数据分布专业分析

Below is a distribution-focused description of app behavior logs for DAU, time-on-app, feature reach and funnel, and user segmentation (novice/heavy), explicitly considering version and date dimensions. This is designed to guide analysis and modeling; validate these forms on your data with diagnostics before adoption.

Scope and unit of analysis

• Dimensions: date (daily granularity) and app version (current app binary/feature flag state).
• Levels: user-level events/session-level metrics; aggregated daily cohort by version.
• Recommended reporting: for each date×version cohort, compute robust summaries (median, IQR, p90–p99) and distribution diagnostics.

DAU (Daily Active Users)

• Aggregated daily counts (by date×version) typically show:
  • Overdispersed count distribution across days with weekly seasonality and release-driven structural breaks.
  • Negative Binomial fits better than Poisson for day-level counts due to variance > mean and burstiness from campaigns/releases.
  • Distribution shifts across versions (level changes, variance changes). Check for changepoints at release dates.
• User-level activity (binary active per day):
  • Within a date×version cohort, the distribution of “active probability” is heterogeneous; Beta-Binomial models capture overdispersion.
• Practical summaries:
  • Daily time series: mean, variance, overdispersion index (variance/mean), day-of-week effects, holiday effects.
  • Change detection: CUSUM or Bayesian changepoint around version rollouts.

Time on app (session dwell time and per-user daily time)

• Per session:
  • Strong right-skew with heavy tails; log-normal or Gamma typically fit. Some apps exhibit Weibull if session hazard changes over time.
  • Possible multimodality (short utility sessions vs long consumption sessions). A two-component mixture (e.g., mixture of log-normals) often improves fit.
  • Truncation/censoring: SDK inactivity timeouts cap sessions; treat long-running background sessions carefully.
• Per user per day (sum of sessions):
  • Compound right-skew; log1p transform tends to normalize. Robust statistics (median, p90, p99) recommended over mean due to extreme tails.
  • Expect higher variance in heavy users and versions enabling autoplay/streaming.
• Practical summaries:
  • Session-level: median, IQR, p90, p99; fit log-normal/Gamma; QQ plots on log scale; KS/AD tests.
  • Winsorize or trim at 99.9th percentile for reporting; separately track extreme usage.

Feature reach (feature touch/trigger rates)

• Binary reach (user triggered feature at least once per day):
  • Within date×version, reach rate distribution across users is degenerate at {0,1}; model the aggregate rate via Beta (for proportions) or Beta-Binomial (counts).
  • Rare features show zero inflation; hierarchical logistic regression with random effects (version, date, user segment) handles sparse data.
• Frequency of usage (counts per user):
  • Zero-inflated count distribution; Negative Binomial with zero-inflation typically fits better than plain Poisson.
• Practical summaries:
  • Report reach: mean proportion with Wilson/Bayesian intervals; p50–p95 across users for usage count.
  • Compare versions via uplift in reach and frequency; adjust for segment mix to avoid Simpson’s paradox.

Funnel metrics (multi-step flows, e.g., View → Click → Start → Complete)

• Each step’s conversion is a conditional probability; distributions across cohorts are Beta-like with overdispersion.
• Multiplicative structure yields heavy drop-off; earlier steps have higher variance; later steps often sparse.
• Correlation across steps: users who pass early steps more likely to pass later ones; hierarchical models (multilevel logistic) capture this.
• Practical summaries:
  • For each date×version: per-step conversion rate with credible intervals; funnel completion distribution; variance decomposition by step.
  • Small cohorts: use Bayesian shrinkage (Beta priors) to stabilize estimates. Evaluate end-to-end conversion and per-step lifts across versions.

