Poisson process#
- class quantflow.sp.poisson.PoissonProcess(*, intensity: Annotated[float, Ge(ge=0)] = 1.0)#
Methods:
CDF of the number of events at time
t
.Expected value at a time horizon
Probability density function of the number of events at time
t
.Expected variance at a time horizon
Generate a list of jump arrivals times up to time t
Jacobian of the CDF
Characteristic exponent at time t for a given input parameter
Frequency range of the process
For a poisson process this is just a list of 1s
Support of the process at time t
Attributes:
Intensity rate \(\lambda\) of the Poisson process
Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].
- analytical_cdf(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float, n: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) ndarray[tuple[int, ...], dtype[floating[Any]]] | float #
CDF of the number of events at time
t
.It’s given by
(76)#\[F\left(n\right)=\frac{\Gamma\left(\left\lfloor n+1\right\rfloor ,\lambda\right)}{\left\lfloor n\right\rfloor !}\]where \(\Gamma\) is the upper incomplete gamma function.
- analytical_mean(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) ndarray[tuple[int, ...], dtype[floating[Any]]] | float #
Expected value at a time horizon
- analytical_pdf(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float, n: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) ndarray[tuple[int, ...], dtype[floating[Any]]] | float #
Probability density function of the number of events at time
t
.It’s given by
(77)#\[f\left(n\right)=\frac{\lambda^{n}e^{-\lambda}}{n!}\]
- 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] #
Generate a list of jump arrivals times up to time t
- cdf_jacobian(t: ndarray[tuple[int, ...], dtype[floating[Any]]] | float, n: int | float | complex | ndarray | Series) ndarray #
Jacobian of the CDF
It’s given by
(78)#\[\frac{\partial F}{\partial\lambda}=-\frac{\lambda^{\left\lfloor n\right\rfloor }e^{-\lambda}}{\left\lfloor n\right\rfloor !}\]
- characteristic_exponent(t: int | float | complex | ndarray | Series, u: int | float | complex | ndarray | Series) int | float | complex | ndarray | Series #
Characteristic exponent at time t for a given input parameter
- frequency_range(std: float, max_frequency: float | None = None) Bounds #
Frequency range of the process
- sample_jumps(n: int) ndarray #
For a poisson process this is just a list of 1s
- support(mean: float, std: float, points: int) ndarray[tuple[int, ...], dtype[floating[Any]]] #
Support of the process at time t
- intensity: float#
Intensity rate \(\lambda\) of the Poisson process
- model_config: ClassVar[ConfigDict] = {'extra': 'forbid'}#
Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].