LPM: Lower Partial Moment

In NNS: Nonlinear Nonparametric Statistics

Lower Partial Moment

Description

This function generates a univariate lower partial moment for any degree or target.

Usage

LPM(degree, target, variable, excess_ret = FALSE)

Arguments

degree	numeric; (degree = 0) is frequency, (degree = 1) is area.
target	numeric; Set to target = mean(variable) for classical equivalences, but does not have to be. When excess_ret = FALSE, this can be a scalar or a vectorized target for the standard partial moment calculation. When excess_ret = TRUE, it is interpreted element-wise as the benchmark/threshold relative to variable.
variable	a numeric vector. data.frame or list type objects are not permissible.
excess_ret	logical; FALSE (default). If TRUE, switches from the standard vectorized-target partial moment to an element-wise excess-deviation calculation. For LPM, this computes pmax(target - variable, 0) raised to degree and averaged. In this mode, target must have length 1 or the same length as variable.

Value

LPM of variable

Author(s)

Fred Viole, OVVO Financial Systems

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995, 2nd edition: https://ovvo-financial.github.io/NNS/book/)

Examples

set.seed(123)
x <- rnorm(100)
LPM(0, mean(x), x)

NNS documentation built on April 10, 2026, 9:10 a.m.