Distributional Fitting and Tail Analysis of Lead-Time Compositions: Nights vs. Revenue on Airbnb

Paper: arXiv 2601.12175

Authors: Harrison E. Katz, Jess Needleman, Liz Medina

Abstract

We analyze daily lead-time distributions for two Airbnb demand metrics, Nights Booked (volume) and Gross Booking Value (revenue), treating each day’s allocation across 0-365 days as a compositional vector. The data span 2,557 days from January 2019 through December 2025 in a large North American region. Three findings emerge. First, GBV concentrates more heavily in mid-range horizons: beyond 90 days, GBV tail mass typically exceeds Nights by 20-50%, with ratios reaching 75% at the 180-day threshold during peak seasons. Second, Gamma and Weibull distributions fit comparably well under interval-censored cross-entropy. Gamma wins on 61% of days for Nights and 52% for GBV, with Weibull close behind at 38% and 45%. Lognormal rarely wins (<3%). Nonparametric GAMs achieve 18-80x lower CRPS but sacrifice interpretability. Third, generalized Pareto fits suggest bounded tails for both metrics at thresholds below 150 days, though this may partly reflect right-truncation at 365 days; above 150 days, estimates destabilize. Bai-Perron tests with HAC standard errors identify five structural breaks in the Wasserstein distance series, with early breaks coinciding with COVID-19 disruptions. The results show that volume and revenue lead-time shapes diverge systematically, that simple two-parameter distributions capture daily pmfs adequately, and that tail inference requires care near truncation boundaries.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 6.0/10 (capped from 8.5: no out-of-sample test; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous empirical examination of lead-time distributions using a large, multi-year dataset with solid statistical methodologies, including generalized Pareto distributions, Wasserstein distances, and Bai-Perron structural break tests. The insight regarding the systematic divergence between booking volume and revenue timing offers high practical and novel value for revenue management.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Lead-Time Distributions for Airbnb Nights vs. Revenue] --> B[Data: 2,557 Daily Lead-Time Vectors 0-365 Days, 2019-2025]
    B --> C[Methodology: Compositional Analysis & Distance Metrics]
    C --> D[Model Fitting & Analysis: Parametric Gamma/Weibull/Lognormal, Nonparametric GAMs, GPD Tails, Bai-Perron Structural Breaks]
    D --> E[Finding 1: Revenue GBV concentrates more in mid-to-long horizons than Volume Nights]
    D --> F[Finding 2: Gamma 52-61% & Weibull 38-45% best fit daily PMFs; GAMs optimize CRPS]
    D --> G[Finding 3: EVT shows bounded tails below 150 days; 5 COVID-linked structural breaks detected]

Cited References (58)

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8. Cancellation policies in the hotel, airline and restaurant industries (2016)

0 of 58 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.