# Generating Random Samples from Non-Identical Truncated Order Statistics

## TL;DR

This paper introduces an efficient algorithm for sampling from the bounded kth order statistic of independent, non-identically distributed variables, especially effective in sparse density regions with boundary constraints.

## Contribution

The paper presents a novel algorithm for generating samples from non-identical truncated order statistics, improving efficiency over rejection sampling in sparse density scenarios.

## Key findings

- Algorithm is faster in sparse density regions.
- Effective for tight boundary conditions.
- Outperforms rejection sampling in specific cases.

## Abstract

We provide an efficient algorithm to generate random samples from the bounded kth order statistic in a sample of independent, but not necessarily identically distributed, random variables. The bounds can be upper or lower bounds and need only hold on the kth order statistic. Furthermore, we require access to the inverse CDF for each statistic in the ordered sample. The algorithm is slightly slower than rejection sampling when the density of the bounded statistic is large, however, it is significantly faster when the bounded density becomes sparse. We provide a practical example and a simulation that shows the superiority of this method for sparse regions arising from tight boundary conditions and/or over regions of low probability density.