KDE-based Inverse CDF Sampling for Synthetic Data

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.

Value

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

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.

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)