# pm: Partial Moments In enricoschumann/NMOF: Numerical Methods and Optimization in Finance

## 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.

numeric

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.