Calculating peak percentile

Peak Percentile is a statistical estimate (based on the Normal Distribution) that provides an upper limit value of when nn% of tasks completed processing. For example 90% of transactions had a response time of 1 second or less. Peak Percentile allows you to measure whether workload targets are being met.

The following query calculates the 90% peak percentile of response time. The CASE statement shows the function required to calculate peak percentile.
SELECT TRAN,                                                          
       INT(SUM(TASKCNT))                        AS TASK_COUNT,          
       DEC(SUM(RESPONSE_TIME),8,6)              AS RESPONSE_TIME_TOT, 
       DEC(SUM(RESPONSE_TIME)/SUM(TASKCNT),8,6) AS RESPONSE_TIME_AVE, 
       CASE WHEN (SUM(TASKCNT) > 1) THEN                              
         DEC((1.282*SQRT(((SUM(TASKCNT)*SUM(RESPONSE_TIME_SSQ))       
                         -POWER(SUM(RESPONSE_TIME),2))                
                         /(SUM(TASKCNT)*(SUM(TASKCNT)-1))))           
                         +SUM(RESPONSE_TIME)/SUM(TASKCNT),10,8)       
       ELSE DEC(SUM(RESPONSE_TIME)/SUM(TASKCNT),10,8)                 
       END                             AS "RESPONSE_PEAK_90%"         
FROM CICSPA.CICSP1H                                                 
GROUP BY TRAN                                                         
ORDER BY TRAN                                                         
This query produces output like the following:
Figure 1. SQL query calculating 90% peak percentile of response time
                      RESPONSE     RESPONSE       RESPONSE     
            TASK        TIME         TIME           PEAK       
TRAN        COUNT       TOT          AVE            90%        
----  -----------  -----------  -----------  -------------     
ABAL            3     0.002592     0.000864     0.00095340     
APOS            4     0.003392     0.000848     0.00094987     
ASUM            4     0.003488     0.000872     0.00092082     
AUTS            1     0.000752     0.000752     0.00075200     
BALA            4     0.004016     0.001004     0.00163763     
BDEP            1     0.000704     0.000704     0.00070400     
CATA            2     0.006336     0.003168     0.00316800     
CSMI           11     0.009120     0.000829     0.00138661     
EORE            3     0.004272     0.001424     0.00215297     
ERLE            2     0.002336     0.001168     0.00148709     
MBOX            1     0.000816     0.000816     0.00081600     
NEWS            2     0.001952     0.000976     0.00138211     
Peak Percentiles are calculated using the formula:
Factor*Standard Deviation+Average
In the example, the Factor for 90% is 1.282. The following table shows the Factors for each 5 percentile above 50% (the average):
0.126           55%
0.253           60%
0.385           65%
0.524           70%
0.674           75%
0.842           80%
1.036           85%
1.282           90%
1.645           95%