Student T Distribution

stamox.distribution.pt(q: Union[Float, ArrayLike], df: Union[Int, Float, ArrayLike], loc: Union[Float, ArrayLike] = 0.0, scale: Union[Float, ArrayLike] = 1.0, lower_tail: bool = True, log_prob: bool = False, dtype = <class 'jax.numpy.float64'>) -> ArrayLike

Calculates the probability of a given value for Student T distribution.

Parameters:

Name	Type	Description	Default
q	Union[Float, ArrayLike]	The value to calculate the probability of.	required
df	Union[Int, Float, ArrayLike]	The degrees of freedom of the distribution.	required
loc	Union[Float, ArrayLike]	The location parameter of the distribution.	0.0
scale	Union[Float, ArrayLike]	The scale parameter of the distribution.	1.0
lower_tail	bool	Whether to calculate the lower tail probability or not.	True
log_prob	bool	Whether to return the log probability or not.	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 for Student T distribution.

Examples:

>>> pt(1.0, 1.0)
Array(0.74999994, dtype=float32, weak_type=True)

---

stamox.distribution.qt(p: Union[Float, ArrayLike], df: Union[Int, Float, ArrayLike], loc: Union[Float, ArrayLike] = 0.0, scale: Union[Float, ArrayLike] = 1.0, lower_tail = True, log_prob = False, dtype = <class 'jax.numpy.float64'>) -> ArrayLike

Calculates the quantile of Student T distribution.

Parameters:

Name	Type	Description	Default
p	Union[Float, ArrayLike]	A float or array-like object representing the quantile to be calculated.	required
df	Union[Int, Float, ArrayLike]	An int, float, or array-like object representing the degrees of freedom.	required
loc	Union[Float, ArrayLike]	An optional float or array-like object representing the location parameter. Defaults to 0.0.	0.0
scale	Union[Float, ArrayLike]	An optional float or array-like object representing the scale parameter. Defaults to 1.0.	1.0
lower_tail		A boolean indicating whether the lower tail should be used. Defaults to True.	True
log_prob		A boolean indicating whether the probability should be logged. Defaults to False.	False
dtype		The dtype of the output. Defaults to jnp.float_.	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	The quantile of the Student T distribution.

Examples:

>>> qt(0.5, 1.0)
Array(0., dtype=float32, weak_type=True)

---

stamox.distribution.dt(x: Union[Float, ArrayLike], df: Union[Int, Float, ArrayLike], loc: Union[Float, ArrayLike] = 0.0, scale: Union[Float, ArrayLike] = 1.0, lower_tail: bool = True, log_prob: bool = False, dtype = <class 'jax.numpy.float64'>) -> ArrayLike

Calculates the probability density function of a Student's t-distribution.

Parameters:

Name	Type	Description	Default
x	Union[Float, ArrayLike]	A float or array-like object representing the values at which to evaluate	required
df	Union[Int, Float, ArrayLike]	Degrees of freedom for the Student's t-distribution.	required
loc	Union[Float, ArrayLike]	Location parameter for the Student's t-distribution. Defaults to 0.0.	0.0
scale	Union[Float, ArrayLike]	Scale parameter for the Student's t-distribution. Defaults to 1.0.	1.0
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.float_.	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	The probability density function evaluated at x.

Examples:

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

---

stamox.distribution.rt(key: PRNGKeyArray, sample_shape: Optional[Sequence[int]] = None, df: Union[Int, Float, ArrayLike] = None, loc: Union[Float, ArrayLike] = 0.0, scale: Union[Float, ArrayLike] = 1.0, lower_tail: bool = True, log_prob: bool = False, dtype = <class 'jax.numpy.float64'>) -> ArrayLike

Generates random numbers from a t-distribution.

Parameters:

Name	Type	Description	Default
key	PRNGKeyArray	Type of the random number generator.	required
sample_shape	Optional[Sequence[int]]	Shape of the output array.	None
df	Union[Int, Float, ArrayLike]	Degrees of freedom.	None
loc	Union[Float, ArrayLike]	Location parameter.	0.0
scale	Union[Float, ArrayLike]	Scale parameter.	1.0
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.float_.	<class 'jax.numpy.float64'>

Returns:

Type	Description
ArrayLike	Random numbers from a t-distribution.

Examples:

>>> rt(key, (2, 3), 1.0)
Array([[1.9982358e+02, 2.3699088e-01, 6.6509140e-01],
        [5.3681795e-02, 3.3967651e+01, 6.8611817e+00]], dtype=float32)