distribution based on the geometry.
`geometry`	Return the geometry of the distribution.
`is_cond`	Returns True if instance (self) is a conditional distribution.
`name`	Name of the random variable associated with the density.