density_inversion: KDE-based Inverse CDF Sampling for Synthetic Data

In JWileymisc: Miscellaneous Utilities and Functions

KDE-based Inverse CDF Sampling for Synthetic Data

Description

Generate synthetic samples that try to follow an observed distribution by inverting a smooth kernel density estimate (KDE).

Usage

density_inversion(x, n, KDEn = 100, seed = NULL)

Arguments

x	Numeric vector containing the observed data. Should be numeric or integer. Vector only (no datasets at this stage).
n	Integer scalar, the number of synthetic samples to generate.
KDEn	Integer scalar passed to [stats::density()] as the 'n' grid size for the KDE; larger values yield a finer grid for integration (default '100').
seed	Optional integer to set the random seed for reproducibility.

Details

This utility estimates a univariate density for the input vector, numerically integrates it to obtain a smooth cumulative distribution function (CDF), and then samples synthetic values by inverting that CDF for uniformly distributed probabilities. The result is a set of values that follow the shape of the observed data without reproducing exact observations.

The KDE is fit using [stats::density()] with bandwidth rule 'bw = "nrd0"'. The CDF is computed via trapezoidal integration of the KDE on its grid and normalized to \[0, 1\]. An inverse-CDF function is obtained via linear interpolation ([stats::approxfun()]), which is then evaluated at 'n' independent uniforms from \[0, 1\].

This approach produces smooth synthetic samples that closely match the observed density.

Value

A numeric vector of length 'n' containing the synthetic values.

See Also

[stats::density()], [stats::approxfun()], [stats::runif()].

Examples

sim_iris <- density_inversion(iris$Sepal.Length, n = 200, seed = 1234)

hist(iris$Sepal.Length)
hist(sim_iris)

# cleanup
rm(sim_iris)

JWileymisc documentation built on June 18, 2026, 9:06 a.m.