**Instructions**

**Determine how many sources (N) nationwide**

**Determine number of sources in MA CT floor sample set**  **For solid waste incineration sources follow CA A** **Section 129(a)(2) guidance:** Take 12 percent of units in the category, and round up to next whole number for MACT floor sample set

**For all other sources follow CA A** **Section 112(d)(3):** N nationwide≥30, take top 12% of sources with data, and round up to next whole number for MACT floor sample N nationwide <30, take top 5 sources with data for MACT floor sample set

**Rank sources to Determine the MA CT floor sample set**  Calculate the UPL for each source using a confidence interval of 99% and rank the sources by the UPL to determine the best performing 12 percent (existing source MACT) and best performing source (new source
**Identify the distribution of sample set** Statistical tests of the kurtosis and skewness are used to evaluate the normality assumption.
For data sets with greater than 3 runs (n>3) use the "n>3Distribution" tab to determine the distribution. Enter run values for each source in the Raw Data section.
For data sets with 3 runs (n=3) use the "n=3Distribution" tab to determine the distribution. Enter run values for each source in the Raw Data section.
The skewness, kurtosis, standard error of skewness, and standard error of kurtosis will be calculated for the raw data and the logtransformed data.
For n>3 data sets, if the Result Raw Data says "Normal" the data can be considered normally distributed, use

"**UPL Pooled Template**"
for n>3 data sets, if the Result Log Data says "Normal" the data can be considered lognormally distributed, use

"**Lognormal Template**"
For n>3 data sets, if the Result Ray Data says "Non Normal" and the Result Log Data says "Non Normal" than the data have an unknown/skewed distribution, use "**Template_skewed**"
For n=3 data sets, the distribution will be specified as normal or lognormal in row 24.
**Templates** Plug the sources' raw run data into the appropriate template based on distribution.

Determine the confidence interval % to use fot the t-statistic and z-statistic based on "n" number of runs. 99% is the default in all the templates.

For "**UPL Pooled Template**" the UPL will be calculated in cell F107.

For "**Lognormal Template**", use the "lognormal z-stat" worksheet to find the z-statistic at the specified confidentce interval. The UPL will be calculated in cell D165

For the "**Template_skewed**" Template:

Cell E173 of the "**Template_skewed**" tab shows the actual confidence level (1 - 'Calculations for Template skew'!J139) after accounting for the skewness and kurtosis. If the confidence level is larger or lower than specified confidence level % [Default is 99%] then need to adjust the t-statistic.To adjust the t-statistic go to the “Recalculate t-stat skew” tab. This tab starts with the t-statistic in cell H161 from

the “**Template_skewed**” tab. If the confidence level from cell E171 of the "**Template_skewed**" tab was larger or lower than specified confidence level %, need to decrease or increase the t-statistic to get closer to the specified confidence level %.

Cell G3 of "Recaltulate t-stat skew" tab has the value of the increase also called "interval", the candidate t-values will be calculated as the t-value in cell H102 plus multiples of the interval. These are calculated automatically for you in row 5 after a value is placed in cell G3. The corresponding p-values and confidence levels are also calculated automatically for you. Cell G3 of "Recaltulate t-stat skew" tab, the “interval” can be manipulated. For example, start with 0.1 and notice what the values in row 9 are. If they are not at specified confidence level % keep increasing or decreasing the value in G3 until one of the values in row 9 is the specified confidence level percent %. May have to go out to several significant figures.

Calculations are in the tabs: "Recalculations1 skew" through "Recalculations6 skew". Don’t need to do any thing in them, they

are basically

duplicates of tab “Calculations_for_Template skew” and each one use a different value of the candidate t-values in row 5.

Sometimes the actual significance level in cell E173 of tab “**Template_skewed**” is larger than specified confidence level %, then you have to use a negative interval (meaning that your value in cell G3, tab “Recalculate tstat skew” has to be negative).
Once the adjusted t-value from tab “Recalculate t-stat skew” is at specified confidence interval %, copy the recalculated t-value and paste special the value into cell E178 in tab “**Template_skewed**”. Also paste special the "interval of differences for t-values" from the "Recalculate t-stat skew" tab into cell E176 of "**Template_skewed**".

Note: Cell E173 of "**Template_skewed**" is linked to the "Calculations for Template skew" and Cell B174 of "Template_skewed" is linked to the "Recalculations1 skew" worksheet. In order to use "**Template_skewed**" for
multiple data sets of UPL calculations make a copy of the worksheet and rename. Paste special Cell E173 and B174 values to freeze the values and remove reference to other worksheets.

