arch.univariate.distribution.Distribution.partial_moment

abstract Distribution.partial_moment(n: int, z: float = 0.0, parameters: Sequence[float] | ndarray | Series | None = None) float[source]

Order n lower partial moment from -inf to z

Parameters:
n: int

Order of partial moment

z: float = 0.0

Upper bound for partial moment integral

parameters: Sequence[float] | ndarray | Series | None = None

Distribution parameters. Use None for parameterless distributions.

Returns:

Partial moment

Return type:

float

References

Notes

The order n lower partial moment to z is

\[\int_{-\infty}^{z}x^{n}f(x)dx\]

See [1] for more details.