Poisson Distribution

stamox.distribution.ppoisson(q: Union[Float, ArrayLike], rate: Union[Float, ArrayLike], lower_tail = True, log_prob = False, dtype = <class 'jax.numpy.float64'>) -> ArrayLike

Computes the cumulative distribution function of the Poisson distribution.

Parameters:

Name	Type	Description	Default
q	Union[Float, ArrayLike]	The value at which to evaluate the CDF.	required
rate	Union[Float, ArrayLike]	The rate parameter of the Poisson distribution.	required
lower_tail	bool	Whether to compute the lower tail of the CDF. 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 jnp.float_.	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	The cumulative distribution function of the Poisson distribution evaluated at q.

Examples:

>>> ppoisson(1.0, rate=1.0)

---

stamox.distribution.qpoisson(p: Union[Float, ArrayLike], rate: Union[Float, ArrayLike], lower_tail: Bool = True, log_prob: Bool = False, dtype = <class 'jax.numpy.int64'>) -> ArrayLike

Computes the quantile function of the Poisson distribution.

Parameters:

Name	Type	Description	Default
p	Union[Float, ArrayLike]	The probability at which to evaluate the quantile function.	required
rate	Union[Float, ArrayLike]	The rate parameter of the Poisson distribution.	required
lower_tail	bool	Whether to compute the lower tail of the quantile function. 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 jnp.int_.	<class 'jax.numpy.int64'>

Returns:

Type	Description
ArrayLike	The quantile function of the Poisson distribution evaluated at p.

Examples:

>>> qpoisson(0.5, rate=1.0)

---

stamox.distribution.dpoisson(x: Union[Float, ArrayLike], rate: Union[Float, ArrayLike], lower_tail = True, log_prob = False, dtype = <class 'jax.numpy.float64'>) -> ArrayLike

Computes the probability density function of the Poisson distribution.

Parameters:

Name	Type	Description	Default
x	Union[Float, ArrayLike]	The value at which to evaluate the PDF.	required
rate	Union[Float, ArrayLike]	The rate parameter of the Poisson distribution.	required
lower_tail	bool	Whether to compute the lower tail of the PDF. 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 jnp.float_.	<class 'jax.numpy.float64'>

Returns:

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

Examples:

>>> dpoisson(1.0, rate=1.0)

---

stamox.distribution.rpoisson(key: PRNGKeyArray, sample_shape: Optional[Sequence[int]] = None, rate: Union[Float, ArrayLike] = None, lower_tail = True, log_prob = False, dtype = <class 'jax.numpy.int64'>) -> ArrayLike

Generates samples from the Poisson distribution.

Parameters:

Name	Type	Description	Default
key	KeyArray	Random number generator state used for random sampling.	required
rate	Union[Float, ArrayLike]	The rate parameter of the Poisson distribution.	None
sample_shape	Optional[Shape]	Shape of the output array. Defaults to None.	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	jnp.dtype	The dtype of the output. Defaults to jnp.int_.	<class 'jax.numpy.int64'>

Returns:

Type	Description
ArrayLike	Samples from the Poisson distribution.

Examples:

>>> key = jrand.PRNGKey(0)
>>> rpoisson(key, rate=1.0)