User segmentation (novice vs heavy)

• Example operational definitions (tune to your context):
  • Novice: install age ≤ 7 days or cumulative active days ≤ 3; low session count and short dwell time.
  • Heavy: top decile/quartile of weekly sessions or daily dwell time; or RFM-based thresholds.
• Distributional differences:
  • Novice: shorter sessions, lower feature reach, higher variance day-to-day (learning phase). Dwell time often unimodal with a short-session peak.
  • Heavy: pronounced heavy tails in dwell time and usage counts; higher feature reach; more stable activity patterns but larger outliers.
• Modeling:
  • Mixture models (e.g., two-component log-normal for dwell time) reflect segment heterogeneity.
  • Include segment as a random/fixed effect when comparing versions to avoid compositional bias.

Version and date dimensions

• Temporal patterns:
  • Weekly seasonality (weekday/weekend), monthly cycles, campaign spikes, holidays.
  • Structural breaks at releases; evaluate pre/post windows to attribute shifts.
• Version effects:
  • Treat version as a categorical factor or hierarchical level; consider rollout fraction (staged releases).
  • Use cohorting by install-date to separate composition changes from version treatment effects.
• Recommended modeling:
  • Panel models with date fixed effects and version random/fixed effects for DAU/reach.
  • Time-series with regressors: ARIMA/ETS or BSTS with release dummies for DAU.
  • Distributional comparison: eCDF, KS/AD tests, quantile regression to detect shifts beyond the mean.

Diagnostics and data quality

• Sessionization rules: confirm inactivity timeout and foreground/background definitions.
• Bot/fraud filters: identify anomalous ultra-high session counts or durations.
• Missing/late events: quantify skew from delayed logging; use lag-adjusted windows for funnels.
• Metric stability: track p95–p99 volatility; apply robust methods (median, MAD) for alerting.

Reporting checklist per date×version

• DAU: count, variance/mean ratio, weekday effect, changepoints.
• Time on app: session-level and user-day level median/IQR/p90/p99; fitted distribution family and GOF.
• Feature reach: proportion with intervals; zero-inflation indicators; usage count distribution.
• Funnel: per-step conversion with intervals; end-to-end conversion; stepwise lifts vs previous version.
• Segments: split all above by novice/heavy; compare distributional shifts; note composition shares.

Key takeaways

• Expect overdispersed counts (Negative Binomial) for DAU and zero-inflated counts for feature usage.
• Expect right-skew and heavy tails for dwell time; log-normal/Gamma fits are standard, often with mixtures across user segments.
• Use Beta/Beta-Binomial families for reach and funnel conversion, with hierarchical modeling to stabilize small cohorts.
• Always stratify by version and date, and control for segment composition to avoid misleading lifts.

Below is a report-ready specification to describe and flag the distributions of four key metrics—UV (Unique Visitors), Session Duration, Retention, and Conversion—across three dimensions (Channel, Region, Device). It is designed for accurate, consistent generation of executive summaries and operational reports.

1. Scope and metric definitions

• Dimensions (labels):
  • Channel: marketing/acquisition source (e.g., Organic, Paid, Referral)
  • Region: geographic market (use ISO country or market codes)
  • Device: device category (Desktop, Mobile Web, App, Tablet)
• Metrics:
  • UV: unique visitors per reporting period per dimension cell (deduplicated user IDs)
  • Session Duration: average session duration per cell; compute from session-level durations. Prefer robust central tendency (median) and also track mean
  • Retention: cohort-based return rate; commonly D1 and D7
    • D1 retention = retained_next_day_new_users / new_users_in_cohort
    • D7 retention = retained_within_7_days_new_users / new_users_in_cohort
  • Conversion: rate of users completing target event
    • Conversion rate = converters / eligible_users (define eligibility clearly; often UV or sessions with exposure)

2. Distribution summary method (per metric, across all Channel×Region×Device cells)

• Core descriptors:
  • Count of cells (N)
  • Median and Interquartile Range (IQR = Q3 − Q1)
  • Mean and Standard Deviation (SD)
  • Percentiles: P5, P25, P50, P75, P95, P99
  • Coefficient of Variation (CV = SD/Mean) for comparability
  • Percentile rank for each cell value (to enable “top/bottom x%” reporting)
• Rate metrics (Retention, Conversion) are bounded [0,1]; use logit transform for stability in distribution analytics when needed:
  • logit(p) = ln(p / (1 − p)), applied only for 0 < p < 1 and sufficient denominators

