sql实现均衡度计算(洛伦兹曲线，基尼系数)

1.基本介绍

均衡度：使用洛伦兹曲线计算基尼系数，基尼系数代表均衡度，系数值越大证明越不均衡度，值约小证明越均衡。【例：拿贫富差距人口收入举例，将累计人口百分比作X轴，累计收入百分比作Y轴，绘制贫富差距洛伦兹曲线如下图，使用面积法计算：基尼系数=A面积/（A面积+B面积）】（这里基尼系数不会大于1，也不会小于零）。

2.使用场景

（一）职权履行均衡度

假设某执法单位有职权2000项，按照职权触发次数由低到高排序，等分10份，及每200个职权分一个挡位，计算X轴（累计职权数百分比）、Y轴（累计职权触发次数百分比）如下表：

职权分档排序	每档职权触发次数	X轴（职权累计百分比）	y轴（职权累计触发次数百分比）
1-200	0	10%	0
201-400	200	20%	0.7%
401-600	300	30%	1.8%
601-800	500	40%	3.6%
801-1000	550	50%	5.6%
1001-1200	999	60%	9.3%
1201-1400	1111	70%	14%
1401-1600	1765	80%	20%
1600-1800	1800	90%	26%
1800-2000	20000	100%	100%

绘制洛伦兹曲线如下图：

如图计算A、B区域面积得基尼系数为0.8，可得此单位处罚职权履行不均衡。

（二）案件月度分布均衡度

将某一执法单位每月案件量按照由小到大顺序排序，计算X轴（累计月份百分比）、Y轴（累计月案件量百分比）如下表：

月份	月检查量（万）	X轴(累计月份百分比)	Y轴(累计月检查量百分比)
6月	1	8%	2%
11月	1	16%	3%
12月	1	25%	5%
1月	2	33%	8.3%
4月	4	42%	15%
2月	5	50%	23.3%
8月	5	58%	31.6%
3月	6	67%	42%
7月	8	75%	55%
5月	9	83%	70%
9月	9	92%	85%
10月	9	100%	100%

绘制洛伦兹曲线如下图：

如图计算A、B区域面积得基尼系数为0.36，可得此单位检查月度分布较为均衡。

3.sql实现(函数)

计算均衡度(基尼系数)自定义函数(十等份计算，参数为查询到数据的sql语句的字符形式)
​
-- 根据批量数据进行分值切割从而计算均衡度
CREATE OR REPLACE FUNCTION JHD_JN(TABLENAME VARCHAR2) RETURN NUMBER 
AS
T_COUNT NUMBER;
QUERY_SQL VARCHAR2(20000);
BEGIN
QUERY_SQL:='
-- 先计算得到各维度不同职权code的被触发数量
WITH POWER_ALL AS (' || TABLENAME || '
),
-- 对上方进行10等分切割得到每段的长度以及需要在第一段补充(0,0)的长度
-- eg: aa:73 bb:2   (每段73个但是第一段73-2个)
POWER_SUM AS (
SELECT 
    CASE 
        WHEN MOD((SELECT COUNT(1) FROM POWER_ALL), 10) > 0 
            THEN TRUNC(ROUND((SELECT COUNT(1) FROM POWER_ALL)/10, 1))+1 
        ELSE ROUND((SELECT COUNT(1) FROM POWER_ALL)/10) 
    END aa,
    CASE 
        WHEN MOD((SELECT COUNT(1) FROM POWER_ALL), 10) > 0 THEN
            10-MOD((SELECT COUNT(1) FROM POWER_ALL),10)
        ELSE 0
    END bb
FROM dual
),
-- 如果当前列数不满足等份便在开头增加上一步的余数个0,0
POWER_ALL_DATA AS (
    SELECT tb1.*,ROWNUM SORT FROM (
        SELECT 
            ''0'' NAME,
            CASE 
                WHEN (SELECT bb-aa FROM POWER_SUM) > 0 THEN 0
                ELSE NULL
            END ALL_COUNT 
        FROM (SELECT 1 FROM dual CONNECT BY LEVEL <= (SELECT bb FROM POWER_SUM))
    