The UPL will be calculated in cell E181 of "**Template_skewed**" If the new source UPL is greater in value (less stringent) than the existing source UPL, run the t-test to determine if there is statistical difference between the existing source MACT floor pool and the best performing source. In the "t-test" tab enter the new source run data into the new source column and enter the existing source run data into the existing source columns. If the results in cell B127 of "t-test" tab say "Means are not different" then can default to the existing source UPL for the new source UPL. If the results say "Means are different", then cannot default to the existing source UPL for the new source UPL.

**Other Notes and Terms** Type of data affects m (number of future runs) that will be used in calculation, for example: If using individual test runs (typically three to a test) to determine compliance; m=3 If 30-day averages are used to determine compliance; m=30 If using the average of test runs to determine compliance; m=1 Default m future runs is 3 in each template.
Does data set have non-detect issues, if so take extra step to do UPL v. 3xRDL comparison.

N = total number of sources
n = number of individual runs df = degrees of freedom = n - 1 X = mean of datas2= pooled variance of data

m = number of future runs tdf = t-statistic: t-distribution with df degrees of freedom at 99% [Default] confidence level
Templates can hold up to 30 sources (N); if data set has more than 30 sources, need to expand template.
Templates can hold up to 35 runs (n) for each source (N), if data set has more than 35 runs of data per source, need to expand template.

### Raw Data Raw Data Raw Data Raw Data

Runs SPPD_FAC_10 Example 2 Example 3 Example 4 1 8.70E+00 2 1.06E+01 3 1.74E+01

Average 1.22E+01 #DIV/0! #DIV/0! #DIV/0! Standard Deviation 4.59E+00 #DIV/0! #DIV/0! #DIV/0!

1 1.58E+02 #DIV/0! #DIV/0! #DIV/0! 2 7.29E+00 #DIV/0! #DIV/0! #DIV/0! 3 7.24E+02 #DIV/0! #DIV/0! #DIV/0!

Testing Normality Raw Data Raw Data Raw Data Raw Data Sample Size 3.00 0.00 0.00 0.00 Kurtosis -2.00 #DIV/0! #DIV/0! #DIV/0! SE Kurtosis 2.83 #DIV/0! #DIV/0! #DIV/0! Result Kurtosis normal #DIV/0! #DIV/0! #DIV/0! Skewness 1.40 #DIV/0! #DIV/0! #DIV/0! SE Skewness 1.22 0.00 0.00 0.00 Result Skewness normal #DIV/0! #DIV/0! #DIV/0!

Ratio S/SES 

### 1.146645636 #DIV/0! #DIV/0! #DIV/0! Distribution 

### Lognormal #DIV/0! #DIV/0! #DIV/0! 1 2 3 4

### Raw Data Raw Data Raw Data Raw Data Raw Data

Example 5 Example 6 Example 7 Example 8 Example 9

#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Raw Data Raw Data Raw Data Raw Data Raw Data 0.00 0.00 0.00 0.00 0.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0.00 0.00 0.00 0.00 0.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!


### #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 5 6 7 8 9

### Raw Data Raw Data Raw Data Raw Data Raw Data

Example 10 Example 11 Example 12 Example 13 Example 14

#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Raw Data Raw Data Raw Data Raw Data Raw Data 0.00 0.00 0.00 0.00 0.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0.00 0.00 0.00 0.00 0.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!


### #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 10 11 12 13 14

### Raw Data Raw Data Raw Data Raw Data

Example 15 Example 16 Example 17 Example 18

#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Raw Data Raw Data Raw Data Raw Data 0.00 0.00 0.00 0.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0.00 0.00 0.00 0.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0!


### #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 15 16 17 18

### Logtransformed Logtransformed Logtransformed Logtransformed Logtransformed

Example 1 Example 2 Example 3 Example 4 Example 5 2.16E+00 #NUM! #NUM! #NUM! #NUM! 2.36E+00 #NUM! #NUM! #NUM! #NUM! 2.86E+00 #NUM! #NUM! #NUM! #NUM!

2.46E+00 #NUM! #NUM! #NUM! #NUM! 3.58E-01 #NUM! #NUM! #NUM! #NUM!

7.83E-03 #NUM! #NUM! #NUM! #NUM! 9.97E-05 #NUM! #NUM! #NUM! #NUM! 2.49E-02 #NUM! #NUM! #NUM! #NUM!

Log Data Log Data Log Data Log Data Log Data 3.00 0.00 0.00 0.00 0.00 -2.00 #NUM! #NUM! #NUM! #NUM! 2.83 #DIV/0! #DIV/0! #DIV/0! #DIV/0! normal #NUM! #NUM! #NUM! #NUM! 1.16 #NUM! #NUM! #NUM! #NUM! 1.22 0.00 0.00 0.00 0.00 normal #NUM! #NUM! #NUM! #NUM!



