arch.univariate.distribution.Distribution.partial_moment

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

Order n lower partial moment from -inf to z

Parameters
nint

Order of partial moment

zfloat, optional

Upper bound for partial moment integral

parametersndarray, optional

Distribution parameters. Use None for parameterless distributions.

Returns
float

Partial moment

Notes

The order n lower partial moment to z is

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

See [1] for more details.

References

1

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

Return type

float