Reducing bias and variance in quantile estimates with an exponential model

TL;DR

This paper introduces a novel exponential model-based approach for estimating quantiles that reduces bias and variance, outperforming traditional methods especially when the data distribution is exponential or similar.

Contribution

The paper presents a new exponential model-based estimator for quantiles that achieves lower bias and variance, with good generalization beyond exponential distributions.

Findings

Outperforms standard estimators on exponential data

Achieves lower bias and variance in quantile estimation

Generalizes well to non-exponential distributions

Abstract

Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and median, that becomes the medians. There are different ways to estimate quantiles from finite samples described in the literature and implemented in statistics packages. It is possible to leverage the memory-less property of the exponential distribution and design high quality estimators that are unbiased and have low variance and mean squared errors. Naturally, these estimators out-perform the ones in statistical packages when the underlying distribution is exponential. But, they also happen to generalize well when that assumption is violated.