### 0.945625468 #NUM! #NUM! #NUM! #NUM!

### Logtransformed Logtransformed Logtransformed Logtransformed Logtransformed

Example 6 Example 7 Example 8 Example 9 Example 10 #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

Log Data Log Data Log Data Log Data Log Data 0.00 0.00 0.00 0.00 0.00 #NUM! #NUM! #NUM! #NUM! #NUM! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! 0.00 0.00 0.00 0.00 0.00 #NUM! #NUM! #NUM! #NUM! #NUM!



### #NUM! #NUM! #NUM! #NUM! #NUM!

### Logtransformed Logtransformed Logtransformed Logtransformed Logtransformed

Example 11 Example 12 Example 13 Example 14 Example 15 #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

Log Data Log Data Log Data Log Data Log Data 0.00 0.00 0.00 0.00 0.00 #NUM! #NUM! #NUM! #NUM! #NUM! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! 0.00 0.00 0.00 0.00 0.00 #NUM! #NUM! #NUM! #NUM! #NUM!



### #NUM! #NUM! #NUM! #NUM! #NUM!

### Logtransformed Logtransformed Logtransformed

Example 16 Example 17 Example 18 #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

Log Data Log Data Log Data 0.00 0.00 0.00 #NUM! #NUM! #NUM! #DIV/0! #DIV/0! #DIV/0! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! 0.00 0.00 0.00 #NUM! #NUM! #NUM!



### #NUM! #NUM! #NUM!Raw Data Runs SPPD_FAC_10 1 8.70E+00 2 1.06E+01 3 1.74E+01 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Testing Normality Raw Data Logtransformed Data Sample Size 3.00 3.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis #DIV/0! #DIV/0! Average of Raw Data 1.22E+01 Result Kurtosis #DIV/0! #DIV/0! Variance of Raw Data 2.11E+01 Skewness 1.40 1.16 SE Skewness 1.22 1.22 Result Raw Data Result Log Data Result Skewness normal normal #DIV/0! #DIV/0!
1. Take LN( ) of Raw Data Runs SPPD_FAC_10 1 2.16E+00 2 2.36E+00 3 2.86E+00 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

3

3. Calculate 2.46E+00

0.128201419 4. Calculate

5. m= number future runs = 3

6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n

i

i x

n   

 2

2 1 ˆ 1

n

i i x x

n   



 

### 

  222

2 ˆˆˆ 4 3 2

2 2

ˆ 233 1 3 1 1 z e e e

m

m e 

      

    



0900006481946321 Lognormal Template 12/8/20145.48485531

0.056127905

99.72064987

7. Calculate 0.669789132

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "lognormal z-stat"

a- Calculate 12.48952973

b- Calculate 155.9883528

c- Calculate 0.136781949

d-calculate 0.046842707

e- Calculate 11.39173

f- Calculate UPL 26 11. In column B, go down the the row number from Step 10. above, and copy the z value.

12. calculate the UPL using the formula b- denominator first term a- Numerator first term

8. Go to tab distribution for 99 percentile "lognormal z-stat"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e   

##   2 2

ˆ 1 m e



2z  

###   2 2 ˆ ˆ

1 1 2

z e e

m     



2z

 1z 

2 ˆ 2 2 2 2 2 4

ˆ ˆ ˆ ˆ ˆ ˆ 2 22 .99 ˆ ˆ

( 1) 2( 1) z UPL e me e m e

m n n                   

  

2 ˆ 2 ˆ e  

2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2( 1) n n       

  

2 2 2 2 4

ˆ ˆ ˆ ˆˆ 2 22 ˆ ˆ ( 1) 2( 1) me e me n n            

 

     2 2 2

ˆ 1 z m

m e    



0900006481946321 Lognormal Template 12/8/2014

### ∆z z

0.101 23.80249 1.377354

-5=f(a) 390.0648 1 -4.899 354.4355 2 -4.798 321.1779 3 -4.697 290.1895 4 -4.596 261.37 5 -4.495 234.6213 6 -4.394 209.8473 7 -4.293 186.9542 8 -4.192 165.8504 9 -4.091 146.4462 10 -3.99 128.6545 11 -3.889 112.3899 12 -3.788 97.56945 13 -3.687 84.11235 14 -3.586 71.93989 15 -3.485 60.97555 16 -3.384 51.14496 17 -3.283 42.37594 18 -3.182 34.59846 19 -3.081 27.74465 20 -2.98 21.74883 21 -2.879 16.54744 22 -2.778 12.07914 23 -2.677 8.284705 24 -2.576 5.107107 25 -2.475 2.491468 26 -2.374 0.38508 27 -2.273 -1.2626 28 -2.172 -2.49996 29 -2.071 -3.37321 30 -1.97 -3.92639 31 -1.869 -4.20141 32 -1.768 -4.23797 33 -1.667 -4.07363 34 -1.566 -3.74379 35 -1.465 -3.28168 36 -1.364 -2.71835 37 -1.263 -2.0827

