Heavy-Tailed and Zero-Inflated Distribution Analysis

What it is Heavy-tailed data have a non-negligible chance of producing very large values (e.g., Pareto/lognormal tails), so means/variances can be unstable. Zero-inflated data are counts with more zeros than standard Poisson/NB models expect; models explicitly add a “zero-generating” process alongside the count process.

Why interviewers ask about it Product metrics at scale often look like this: ad clicks per impression are mostly zero; creator revenue and session lengths have rare but huge values. Choosing appropriate models and estimators affects A/B test sensitivity, anomaly detection, and business decisions in systems like News Feed ranking or Ads delivery.

Core ideas to know

A common pitfall Candidates often jump to Poisson or log-transform everything, ignoring overdispersion and zero inflation. That leads to underfit, anticonservative p-values, and misleading average effects dominated by a few “whales.” Another miss is reporting only mean differences on heavy-tailed metrics without robust intervals or sensitivity checks. Strong answers name diagnostics (Hill/rank plots, zero-probability fit), justify ZIP/ZINB versus hurdle, and outline bootstrap-based inference.

Further reading