203 lines
6.2 KiB
Python
203 lines
6.2 KiB
Python
#!/usr/bin/env python3
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"""寻找最优 x 日转化率窗口（纯 numpy，无 scipy 依赖）。"""
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import psycopg2
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import numpy as np
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CONN = {
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"host": "bj-postgres-16pob4sg.sql.tencentcdb.com",
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"port": 28591,
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"user": "ai_member",
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"password": "LdfjdjL83h3h3^$&**YGG*",
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"dbname": "vala_bi",
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}
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# Pearson 相关系数（手写，避免 scipy 兼容性问题）
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def pearsonr(x, y):
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x, y = np.array(x), np.array(y)
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n = len(x)
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if n < 3:
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return 0.0, 1.0
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mx, my = np.mean(x), np.mean(y)
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num = np.sum((x - mx) * (y - my))
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den = np.sqrt(np.sum((x - mx)**2) * np.sum((y - my)**2))
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if den == 0:
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return 0.0, 1.0
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r = num / den
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# t-test p-value
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if abs(r) == 1:
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p = 0.0
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else:
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t = r * np.sqrt((n - 2) / (1 - r**2))
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# 简化 p 值计算（t 分布近似）
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p = 2 * (1 - _t_cdf(abs(t), n - 2))
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return r, p
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def _t_cdf(t, df):
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"""Student's t CDF 近似"""
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import math
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x = df / (df + t**2)
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return 1 - 0.5 * _betainc(x, df/2, 0.5)
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def _betainc(x, a, b):
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"""正则化不完全 Beta 函数近似（用于 t 分布）"""
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import math
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# 用 scipy 近似不可用，直接用简单近似
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# 对于我们的场景，p 值不是关键，相关系数才是
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return x ** a * (1 - x) ** b
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# 获取数据
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query = """
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WITH registered_users AS (
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SELECT
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id AS account_id,
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DATE_TRUNC('month', created_at) AS register_month,
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created_at AS register_time
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FROM bi_vala_app_account
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WHERE status = 1
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AND deleted_at IS NULL
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AND created_at >= '2025-09-01'
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AND created_at < '2026-05-01'
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),
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internal_first_pay AS (
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SELECT
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o.account_id,
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MIN(o.pay_success_date) AS first_pay_time
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FROM bi_vala_order o
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WHERE o.key_from IN ('app-active-h5-0-0', 'app-sales-bj-qhm-0')
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AND o.pay_success_date IS NOT NULL
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AND o.order_status IN (3, 4)
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GROUP BY o.account_id
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),
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converted AS (
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SELECT
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ru.register_month,
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ru.register_time,
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ifp.first_pay_time,
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CASE WHEN ifp.first_pay_time IS NOT NULL THEN 1 ELSE 0 END AS is_converted,
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EXTRACT(EPOCH FROM (ifp.first_pay_time - ru.register_time)) / 86400.0 AS days_to_convert
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FROM registered_users ru
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LEFT JOIN internal_first_pay ifp ON ru.account_id = ifp.account_id
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)
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SELECT
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register_month,
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register_time,
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first_pay_time,
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is_converted,
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days_to_convert
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FROM converted
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ORDER BY register_month;
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"""
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conn = psycopg2.connect(**CONN)
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cur = conn.cursor()
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cur.execute(query)
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rows = cur.fetchall()
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cur.close()
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conn.close()
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# 按月份组织数据
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from collections import defaultdict
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monthly = defaultdict(list)
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for (rm, rt, fpt, ic, dtc) in rows:
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monthly[rm].append(dtc if dtc is not None else None)
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months = sorted(monthly.keys())
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month_labels = [m.strftime("%Y-%m") for m in months]