        UNION ALL
        
        SELECT NAME,ALL_COUNT FROM POWER_ALL
    ) tb1 WHERE tb1.ALL_COUNT IS NOT NULL
),
-- 先根据上方的aa对数据进行分割，假如有余数的话便先加上这个余数进行分割
POWER_LB1 AS (
SELECT tb1.ll-((SELECT aa FROM POWER_SUM)-1) s,tb1.ll e 
FROM (
    SELECT LEVEL ll FROM dual CONNECT BY LEVEL < (SELECT COUNT(1) FROM POWER_ALL_DATA) + 1 + CASE WHEN (SELECT aa-bb FROM POWER_SUM) > 0 AND (SELECT bb FROM POWER_SUM) > 0 THEN (SELECT bb FROM POWER_SUM) ELSE 0 END
) tb1 WHERE MOD(tb1.ll, (SELECT aa FROM POWER_SUM)) = 0
),
-- 如果有余数的话再次进行处理，从而实现如果有余数的话将第一段减少
POWER_LB AS (
SELECT 
    CASE 
        WHEN (SELECT aa-bb FROM POWER_SUM) > 0 AND (SELECT bb FROM POWER_SUM) > 0 AND s != 1 THEN s - (SELECT bb FROM POWER_SUM)
        ELSE s
    END s,
    CASE 
        WHEN (SELECT aa-bb FROM POWER_SUM) > 0 AND (SELECT bb FROM POWER_SUM) > 0 THEN e - (SELECT bb FROM POWER_SUM)
        ELSE e
    END e,
    ROWNUM*10 r
FROM POWER_LB1
),
-- 获取x和y轴数据(包含原点一共11个)
POWER_RESULT AS (
SELECT tb1.*,ROWNUM so FROM (
    SELECT 0 bfb,0 r FROM dual
​
    UNION
​
    SELECT  
        CASE 
            WHEN (SELECT SUM(ALL_COUNT) FROM POWER_ALL_DATA) = 0 THEN 0
            ELSE ROUND((SELECT SUM(ALL_COUNT)*100 FROM POWER_ALL_DATA WHERE SORT <= tb1.e)/(SELECT SUM(ALL_COUNT) FROM POWER_ALL_DATA),5)
        END bfb,
        r
    FROM POWER_LB tb1
) tb1 ORDER BY r
),
-- 计算面积一个三角形，九个梯形的和
POWER_DOWN_AREA AS (
SELECT SUM(jhd) DOWN_AREA FROM (
    SELECT 
        CASE 
            -- 三角形面积
            WHEN tb1.r < 1 THEN (SELECT ROUND(bfb*r/2 , 2)FROM POWER_RESULT WHERE so = 2)
            WHEN tb1.r = 11 THEN 0
            -- 九个梯形面积
            ELSE ROUND((tb1.bfb+(SELECT bfb FROM POWER_RESULT WHERE so = tb1.so + 1))*((SELECT r FROM POWER_RESULT WHERE so = tb1.so + 1) - tb1.r)/2,2)
        END jhd,
        tb1.*
    FROM POWER_RESULT tb1
))
​
-- 基尼系数(如果参数查询无数据则返回1,基尼系数最大为1。如果总面积为0则设置基尼系统为1)
-- 返回结果为百分数 eg：0.3 返回30
SELECT 
    CASE 
        WHEN ROUND(bfb*r/2, 2) = 0 THEN 100
        ELSE
            --NVL(ROUND(bfb*r/2, 2) - (SELECT * FROM POWER_DOWN_AREA),100)
            --ROUND(bfb*r/2, 2)
            NVL(ROUND((ROUND(bfb*r/2, 2) - (SELECT * FROM POWER_DOWN_AREA))/ROUND(bfb*r/2, 2),2),1)*100
    END AREA 
FROM (SELECT * FROM POWER_RESULT ORDER BY SO DESC) WHERE ROWNUM < 2';
EXECUTE IMMEDIATE QUERY_SQL  INTO T_COUNT;
RETURN  T_COUNT;   
END JHD_JN;
​
​
​
-- 直接根据X,Y数组进行均衡度计算
CREATE OR REPLACE FUNCTION JHD_JN1(TABLENAME VARCHAR2) RETURN NUMBER 
AS
T_COUNT NUMBER;
QUERY_SQL VARCHAR2(20000);
BEGIN
QUERY_SQL:='
WITH POWER_RESULT AS (
' || TABLENAME || '
),
POWER_DOWN_AREA AS (
SELECT SUM(jhd) DOWN_AREA FROM (
    SELECT 
        CASE 
            -- 三角形面积
            WHEN tb1.X < 1 THEN (SELECT ROUND(Y*X/2 , 2)FROM POWER_RESULT WHERE so = 2)
            WHEN tb1.X = (SELECT COUNT(1) FROM POWER_RESULT) THEN 0
            -- 多个梯形面积
            ELSE ROUND((tb1.Y+(SELECT Y FROM POWER_RESULT WHERE so = tb1.so + 1))*((SELECT X FROM POWER_RESULT WHERE so = tb1.so + 1) - tb1.X)/2,2)
        END jhd,
        tb1.*
    FROM POWER_RESULT tb1
))
​
-- 基尼系数(如果参数查询无数据则返回1,基尼系数最大为1。如果总面积为0则设置基尼系统为1)
-- 返回结果为百分数 eg：0.3 返回30
SELECT 
    CASE 
        WHEN ROUND(Y*X/2, 2) = 0 THEN 100
        ELSE
            NVL(ROUND((ROUND(Y*X/2, 2) - (SELECT * FROM POWER_DOWN_AREA))/ROUND(Y*X/2, 2),2),1)*100
    END AREA 
FROM (SELECT * FROM POWER_RESULT ORDER BY SO DESC) WHERE ROWNUM < 2';
EXECUTE IMMEDIATE QUERY_SQL  INTO T_COUNT;
RETURN  T_COUNT;   
END JHD_JN1;