3. Outlier marking (robust, report-friendly)

• General approach: use robust thresholds to avoid false positives in skewed data
• For UV and Duration (skewed counts/times):
  • Apply Tukey fences on log scale for stability:
    • Compute Z = log(value)
    • Identify mild outliers: Z < Q1(Z) − 1.5×IQR(Z) or Z > Q3(Z) + 1.5×IQR(Z)
    • Identify extreme outliers: Z beyond 3×IQR(Z) from the quartiles
• For Retention and Conversion (rates):
  • Require minimum denominator per cell (e.g., n ≥ 100 eligible users or new users) to reduce noise; otherwise flag as “Insufficient sample”
  • Use robust fences on logit scale:
    • Compute Y = logit(p)
    • Mild outliers: Y < Q1(Y) − 1.5×IQR(Y) or Y > Q3(Y) + 1.5×IQR(Y)
    • Extreme outliers: 3×IQR(Y) thresholds
  • Optionally corroborate with Wilson interval for cell-level confidence bounds; flag as outlier if outside the global median’s Wilson band and passes denominator threshold

4. Report-ready output fields (for each metric and each Channel×Region×Device cell)

• period: reporting window identifier (e.g., 2025-09 W38)
• channel, region, device: dimension labels
• metric_name: one of [UV, Session_Duration, Retention_D1, Retention_D7, Conversion]
• value: metric value for the cell
• denominator:
  • UV: visitors (if applicable, equals value)
  • Session Duration: number of sessions contributing
  • Retention: new_users_in_cohort
  • Conversion: eligible_users
• global_distribution:
  • global_median, global_IQR, global_mean, global_SD
  • p5, p25, p50, p75, p95, p99 (global percentiles across all cells)
• cell_positioning:
  • percentile_rank (0–100)
  • deviation_from_global_median (absolute and percent)
• outlier_flag:
  • values: None, Mild, Extreme, Insufficient_Sample
  • direction: High, Low, NA
  • method: Tukey_log (for UV/Duration) or Tukey_logit (for rates)
• quality_tags:
  • sample_ok: True/False (based on denominator threshold)
  • data_completeness: percent of expected data present
  • notes: optional diagnostic (e.g., “new campaign launch,” “tracking change detected”)

5. Narrative guidelines for report generation (per metric)

• UV distribution:
  • Summarize central tendency (median) and spread (IQR, P95)
  • State the proportion of cells in top decile and bottom decile by UV
  • Highlight outliers with dimension tags, e.g., “Extreme High UV in [Channel=Paid, Region=US, Device=Mobile Web]”
• Session Duration distribution:
  • Use median duration and IQR; mention skew (without assuming shape)
  • Identify cells with unusually high or low durations and check sample_ok
• Retention (D1/D7):
  • Report global median and spread, then list outliers where denominators are sufficient
  • Clearly differentiate “statistical outlier” vs. “low sample size”
• Conversion distribution:
  • Provide central tendency and spread; call out high/low outliers with adequate denominators
  • Optionally include Wilson CI for the top flagged cells

6. Implementation notes to preserve accuracy

• Consistency:
  • Use the same period and cohort definitions across dimensions
  • Clearly define eligibility for conversion and new-user criteria for retention
• Stability:
  • Apply log or logit transforms only for distribution analytics, not for reporting raw values
  • Maintain dimension-level minimum denominators to avoid unstable rate estimates
• Governance:
  • Track changes in tracking/attribution that can affect UV, conversion, or retention
  • Version the report specification and note any method updates

This specification enables automated, consistent distribution analysis with explicit outlier marking and clear dimension labels. It supports concise executive summaries while preserving methodological rigor for operational teams.