Compound Poisson

class quantflow.sp.poisson.CompoundPoissonProcess(*, intensity: Annotated[float, Ge(ge=0)] = 1.0, jumps: D)

A generic Compound Poisson process.

Methods:

analytical_mean	Expected value at a time horizon
analytical_variance	Expected variance at a time horizon
arrivals	Same as Poisson process
characteristic_exponent	The characteristic exponent of the Compound Poisson process, given by
sample_jumps	Sample jump sizes from an exponential distribution with rate parameter :class:b

Attributes:

intensity	Intensity rate \(\lambda\) of the Poisson process
jumps	Jump size distribution
model_config	Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

analytical_mean(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Expected value at a time horizon

analytical_variance(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Expected variance at a time horizon

arrivals(time_horizon: float = 1) → list[float]

Same as Poisson process

characteristic_exponent(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float, u: int | float | complex | ndarray | Series) → int | float | complex | ndarray | Series

The characteristic exponent of the Compound Poisson process, given by

\[\phi_{x_t,u} = t\lambda \left(1 - \Phi_{j,u}\right)\]

where \(\Phi_{j,u}\) is the characteristic function of the jump distribution

sample_jumps(n: int) → ndarray[tuple[int, ...], dtype[floating[Any]]]

Sample jump sizes from an exponential distribution with rate parameter :class:b

intensity: float

Intensity rate \(\lambda\) of the Poisson process

It determines the number of jumps in the same way as the PoissonProcess

jumps: D

Jump size distribution

model_config: ClassVar[ConfigDict] = {'extra': 'forbid'}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].