pcntoolkit.math_functions.shash

Sinh-Arcsinh (SHASH) Distribution Implementation Module.

This module implements the Sinh-Arcsinh (SHASH) distribution and its variants as described in Jones and Pewsey (2009) [1]. The SHASH distribution is a flexible distribution family that can model skewness and kurtosis through separate parameters.

The module provides:

Basic SHASH transformations (S, S_inv, C)
SHASH distribution (base implementation)
SHASHo distribution (location-scale variant)
SHASHo2 distribution (alternative parameterization)
SHASHb distribution (standardized variant)

References

Notes

The implementation uses PyMC and PyTensor for probabilistic programming capabilities. All distributions support random sampling and log-probability calculations.

Attributes

`CONST1`
`CONST2`
`KV_GRADIENT_DP`
`kv`
`shash`
`shashb`
`shasho`
`shasho2`

Classes

`Kv`
`SHASH`
`SHASHb`
`SHASHbRV`
`SHASHo`
`SHASHo2`
`SHASHo2RV`
`SHASHoRV`
`SHASHrv`

Functions

`K`(p, x[, chunks])
`P`(→ numpy.typing.NDArray[numpy.float64])	The P function as given in Jones et al.
`S`(→ numpy.typing.NDArray[numpy.float64])	Sinh arcsinh transformation.
`S_inv`(→ numpy.typing.NDArray[numpy.float64])	Inverse sinh arcsinh transformation.
`m`(→ numpy.typing.NDArray[numpy.float64])	The r'th uncentered moment as given in Jones et al.
`m1m2`(→ Tuple[float, float])

Module Contents

class Kv

Bases: pytensor.scalar.basic.BinaryScalarOp

grad(inputs: Sequence[pytensor.graph.basic.Variable[Any, Any]], output_gradients: Sequence[pytensor.graph.basic.Variable[Any, Any]]) → List[pytensor.graph.basic.Variable]

impl(p: float | int, x: float | int) → float

static st_impl(p: float | int, x: float | int) → float

nfunc_spec = ('scipy.special.kv', 2, 1)

class SHASH

Bases: pymc.distributions.Continuous

static P(q: float) → float

classmethod dist(epsilon: pytensor.tensor.TensorLike, delta: pytensor.tensor.TensorLike, **kwargs: Any) → Any

logp(epsilon: float, delta: float) → float

static m1(epsilon: float, delta: float) → float

static m1m2(epsilon: float, delta: float) → Tuple[float, float]

static m2(epsilon: float, delta: float) → float

my_K

rv_op

class SHASHb

Bases: pymc.distributions.Continuous

classmethod dist(mu: pytensor.tensor.TensorLike, sigma: pytensor.tensor.TensorLike, epsilon: pytensor.tensor.TensorLike, delta: pytensor.tensor.TensorLike, **kwargs: Any) → Any

logp(mu: float, sigma: float, epsilon: float, delta: float) → float

rv_op

class SHASHbRV

Bases: pytensor.tensor.random.op.RandomVariable

classmethod rng_fn(rng: numpy.random.Generator, mu: float, sigma: float, epsilon: float, delta: float, size: int | Tuple[int, Ellipsis] | None = None) → numpy.typing.NDArray[numpy.float64]

dtype = 'floatX'

name = 'shashb'

signature = '(),(),(),()->()'

class SHASHo

Bases: pymc.distributions.Continuous

classmethod dist(mu: pytensor.tensor.TensorLike, sigma: pytensor.tensor.TensorLike, epsilon: pytensor.tensor.TensorLike, delta: pytensor.tensor.TensorLike, **kwargs: Any) → Any

logp(mu: float, sigma: float, epsilon: float, delta: float) → float

rv_op

class SHASHo2

Bases: pymc.distributions.Continuous

classmethod dist(mu: pytensor.tensor.TensorLike, sigma: pytensor.tensor.TensorLike, epsilon: pytensor.tensor.TensorLike, delta: pytensor.tensor.TensorLike, **kwargs: Any) → Any

logp(mu: float, sigma: float, epsilon: float, delta: float) → float

rv_op

class SHASHo2RV

Bases: pytensor.tensor.random.op.RandomVariable

classmethod rng_fn(rng: numpy.random.Generator, mu: pytensor.tensor.TensorLike, sigma: pytensor.tensor.TensorLike, epsilon: pytensor.tensor.TensorLike, delta: pytensor.tensor.TensorLike, size: int | Tuple[int, Ellipsis] | None = None) → numpy.typing.NDArray[numpy.float64]

dtype = 'floatX'

name = 'shasho2'

signature = '(),(),(),()->()'

class SHASHoRV

Bases: pytensor.tensor.random.op.RandomVariable

classmethod rng_fn(rng: numpy.random.Generator, mu: pytensor.tensor.TensorLike, sigma: pytensor.tensor.TensorLike, epsilon: pytensor.tensor.TensorLike, delta: pytensor.tensor.TensorLike, size: int | Tuple[int, Ellipsis] | None = None) → numpy.typing.NDArray[numpy.float64]

dtype = 'floatX'

name = 'shasho'

signature = '(),(),(),()->()'

class SHASHrv

Bases: pytensor.tensor.random.op.RandomVariable

classmethod rng_fn(rng: numpy.random.Generator, epsilon: float, delta: float, size: int | Tuple[int, Ellipsis] | None = None) → numpy.typing.NDArray[numpy.float64]

dtype = 'floatX'

name = 'shash'

signature = '(),()->()'

K(p, x, chunks=None)

P(q: numpy.typing.NDArray[numpy.float64]) → numpy.typing.NDArray[numpy.float64]: The P function as given in Jones et al.

S(x: numpy.typing.NDArray[numpy.float64], e: numpy.typing.NDArray[numpy.float64], d: numpy.typing.NDArray[numpy.float64]) → numpy.typing.NDArray[numpy.float64]: Sinh arcsinh transformation.

S_inv(x: numpy.typing.NDArray[numpy.float64], e: numpy.typing.NDArray[numpy.float64], d: numpy.typing.NDArray[numpy.float64]) → numpy.typing.NDArray[numpy.float64]: Inverse sinh arcsinh transformation.

m(epsilon: numpy.typing.NDArray[numpy.float64], delta: numpy.typing.NDArray[numpy.float64], r: int) → numpy.typing.NDArray[numpy.float64]: The r’th uncentered moment as given in Jones et al.

m1m2(epsilon: float, delta: float) → Tuple[float, float]

CONST1

CONST2

KV_GRADIENT_DP = 1e-08

kv

shash

shashb

shasho

shasho2