pm: Partial Moments

Description Usage Arguments Details Value Author(s) References Examples

View source: R/pm.R

Description

Compute partial moments.

Usage

1
2
  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:

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.

Value

numeric

Author(s)

Enrico Schumann

References

Gilli, M., Maringer, D. and Schumann, E. (2011) Numerical Methods and Optimization in Finance, Chapter 13. Elsevier. http://www.elsevierdirect.com/product.jsp?isbn=9780123756626

Schumann, E. (2017) Financial Optimisation with R (NMOF Manual). http://enricoschumann.net/NMOF.htm#NMOFmanual

Examples

1
2
3
4
5
pm(x <- rnorm(100), 2)
var(x)/2

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

enricoschumann/NMOF documentation built on Feb. 14, 2019, 2:21 p.m.