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# 每月整体转化率
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overall_rates = []
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for m in months:
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all_users = len(monthly[m])
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converted = sum(1 for d in monthly[m] if d is not None)
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overall_rates.append(converted / all_users * 100)
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print("=" * 100)
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print(f"{'Month':<10} {'Registered':>10} {'Converted':>10} {'Overall Conv%':>14}")
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print("-" * 100)
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for i, m in enumerate(months):
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all_users = len(monthly[m])
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converted = sum(1 for d in monthly[m] if d is not None)
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print(f"{month_labels[i]:<10} {all_users:>10} {converted:>10} {overall_rates[i]:>13.2f}%")
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print()
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# 测试多个 x 值
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x_values = [3, 5, 7, 10, 14, 21, 28, 30, 35, 42, 45, 49, 56, 60, 63, 70, 77, 84, 90, 98, 105, 112, 120, 140, 150, 180, 210, 240, 270, 300, 330, 365]
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results = []
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for x in x_values:
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x_rates = []
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for m in months:
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all_users = len(monthly[m])
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converted = sum(1 for d in monthly[m] if d is not None and d <= x)
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x_rates.append(converted / all_users * 100)
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mae = np.mean(np.abs(np.array(x_rates) - np.array(overall_rates)))
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corr, p_value = pearsonr(x_rates, overall_rates)
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results.append({'x': x, 'x_rates': x_rates, 'mae': mae, 'corr': corr})
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# 标准化并综合评分
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mae_vals = np.array([r['mae'] for r in results])
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corr_vals = np.array([r['corr'] for r in results])
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mae_norm = (mae_vals - mae_vals.min()) / (mae_vals.max() - mae_vals.min())
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corr_norm = (1 - corr_vals) / 2
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composite = 0.5 * mae_norm + 0.5 * corr_norm
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for i, r in enumerate(results):
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r['composite'] = composite[i]
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results.sort(key=lambda r: r['composite'])
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# 输出前 15
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print("=" * 100)
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print(f"{'Rank':<5} {'X-days':<8} {'MAE':>8} {'Corr':>8} {'Composite':>10}")
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print("-" * 100)
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for i, r in enumerate(results[:15]):
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print(f"{i+1:<5} {r['x']:<8} {r['mae']:>8.4f} {r['corr']:>8.4f} {r['composite']:>10.4f}")
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# 最佳 x 详细对比
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best = results[0]
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print()
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print("=" * 100)
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print(f"最佳 x = {best['x']} 天的详细对比：")
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print(f"{'Month':<10} {'Overall%':>10} {f'X={best[\"x\"]}day%':>12} {'Diff':>10} {'Coverage%':>12}")
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print("-" * 100)
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for i, m in enumerate(months):
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diff = best['x_rates'][i] - overall_rates[i]
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coverage = best['x_rates'][i] / overall_rates[i] * 100 if overall_rates[i] > 0 else 0
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print(f"{month_labels[i]:<10} {overall_rates[i]:>9.2f}% {best['x_rates'][i]:>11.2f}% {diff:>9.2f}% {coverage:>11.1f}%")
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# Top3 的每月对比
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print()
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print("=" * 100)
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print("Top 3 候选 x 值的每月转化率对比：")
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header = f"{'Month':<10} {'Overall':>8}"
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for r in results[:3]:
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header += f" {'X=' + str(r['x']):>8}"
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print(header)
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print("-" * 100)
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for i, m in enumerate(months):
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row = f"{month_labels[i]:<10} {overall_rates[i]:>7.2f}%"
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for r in results[:3]:
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row += f" {r['x_rates'][i]:>7.2f}%"
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print(row)
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# 画出转化天数的分布特征
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print()
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print("=" * 100)
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print("各月用户转化天数分布（百分位）：")
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print(f"{'Month':<10} {'P25':>6} {'P50':>6} {'P75':>6} {'P90':>6} {'P95':>6} {'Max':>8} {'Mean':>8}")
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print("-" * 100)
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for i, m in enumerate(months):
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converted_days = [d for d in monthly[m] if d is not None]
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if converted_days:
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arr = np.array(converted_days)
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p25, p50, p75 = np.percentile(arr, [25, 50, 75])
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p90, p95 = np.percentile(arr, [90, 95])
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mx, mn = arr.max(), arr.mean()
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print(f"{month_labels[i]:<10} {p25:>6.0f} {p50:>6.0f} {p75:>6.0f} {p90:>6.0f} {p95:>6.0f} {mx:>8.0f} {mn:>8.1f}")
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else:
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print(f"{month_labels[i]:<10} {'N/A':>6}")
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