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.