F Distribution

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

Calculates the cumulative distribution function of the F-distribution.

Parameters:

Name	Type	Description	Default
q	Union[Float, ArrayLike]	The value at which to evaluate the cdf.	required
dfn	Union[Float, ArrayLike]	The numerator degrees of freedom.	required
dfd	Union[Float, ArrayLike]	The denominator degrees of freedom.	required
lower_tail	bool	If True (default), the lower tail probability is returned.	True
log_prob	bool	If True, the logarithm of the probability is returned.	False
dtype	jnp.dtype	The dtype of the output (default is jnp.float_).	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	The cumulative distribution function evaluated at q.

Examples:

>>> pF(1.0, 1.0, 1.0)
Array(0.5000001, dtype=float32, weak_type=True)

---

stamox.distribution.qF(p: Union[Float, ArrayLike], dfn: Union[Float, ArrayLike], dfd: Union[Float, ArrayLike], lower_tail: bool = True, log_prob: bool = False, dtype = <class 'jax.numpy.float64'>) -> ArrayLike

Calculates the quantile function of a given distribution.

Parameters:

Name	Type	Description	Default
p	Union[Float, ArrayLike]	The quantile to calculate.	required
dfn	Union[Float, ArrayLike]	The degrees of freedom for the numerator.	required
dfd	Union[Float, ArrayLike]	The degrees of freedom for the denominator.	required
lower_tail	bool	Whether to calculate the lower tail or not. Defaults to True.	True
log_prob	bool	Whether to calculate the log probability or not. 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 calculated quantile.

Examples:

>>> qF(0.5, 1.0, 1.0)
Array([0.99999714], dtype=float32)

---

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

Calculates the gradient of the cumulative distribution function for a given x, dfn and dfd.

Parameters:

Name	Type	Description	Default
x	Union[Float, ArrayLike]	The value at which to calculate the gradient of the cumulative distribution function.	required
dfn	Union[Float, ArrayLike]	The numerator degrees of freedom.	required
dfd	Union[Float, ArrayLike]	The denominator degrees of freedom.	required
lower_tail	bool	Whether to calculate the lower tail of the cumulative distribution 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.float_.	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	The gradient of the cumulative distribution function.

Examples:

>>> dF(1.0, 1.0, 1.0)
Array(0.1591549, dtype=float32, weak_type=True)

---

stamox.distribution.rF(key: Union[jax.Array, jax._src.prng.PRNGKeyArray], sample_shape: Optional[Sequence[int]] = None, dfn: Union[Float, ArrayLike] = None, dfd: Union[Float, ArrayLike] = None, lower_tail: bool = True, log_prob: bool = False, dtype = <class 'jax.numpy.float64'>)

Generate random variates from F-distribution.

Parameters:

Name	Type	Description	Default
key	KeyArray	Random key used for PRNG.	required
sample_shape	Optional[Shape]	Shape of the samples to be drawn. Defaults to None.	None
dfn	Union[Float, ArrayLike]	Degrees of freedom in numerator.	None
dfd	Union[Float, ArrayLike]	Degrees of freedom in denominator.	None
lower_tail	bool	Whether to calculate 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 float32.	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	Random variates from F-distribution.

Examples:

>>> rF(jax.random.PRNGKey(0), dfn=1.0, dfd=1.0)
Array(40.787617, dtype=float32)