This function generates a univariate lower partial moment for any degree or target.

NNS (Nonlinear Nonparametric Statistics) leverages partial moments – the fundamental elements of variance that asymptotically approximate the area under f(x) – to provide a robust foundation for nonlinear analysis while maintaining linear equivalences. Designed for real-world data that violates symmetry, linearity, or distributional assumptions, NNS delivers a comprehensive suite of advanced statistical techniques, including: Numerical integration, Numerical differentiation, Clustering, Correlation, Dependence, Causal analysis, ANOVA, Regression, Classification, Seasonality, Autoregressive modeling, Normalization, Stochastic superiority / dominance and Advanced Monte Carlo sampling. All routines based on: Viole, F. and Nawrocki, D. (2013), Nonlinear Nonparametric Statistics: Using Partial Moments (ISBN: 1490523995, Second edition: <https://ovvo-financial.github.io/NNS/book/>).

Fred Viole

Nonlinear Nonparametric Statistics

Roberto Spadim

Rasheed Khoshnaw

LPM function

<dl><dt>degree</dt>
<dd>numeric; <code>(degree = 0)</code> is frequency, <code>(degree = 1)</code> is area.</dd>
<dt>target</dt>
<dd>numeric; Set to <code>target = mean(variable)</code> for classical equivalences, but does not have to be.
When <code>excess_ret = FALSE</code>, this can be a scalar or a vectorized target for the standard partial moment calculation.
When <code>excess_ret = TRUE</code>, it is interpreted element-wise as the benchmark/threshold relative to <code>variable</code>.</dd>
<dt>variable</dt>
<dd>a numeric vector. <a href="/link/data.frame?package=NNS&version=13.1" data-mini-rdoc="NNS::data.frame">data.frame</a> or <a href="/link/list?package=NNS&version=13.1" data-mini-rdoc="NNS::list">list</a> type objects are not permissible.</dd>
<dt>excess_ret</dt>
<dd>logical; <code>FALSE</code> (default). If <code>TRUE</code>, switches from the standard vectorized-target
partial moment to an element-wise excess-deviation calculation. For <code>LPM</code>, this computes
<code>pmax(target - variable, 0)</code> raised to <code>degree</code> and averaged. In this mode, <code>target</code>
must have length 1 or the same length as <code>variable</code>.</dd></dl>

Arguments

Fred Viole, OVVO Financial Systems

Author

Lower Partial Moment — LPM

<dl>

<dt>degree</dt>
<dd>numeric; <code>(degree = 0)</code> is frequency, <code>(degree = 1)</code> is area.</dd>


<dt>target</dt>
<dd>numeric; Set to <code>target = mean(variable)</code> for classical equivalences, but does not have to be.
When <code>excess_ret = FALSE</code>, this can be a scalar or a vectorized target for the standard partial moment calculation.
When <code>excess_ret = TRUE</code>, it is interpreted element-wise as the benchmark/threshold relative to <code>variable</code>.</dd>


<dt>variable</dt>
<dd>a numeric vector. <a href='https://rdrr.io/r/base/data.frame.html'>data.frame</a> or <a href='https://rdrr.io/r/base/list.html'>list</a> type objects are not permissible.</dd>


<dt>excess_ret</dt>
<dd>logical; <code>FALSE</code> (default). If <code>TRUE</code>, switches from the standard vectorized-target
partial moment to an element-wise excess-deviation calculation. For <code>LPM</code>, this computes
<code>pmax(target - variable, 0)</code> raised to <code>degree</code> and averaged. In this mode, <code>target</code>
must have length 1 or the same length as <code>variable</code>.</dd>

</dl>

LPM: Lower Partial Moment

Description

Usage

Value

Arguments

Author

References

Examples