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

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.