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arxiv: 2604.05188 · v1 · submitted 2026-04-06 · ⚛️ physics.soc-ph · stat.ME

Ratio of Quantiles Indicates Burstiness with Fewer False Negatives than the Conventional Burstiness Parameter

Joshua Z. Stadlan , Michelle Birkett , Jason H. Rife This is my paper

Pith reviewed 2026-05-10 18:45 UTC · model grok-4.3

classification ⚛️ physics.soc-ph stat.ME
keywords burstinessburstiness parameterquantile ratiotemporal activitypower-law distributionsfalse negativeshuman activity patternscomplex systems
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The pith

The Burstiness Tail-based Index uses ratios of quantile differences to identify bursty temporal patterns that the standard Burstiness Parameter misses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Researchers in complexity science use burstiness metrics to detect hidden interactions from fluctuating activity levels in time series. The conventional Burstiness Parameter often fails to flag moderately bursty distributions like certain power laws, leading to false negatives. This paper proposes the Burstiness Tail-based Index, which relies on the ratio of differences between quantiles to better capture tail behaviors. Simulations show BTI correctly classifies more cases and holds up better with small sample sizes or short observation periods. A reanalysis of human activity data demonstrates that switching to BTI alters the inferred timescales of burstiness.

Core claim

The paper establishes that the Burstiness Tail-based Index (BTI), computed from ratios of quantile differences in inter-event times, correctly identifies burstiness in distributions over parameter ranges where the conventional Burstiness Parameter (BP) produces false negatives. BTI maintains the approach of comparing to the exponential distribution but achieves greater sensitivity to heavy tails. It also exhibits improved robustness when applied to limited sample sizes drawn from distributions that BP classifies correctly in their exact form.

What carries the argument

The Burstiness Tail-based Index (BTI), a metric based on the ratio of differences in selected quantiles of the timing distribution, which highlights deviations from exponential timing in the tails.

If this is right

  • BTI will classify additional power-law distributions as bursty that BP misses.
  • BTI provides more stable results than BP when sample sizes are small or observation windows are short.
  • Reanalysis of empirical temporal data using BTI can lead to revised conclusions about the timescales over which burstiness occurs.
  • Complexity researchers can use BTI to more reliably infer the presence of underlying interactions from activity signals.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Many prior studies relying on BP may have underestimated burstiness in human or other complex systems.
  • BTI could be tested on other distribution families like log-normal to check for broader applicability.
  • Integrating BTI with existing modeling tools might improve forecasts of event clustering in time series.

Load-bearing premise

The specific quantiles chosen for the ratio in BTI capture the key tail differences of bursty distributions without creating new misclassifications in other families or under varied sampling.

What would settle it

A counterexample distribution, either analytical or from simulation, where BTI incorrectly labels a non-bursty case as bursty or vice versa, or an empirical dataset where independent measures contradict BTI's classification.

read the original abstract

Complexity researchers view burstiness--fluctuating levels of activity--as evidence of hidden interactions within the system generating the activity signal. Yet, current burstiness metrics miss evidence of burstiness in some moderately bursty distributions and under moderate sampling conditions. The canonical Burstiness Parameter (BP) compares distributions of timing statistics to the exponential distribution, representing the timing of independent random events, but it provides false negatives for some parameter ranges of power laws, with and without cut-offs. We introduce a metric that maintains BP's measurement approach but reduces false negatives: the Burstiness Tail-based Index (BTI). Based on ratios of differences in quantiles, BTI correctly classifies bursty distributions over certain parameter ranges misclassified by BP. Additionally, we find BTI to be more robust than BP in the presence of limited sample sizes and short observation windows, using simulated samples drawn from distributions correctly classified by BP in their analytical form. As a case study, we revisit an analysis of human activity data and find that the choice of BTI over BP influences interpretations of the timescales of burstiness in the dataset. Given these analytical, simulated, and empirical results, we argue for BTI's practical advantage over BP in assessing burstiness in real-world temporal signals for complexity research and time series modeling.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces the Burstiness Tail-based Index (BTI), defined via ratios of differences in quantiles of inter-event time distributions, as an alternative to the conventional Burstiness Parameter (BP). It claims analytically that BTI correctly classifies burstiness in certain power-law parameter ranges where BP yields false negatives, reports simulation evidence of greater robustness to limited sample sizes and short observation windows (using samples from BP-correct analytical distributions), and presents a human-activity case study in which switching to BTI alters conclusions about burstiness timescales.

Significance. If the central claims are substantiated, BTI would supply a practical, quantile-based refinement for burstiness detection in complexity research and time-series modeling, particularly valuable for moderately bursty signals and the small-sample regimes typical of empirical human-dynamics data.

major comments (1)
  1. [Abstract and simulation robustness tests] Abstract and simulation section: the robustness tests to limited sample sizes and short windows are performed exclusively on distributions that are correctly classified by BP in analytical form. This decouples the finite-sample evidence from the critical regimes where BP produces false negatives, so the manuscript does not directly demonstrate that BTI continues to suppress false negatives (or avoids introducing new biases) under the joint conditions of BP-misclassified power laws and small samples.
minor comments (2)
  1. [Abstract] Abstract: the precise quantiles whose differences enter the BTI ratio (e.g., 25th/75th or other percentiles) are not stated, hindering immediate reproducibility and comparison with other quantile-based measures.
  2. [Case study] Case-study section: quantitative details on how the inferred burstiness timescales differ between BP and BTI (e.g., specific numerical shifts in characteristic times) would strengthen the empirical claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract and simulation robustness tests] Abstract and simulation section: the robustness tests to limited sample sizes and short windows are performed exclusively on distributions that are correctly classified by BP in analytical form. This decouples the finite-sample evidence from the critical regimes where BP produces false negatives, so the manuscript does not directly demonstrate that BTI continues to suppress false negatives (or avoids introducing new biases) under the joint conditions of BP-misclassified power laws and small samples.

    Authors: We appreciate the referee for identifying this important gap. As noted in the manuscript, our finite-sample and short-window robustness tests used distributions where BP is analytically correct. We therefore have not directly evaluated whether BTI maintains its advantage in suppressing false negatives when both the analytical misclassification regime and limited sampling are present simultaneously. To address this, we will add new simulations that draw finite samples from power-law distributions (with and without cutoffs) in the parameter ranges where BP analytically yields false negatives, apply varying sample sizes and observation windows, and report the resulting classification performance for both metrics. These results, together with corresponding updates to the abstract and simulation section, will be included in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

BTI defined independently via quantile ratios; no derivation reduces to its inputs by construction

full rationale

The paper defines the Burstiness Tail-based Index (BTI) directly as ratios of differences in quantiles, preserving BP's comparative spirit but without embedding BP values or parameters into the BTI formula itself. Claims of reduced false negatives are supported by direct comparison to analytical BP behavior on power-law distributions and by separate finite-sample simulations (even when those simulations are restricted to BP-analytically-correct cases). No equations equate BTI to a fitted BP quantity, no self-citations supply load-bearing uniqueness theorems, and no ansatz or renaming of known results is smuggled in. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no free parameters, axioms, or invented entities are specified. BTI appears to be a direct definition using existing quantile concepts without additional fitted values or new physical postulates.

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Reference graph

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4 extracted references · 4 canonical work pages

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