LPM.VaR: LPM VaR

In NNS: Nonlinear Nonparametric Statistics

LPM VaR

Description

Generates a value at risk (VaR) quantile based on the Lower Partial Moment ratio.

Usage

LPM.VaR(percentile, degree, x)

Arguments

percentile	numeric [0, 1]; The percentile for left-tail VaR.
degree	integer; (degree = 0) gives the interpolated empirical quantile (quantile(x, percentile, type = 7)), which on tied data need not be an exact inverse of LPM.ratio(0, ., x). Use it for probability statements, such as a VaR exceeded with a given frequency. (degree = 1) gives an area-weighted (severity-weighted) threshold, the percentile-expectile of x (Newey and Powell 1987): percentile of the area of deviations, not of the observations, lies below it, so it is not a quantile of x (for exponential data the degree-1 5% point has about a quarter of the observations below it). Higher degrees weight large deviations more.
x	a numeric vector.

Value

Returns the type-7 empirical quantile (degree = 0), whose strict or inclusive sample tail fraction may differ from percentile because of interpolation or ties, or the threshold with percentile of the directional deviation area below it (degree > 0).

Author(s)

Fred Viole, OVVO Financial Systems

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995, 2nd edition: https://ovvo-financial.github.io/NNS/book/)

Examples

## Not run: 
set.seed(123)
x <- rnorm(100)

## For 5th percentile, left-tail
LPM.VaR(0.05, 0, x)

## End(Not run)

NNS documentation built on Nov. 14, 2026, 1:09 a.m.