Gamma Distribution¤

Computes the cumulative distribution function of the gamma distribution.

Parameters:

Name	Type	Description	Default
`q`	`Union[Float, ArrayLike]`	A float or array-like object representing the input to the gamma function.	required
`shape`	`Union[Float, ArrayLike]`	A float or array-like object representing the shape parameter of the gamma function.	`1.0`
`rate`	`Union[Float, ArrayLike]`	A float or array-like object representing the rate parameter of the gamma function.	`1.0`
`lower_tail`	`bool`	A boolean indicating whether to compute the lower tail of the gamma function.	`True`
`log_prob`	`bool`	A boolean indicating whether to compute the logarithm of the probability density function.	`False`
`dtype`		The dtype of the output. Defaults to jnp.float_.	`<class 'jax.numpy.float64'>`

Returns:

Type	Description
`ArrayLike`	The CDF value of the given value or array of values.

Examples:

>>> pgamma(1.0, 0.5, 0.5)
Array(0.6826893, dtype=float32, weak_type=True)

Computes the quantile of the gamma distribution.

Parameters:

Name	Type	Description	Default
`p`	`Union[Float, ArrayLike]`	A float or array-like object representing the quantile.	required
`shape`	`Union[Float, ArrayLike]`	A float or array-like object representing the shape parameter of the gamma distribution.	`1.0`
`rate`	`Union[Float, ArrayLike]`	A float or array-like object representing the rate parameter of the gamma distribution.	`1.0`
`lower_tail`	`bool`	A boolean indicating whether to compute the lower tail (default) or upper tail.	`True`
`log_prob`	`bool`	A boolean indicating whether to compute the log probability (default False).	`False`
`dtype`		The dtype of the output. Defaults to float_.	`<class 'jax.numpy.float64'>`

Returns:

Type	Description
`ArrayLike`	The quantile of the gamma distribution.

Examples:

>>> qgamma(0.5, 0.5, 0.5)
Array([0.45493677], dtype=float32)

Compute density of gamma distribution.

Parameters:

Name	Type	Description	Default
`x`	`Union[Float, ArrayLike]`	The value at which to evaluate the gamma distribution.	required
`shape`	`Union[Float, ArrayLike]`	The shape parameter of the gamma distribution. Defaults to 1.0.	`1.0`
`rate`	`Union[Float, ArrayLike]`	The rate parameter of the gamma distribution. Defaults to 1.0.	`1.0`
`lower_tail`	`bool`	Whether to compute the lower tail of the gamma distribution. Defaults to True.	`True`
`log_prob`	`bool`	Whether to return the log probability. Defaults to False.	`False`
`dtype`	`jnp.dtype`	The dtype of the output. Defaults to	`<class 'jax.numpy.float64'>`

Returns:

Type	Description
`ArrayLike`	The density of the gamma distribution evaluated at `x`. If `log_prob` is True, returns the log probability.

Examples:

>>> dgamma(1.0, 0.5, 0.5)
Array(0.24197064, dtype=float32, weak_type=True)

Generates random gamma values.

Parameters:

Name	Type	Description	Default
`key`		A PRNGKey to use for the random number generation.	required
`sample_shape`	`Optional[Sequence[int]]`	An optional shape for the output array.	`None`
`shape`	`Union[Float, ArrayLike]`	The shape parameter of the gamma distribution.	`1.0`
`rate`	`Union[Float, ArrayLike]`	The rate parameter of the gamma distribution.	`1.0`
`lower_tail`	`bool`	Whether to return the lower tail of the distribution.	`True`
`log_prob`	`bool`	Whether to return the log probability of the result.	`False`
`dtype`		The dtype of the output. Defaults to jnp.float_.	`<class 'jax.numpy.float64'>`

Returns:

Type	Description
`ArrayLike`	A random gamma value or an array of random gamma values.

Examples:

>>> rgamma(key, shape=0.5, rate=0.5)
Array(0.3384059, dtype=float32)