arch.univariate.distribution.Distribution.partial_moment

abstract Distribution.partial_moment(n, z=0.0, parameters=None)

Order n lower partial moment from -inf to z

Parameters

• n (int) – Order of partial moment

• z (float, optional) – Upper bound for partial moment integral

• parameters (ndarray, optional) – Distribution parameters. Use None for parameterless distributions.

Returns

Partial moment

Return type

float

References

1

Winkler et al. (1972) “The Determination of Partial Moments” Management Science Vol. 19 No. 3

Notes

The order n lower partial moment to z is

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

See 1 for more details.