pm function

Partial Moments

Compute partial moments.

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:

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.

Returns

numeric

References

Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. 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

Author(s)

Enrico Schumann

Examples

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

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