Chisquare Distribution

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

Calculates the chi-squared probability density function.

Parameters:

Name	Type	Description	Default
q	Union[float, array-like]	The value of the chi-squared variable.	required
df	Union[int, float, array-like]	The degrees of freedom.	required
lower_tail	bool	Whether to calculate the lower tail (default True).	True
log_prob	bool	Whether to return the log probability (default False).	False
dtype	dtype	The dtype of the output (default jnp.float_).	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	The chi-squared probability density function.

Examples:

>>> pchisq(2.0, 3)
Array(0.42759317, dtype=float32, weak_type=True)

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stamox.distribution.qchisq(p: Union[Float, ArrayLike], df: Union[Int, Float, ArrayLike], lower_tail = True, log_prob = False, dtype = <class 'jax.numpy.float64'>) -> ArrayLike

Computes the inverse of the chi-squared cumulative distribution function.

Parameters:

Name	Type	Description	Default
p	Union[Float, ArrayLike]	Probability value or array of probability values.	required
df	Union[Int, Float, ArrayLike]	Degrees of freedom.	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	dtype	The dtype of the output (default jnp.float_).	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	The quantiles corresponding to the given probabilities.

Examples:

>>> qchisq(0.95, 10)
Array(18.307034, dtype=float32)

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

Computes the chi-squared distribution.

Parameters:

Name	Type	Description	Default
x	Union[Float, ArrayLike]	A float or array-like object representing the values at which to evaluate the chi-squared distribution.	required
df	Union[Int, Float, ArrayLike]	The degrees of freedom for the chi-squared distribution.	required
lower_tail		A boolean indicating whether to compute the lower tail of the chi-squared distribution (defaults to True).	True
log_prob		A boolean indicating whether to return the log probability (defaults to False).	False
dtype		The dtype of the output (defaults to float32).	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	The chi-squared distribution evaluated at x.

Examples:

>>> dchisq(2.0, 3)
Array(0.20755368, dtype=float32, weak_type=True)

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

Generates random variates from the chi-squared distribution.

Parameters:

Name	Type	Description	Default
key	KeyArray	Random key to generate the random numbers.	required
sample_shape	Optional[Shape]	Shape of the output array. Defaults to None.	None
df	Union[Int, Float, ArrayLike]	Degrees of freedom. 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	dtype	The dtype of the output (default float_).	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	Random variates from the chi-squared distribution.

Examples:

>>> key = jax.random.PRNGKey(0)
>>> rchisq(key, df=2)
Array(1.982825, dtype=float32)