| pm {NMOF} | R Documentation |
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. doi:10.1016/C2017-0-01621-X
Schumann, E. (2023) Financial Optimisation with R (NMOF Manual). http://enricoschumann.net/NMOF.htm#NMOFmanual
Examples
pm(x <- rnorm(100), 2)
var(x)/2
pm(x, 2, normalise = TRUE)
sqrt(var(x)/2)