pm: Partial Moments

In enricoschumann/NMOF: Numerical Methods and Optimization in Finance

Partial Moments

Description

Compute partial moments.

Usage

  pm(x, xp = 2, threshold = 0, lower = TRUE,
     normalise = FALSE, na.rm = FALSE)

Arguments

x	a numeric vector or a matrix
xp	exponent
threshold	a numeric vector of length one
lower	logical
normalise	logical
na.rm	logical

Details

For a vector x of length n, partial moments are computed as follows:

\mathrm{upper\ partial\ moment} = \frac{1}{n} \sum_{x > t}\left(x - t \right)^e

\mathrm{lower\ partial\ moment} = \frac{1}{n} \sum_{x < t}\left(t - x \right)^e

The threshold is denoted t, the exponent xp is labelled e.

If normalise is TRUE, the result is raised to 1/xp. If x is a matrix, the function will compute the partial moments column-wise.

See Gilli, Maringer and Schumann (2019), chapter 14.

Value

numeric

Author(s)

Enrico Schumann

References

Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/C2017-0-01621-X")}

Schumann, E. (2023) Financial Optimisation with R (NMOF Manual). https://enricoschumann.net/NMOF.htm#NMOFmanual

Examples

pm(x <- rnorm(100), 2)
var(x)/2

pm(x, 2, normalise = TRUE)
sqrt(var(x)/2)

enricoschumann/NMOF documentation built on Feb. 15, 2025, 12:28 p.m.