Sampling errors of quantile estimations from finite samples of data

TL;DR

This paper derives empirical formulas to estimate the sampling error of quantile calculations from finite data samples, providing a practical tool for uncertainty assessment in climate science data analysis.

Contribution

It introduces new empirical relationships that relate quantile sampling errors to standard errors, facilitating quick uncertainty estimates for finite samples.

Findings

Derived scaling factors for quantile error estimation

Validated relationships using Monte Carlo experiments

Applicable to common climate data distributions

Abstract

Empirical relationships are derived for the expected sampling error of quantile estimations using Monte Carlo experiments for two frequency distributions frequently encountered in climate sciences. The relationships found are expressed as a scaling factor times the standard error of the mean; these give a quick tool to estimate the uncertainty of quantiles for a given finite sample size.