Beta Distribution¤

Computes the cumulative distribution function of the beta distribution.

Parameters:

Name	Type	Description	Default
`q`	`Union[Float, ArrayLike]`	Quantiles.	required
`a`	`Union[Float, ArrayLike]`	Shape parameter.	required
`b`	`Union[Float, ArrayLike]`	Shape parameter.	required
`lower_tail`	`bool`	If True (default), probabilities are P[X ≤ x], otherwise, P[X > x].	`True`
`log_prob`	`bool`	If True, probabilities are given as log(P).	`False`
`dtype`	`jnp.dtype`	The dtype of the output. Defaults to None.	`<class 'jax.numpy.float64'>`

Returns:

Type	Description
`ArrayLike`	The probability or log of the probability for each quantile.

Examples:

>>> q = jnp.array([0.1, 0.5, 0.9])
>>> a = 2.0
>>> b = 3.0
>>> pbeta(q, a, b)
Array([0.05230004, 0.68749976, 0.9963    ], dtype=float32)

Computes the quantile of beta distribution function.

Parameters:

Name	Type	Description	Default
`p`	`Union[Float, ArrayLike]`	A float or array-like object representing the quantile.	required
`a`	`Union[Float, ArrayLike]`	A float or array-like object representing the alpha parameter.	required
`b`	`Union[Float, ArrayLike]`	A float or array-like object representing the beta parameter.	required
`lower_tail`	`bool`	A boolean indicating whether to compute the lower tail of the	`True`
`log_prob`	`bool`	A boolean indicating whether to compute the log probability	`False`
`dtype`		The dtype of the output. Defaults to None.	`<class 'jax.numpy.float64'>`

Returns:

Type	Description
`ArrayLike`	The value of the beta distribution at the given quantile.

Examples:

>>> qbeta(0.5, 2, 3)
Array(0.38572744, dtype=float32)

Calculates the probability density function of the beta distribution.

Parameters:

Name	Type	Description	Default
`x`	`Union[Float, ArrayLike]`	A float or array-like object representing the value(s) at which to evaluate the PDF.	required
`a`	`Union[Float, ArrayLike]`	A float or array-like object representing the shape parameter of the beta distribution.	required
`b`	`Union[Float, ArrayLike]`	A float or array-like object representing the scale parameter of the beta distribution.	required
`lower_tail`	`bool`	A boolean indicating whether to calculate the lower tail (default True).	`True`
`log_prob`	`bool`	A boolean indicating whether to return the logarithm of the PDF (default False).	`False`
`dtype`		The dtype of the output. Defaults to None.	`<class 'jax.numpy.float64'>`

Returns:

Type	Description
`ArrayLike`	The probability density function of the beta distribution evaluated at x.

Examples:

>>> dbeta(0.5, 2, 3, lower_tail=True, log_prob=False)
Array(1.4999996, dtype=float32, weak_type=True)

Generates random numbers from the Beta distribution.

Parameters:

Name	Type	Description	Default
`key`	`Union[jax.Array, jax._src.prng.PRNGKeyArray]`	A PRNGKey used for random number generation.	required
`sample_shape`	`Optional[Sequence[int]]`	An optional shape for the output samples.	`None`
`a`	`Union[Float, ArrayLike]`	The shape parameter of the Beta distribution. Can be either a float or an array-like object.	`None`
`b`	`Union[Float, ArrayLike]`	The scale parameter of the Beta distribution. Can be either a float or an array-like object.	`None`
`lower_tail`	`bool`	Whether to return the lower tail probability (defaults to True).	`True`
`log_prob`	`bool`	Whether to return the log probability (defaults to False).	`False`
`dtype`		The dtype of the output. Defaults to jnp.float32.	`<class 'jax.numpy.float64'>`

Returns:

Type	Description
`ArrayLike`	Random numbers from the Beta distribution.

Examples:

>>> key = jax.random.PRNGKey(0)
>>> rbeta(key, sample_shape=(3,), a=2, b=3)
Array([0.02809353, 0.13760717, 0.49360353], dtype=float32)