NMOF: pm – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

pm

Partial Moments

Compute partial moments.

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

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

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

upper partial moment = sum_{x > t}(x - t)^e / n

lower partial moment = sum_{x < t}(t - x)^e / n

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 (2011), Section 13.3.

numeric

Enrico Schumann

Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. https://www.elsevier.com/books/numerical-methods-and-optimization-in-finance/gilli/978-0-12-815065-8

Schumann, E. (2019) Financial Optimisation with R (NMOF Manual). http://enricoschumann.net/NMOF.htm#NMOFmanual

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

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

Numerical Methods and Optimization in Finance

v2.4-1

GPL-3

Authors

Enrico Schumann [aut, cre] (<https://orcid.org/0000-0001-7601-6576>)

Initial release

2021-04-09