Annotating and forecasting a long‑tail distribution
Quick Overview
Evaluates robust summarization and forecasting for long-tailed daily share-count distributions. Strong answers compute mean, median, P1, P99, visualize with log scales or percentile bands, and forecast seasonality with heavy-tail-aware methods.
Annotating and forecasting a long‑tail distribution
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Onsite
Scenario:
Page share counts show a heavy‑tail. Annotate key stats (mean, median, P1, P
99) and provide a forecast for future share volumes.
Question 1:
Given long‑tail shares distribution, how would you annotate mean, median, P1, P99 and forecast trend? (Hint: quantile smoothing, seasonal decomposition)
Quick Answer: Evaluates robust summarization and forecasting for long-tailed daily share-count distributions. Strong answers compute mean, median, P1, P99, visualize with log scales or percentile bands, and forecast seasonality with heavy-tail-aware methods.
Annotating and forecasting a long‑tail distribution
Meta
Jul 12, 2025, 6:59 PM
mediumData ScientistOnsiteStatistics & Math
22
0
Annotating and Forecasting a Long-tail Distribution
You are analyzing daily share counts across many pages on a social platform. The cross-sectional distribution of per-page shares on any given day is heavy-tailed: most pages get few or zero shares, while a small fraction get very large counts. You need to summarize the distribution and forecast future share volumes.
Assume you have daily per-page share counts y_p,t and daily total shares Y_t over 6 to 24 months, with weekly seasonality and occasional viral spikes.
Constraints & Assumptions
Use robust statistics because the distribution is zero-inflated and long-tailed.
Compute cross-sectional summaries by day or rolling window.
Visualize the distribution so extreme values do not hide the body.
Forecast both total volume and distributional summaries where useful.
Clarifying Questions to Ask Guidance
Are bot, spam, duplicate, or paid shares already removed?
Should pages with zero exposure be included in the denominator?
Is the forecast for total shares, per-page distribution, or tail risk?
Which horizon matters: daily, weekly, monthly, or campaign planning?
Part 1 - Robust Summaries
For a given day or rolling window, compute and annotate mean, median, P1, and P99 across pages.
What This Part Should Cover Guidance
Define the analysis population and denominator.
Compute mean, median, 1st percentile, and 99th percentile across page share counts.
Explain why mean and median can differ substantially.
Annotate zero inflation and tail behavior.
Part 2 - Visualization
How would you compute and visualize these statistics for interpretability?
What This Part Should Cover Guidance
Use log or log1p scaling, percentile bands, box plots, violin plots, histograms, CCDFs, and time-series bands.
Consider winsorized means or trimmed views while preserving separate tail reporting.
Avoid hiding viral spikes if they matter to the business.
Part 3 - Forecasting
How would you forecast share-volume trends over time while accounting for seasonality and heavy tails?
What This Part Should Cover Guidance
Forecast total shares and robust distributional summaries separately if needed.
Use seasonal decomposition, robust regression, quantile smoothing, median or percentile forecasting, and anomaly handling.
Include uncertainty intervals and backtesting.
Treat viral events as tail risk rather than normal noise.
Follow-up Questions Guidance
What if P1 is always zero?
How would you forecast P99 separately from the median?
How would you explain the long tail to executives?