数据分布专业分析

以下为移动广告投放数据在“渠道 × 人群分层 × A/B版本 × 投放时段”维度下的分布特征与分析口径建议，覆盖曝光、点击、转化、成本及关键派生率指标。内容聚焦统计分布形态与差异点，便于后续诊断与优化决策。

一、数据结构与派生指标
- 基础维度：渠道（Channel）、人群分层（Audience Segment）、A/B版本（Creative/Test Arm）、投放时段标签（Hour/Time Slot）、日期/活动ID。
- 原始指标：曝光（Impressions，计数）、点击（Clicks，计数）、转化（Conversions，计数/二值）、成本（Cost，正值连续）。
- 派生率与单价：
  - CTR = Clicks / Impressions
  - CVR = Conversions / Clicks（或 / Impressions，需明确口径）
  - CPM = Cost / Impressions × 1000
  - CPC = Cost / Clicks
  - CPA = Cost / Conversions

二、总体分布形态（跨层通用特征）
- 曝光（Impressions）：显著右偏、长尾，且在细分人群与小渠道上存在高零占比与波动；相对泊松常见过度离散（负二项更合适）。时段上呈明显周期性（峰谷）。
- 点击（Clicks）：与曝光强相关，右偏且过度离散；CTR分布在低值区密集，呈Beta样态（大量<5%），小样本分箱抖动显著。
- 转化（Conversions）：零膨胀明显（大量0），负二项或零膨胀模型更贴近；CVR多集中在低值区，受样本量显著影响，短期内方差大。
- 成本（Cost）：正值连续型，常见对数正态或Gamma分布；CPC/CPA呈长尾，极端值受竞价和小样本驱动。CPM在高竞争时段上行。

三、分层差异与交互分布特征
- 渠道（Channel）差异：
  - 曝光：大渠道/聚合平台分布更集中，尾部相对收敛；小渠道更稀疏、零占比高。
  - 成本：CPM/CPC跨渠道中位数差异显著；程序化渠道成本方差更高。
  - CTR/CVR：素材匹配度与投放策略差异引发分布偏移，跨渠道比较需控制时段与人群。
- 人群分层（Audience）差异：
  - 精准/高意向人群：CTR/CVR中位数更高但样本量更小，分布易受噪声影响；CPA尾部风险高。
  - 广泛人群：曝光集中度高，CTR中位偏低但方差更稳定。
- A/B版本（Test Arm）差异：
  - CTR分布常对A/B敏感（素材与信息架构直接影响点击）；CVR也会受落地页/流程变化影响但稳定性更差。
  - 合理实验应确保曝光或用户层面均衡，否则各版本的曝光/成本分布会偏移，导致CTR/CVR比较失真。
- 投放时段（Time Slot）差异：
  - 曝光与成本：高流量时段（常见工作时段与晚间）曝光上升、CPM/CPC上行，分布右尾拉长。
  - CTR/CVR：在非峰值时段可能出现CTR提升（竞争低），但CVR峰值可能出现在用户转化行为更活跃的晚间；分布随时段显著重叠但中位数存在系统性偏移。
- 交互效应：
  - Channel × Time Slot：不同渠道在相同时段的CPM与CTR分布差异显著，建议以热力图检视。
  - Audience × A/B：素材信息与人群兴趣匹配会改变CTR/CVR的分布形态，需分层比较而非总体合并。

四、建议的分布摘要与报告口径
- 每个“渠道 × 人群 × A/B × 时段”单元，输出：
  - 原始分布摘要：P50/P75/P90/P95/P99、IQR（四分位距）、零占比（Clicks=0、Conversions=0）、变异系数（CV）。
  - 率值区间：CTR、CVR的Bootstrap或Beta-Binomial区间（建议报告95%区间与样本量）。
  - 成本单价：CPM、CPC、CPA的中位数与上分位（P90/P95），并标注极端值占比。
- 可视化建议：
  - 直方/密度图：成本（对数尺度）、CPC/CPA。
  - 箱线/小提琴图：按渠道/人群对CTR、CVR。
  - 热力图：时段 × 渠道的CTR、CPM；时段 × A/B的CVR。
  - ECDF：比较A/B版本在CTR/CVR全分布的差异而非仅均值。

五、统计分布与建模假设（用于理解与后续分析）
- 计数类：负二项（或零膨胀负二项）优于泊松，处理过度离散与大量零。
- 比例类（CTR/CVR）：Beta或Beta-Binomial，避免正态近似在低率区失真。
- 成本类（CPM/CPC/CPA）：Gamma或对数正态；对极端值采用Winsor化或对数变换。
- 分层比较：采用分层或多层模型（GLM/GLMM）控制渠道、人群、时段，评估A/B的主效应与交互。

六、质量与异常检查（确保分布可用）
- 基本逻辑：Clicks ≤ Impressions、Conversions ≤ Clicks；CTR/CVR ∈ [0,1]；Cost ≥ 0。
- 时间标签：时区统一、跨日与跨时段边界处理一致。
- 异常识别：极端CPA/CPC的分位截断、重复曝光计数、追踪缺失导致的零膨胀异常。
- 样本量门槛：对CVR等低基数指标设置最小曝光/点击阈值，避免分布受噪声主导。

七、关键结论与行动提示
- 分布整体右偏、长尾且分层差异显著；以中位数与高分位数作为稳健摘要优于均值。
- CTR/CVR在A/B与时段维度上表现出系统性偏移，需控制曝光均衡并采用分布级比较。
- 成本相关指标对时段与渠道竞争敏感，分析时应在对数尺度下比较并关注上尾风险。
- 后续优化建议：以“渠道 × 人群 × 时段 × A/B”的单元为核心，优先筛选“高CTR且CPA受控”的分布区域，谨慎扩大在“高CPM高尾风险”时段的投放。

如需要，我可基于实际数据样本提供分层分布的具体数值摘要与置信区间，并输出可直接用于报表的分布诊断模板。

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.