使用sqlite/PHP获得两个不同行/列中两个数字的方差和标准差

Question

我有一个具有以下结构的SQLite数据库:

rowid       ID                  startTimestamp   endTimestamp   subject
1           00:50:c2:63:10:1a   1000             1090           entrance
2           00:50:c2:63:10:1a   1100             1270           entrance
3           00:50:c2:63:10:1a   1300             1310           door1
4           00:50:c2:63:10:1a   1370             1400           entrance
.
.
.

我在这里准备了一个sqlfiddle:http://sqlfiddle.com/#!2/fe8c6/2

使用此SQL-Query,我可以获得endTime和一行与下一行之间的startTime之间的平均差异,按主题和ID排序:

SELECT
    id,
    ( MAX(endtimestamp) - MIN(startTimestamp)
    - SUM(endtimestamp-startTimestamp)
    ) / (COUNT(*)-1) AS averageDifference
FROM
    table1
WHERE ID = '00:50:c2:63:10:1a'
AND subject = 'entrance'
GROUP BY id;

我的问题:要计算平均值是没有问题的,这就是查询.但是,我怎样才能得到标准偏差和这些值的方差？

Answer 1

首先通过将表连接到自身并按 ID 分组来查找感兴趣的时间差异，然后查找平均值、方差V(x) = E(x^2) - (E(x))^2和标准差，如下sqrt(V)所示

SELECT ID, AVG(diff) AS average,
       AVG(diff*diff) - AVG(diff)*AVG(diff) AS variance,
       SQRT(AVG(diff*diff) - AVG(diff)*AVG(diff)) AS stdev
FROM
    (SELECT t1.id, t1.endTimestamp,
            min(t2.startTimeStamp) - t1.endTimestamp AS diff
    FROM table1 t1
    INNER JOIN table1 t2
    ON t2.ID = t1.ID AND t2.subject = t1.subject
    AND t2.startTimestamp > t1.startTimestamp  -- consider only later startTimestamps
    WHERE t1.subject = 'entrance'
    GROUP BY t1.id, t1.endTimestamp) AS diffs
GROUP BY ID