#   1 3 

# 1 3 6 24 z 

# z z      

     2z 

###  1z



# 

### 38 -1.162 -1.40147

39 -1.061 -0.69922 40 -0.96 0.001637 41 -0.859 0.68087 42 -0.758 1.320402 43 -0.657 1.904325 44 -0.556 2.418893 45 -0.455 2.852526 46 -0.354 3.19581 47 -0.253 3.441494 48 -0.152 3.584492 49 -0.051 3.621883 50 0.05 3.55291 51 0.151 3.378983 52 0.252 3.103674 53 0.353 2.73272 54 0.454 2.274026 55 0.555 1.737657 56 0.656 1.135845 57 0.757 0.482988 58 0.858 -0.20435 59 0.959 -0.90745 60 1.06 -1.60542 61 1.161 -2.2752 62 1.262 -2.89157 63 1.363 -3.42715 64 1.464 -3.85238 65 1.565 -4.13556 66 1.666 -4.2428 67 1.767 -4.13806 68 1.868 -3.78313 69 1.969 -3.13764 70 2.07 -2.15904 71 2.171 -0.80265 72 2.272 0.978414 73 2.373 3.233181 74 2.474 6.012847 75 2.575 9.370774 76 2.676 13.36249 77 2.777 18.04568 78 2.878 23.4802 79 2.979 29.72808 80 3.08 36.8535 81 3.181 44.92281 82 3.282 54.00452 83 3.383 64.16932 84 3.484 75.49004

### 85 3.585 88.04169

86 3.686 101.9015 87 3.787 117.1487 88 3.888 133.8648 89 3.989 152.1336 90 4.09 172.0408 91 4.191 193.6745 92 4.292 217.1248 93 4.393 242.484 94 4.494 269.8467 95 4.595 299.3094 96 4.696 330.971 97 4.797 364.9326 98 4.898 401.2971 99 4.999 440.17

### distribution of Z Normal distribution

1.48672E-06 0.000579917 2.45094E-06 0.0008687 3.9995E-06 0.001284552 6.46025E-06 0.001874696 1.03291E-05 0.002699714 1.63472E-05 0.003835413 2.56093E-05 0.005374035 3.97118E-05 0.007424283 6.09553E-05 0.010109452 9.26132E-05 0.013562852 0.000139285 0.017919633 0.000207351 0.023304116 0.000305546 0.029811945 0.000445674 0.037486681 0.000643469 0.0462911 0.000919619 0.056074278 0.001300942 0.066536639 0.001821704 0.077196417 0.002525035 0.087362307 0.003464389 0.09611827 0.004704958 0.102327303 0.006324913 0.104661137 0.008416337 0.101662098 0.011085658 0.091841411 0.014453386 0.073814986 0.018652949 0.046473228 0.023828414 0.00917585 0.030130931 -0.03804338 0.03771375 -0.094282831 0.046725789 -0.1576157 0.057303789 -0.224997187 0.069563239 -0.292263436 0.083588399 -0.354244929 0.099421884 -0.405008262 0.117054396 -0.438227575 0.136415346 -0.447671321 0.157365126 -0.427773224 0.179689839 -0.374240219 

# 

#  

2 4 2 

# 336 6 24 z 

# z z   

    

     

#   2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z      
      

## ( ) z 

### 0.203099244 -0.284637455 0.227228529 -0.158883344 0.251644341 0.000411873 0.275855243 0.18782147 0.299326439 0.395231257 0.321498297 0.612237125 0.341807853 0.8267965 0.359712192 1.026088455 0.37471238 1.197509618 0.386376486 1.329712319 0.394360216 1.413580947 0.398423793 1.443044227 0.398443914 1.415635461 0.394419966 1.33273831 0.386474058 1.199489353 0.374844865 1.024346204 0.359875719 0.818366595 0.34199778 0.594274668 0.32170943 0.365412073 0.299553264 0.144680625 0.276092166 -0.056420378 0.25188591 -0.228574626 0.227469632 -0.365184292 0.203335281 -0.462628185 0.17991684 -0.520241996 0.157579839 -0.540049159 0.136615273 -0.526293985 0.117237788 -0.484843542 0.099587708 -0.422530427 0.083736272 -0.346505441 0.069693339 -0.263658786 0.05741676 -0.180152901 0.046822635 -0.101092161 0.037795734 -0.030336761 0.030199481 0.029547598 0.023885038 0.07722465 0.018699163 0.112435203 0.014490659 0.135788687 0.011115369 0.148528978 0.008439746 0.152300952 0.006343145 0.148938347 0.004718997 0.140286733 0.003475077 0.128068772 0.002533081 0.113793105 0.001827693 0.098703708 0.001305351 0.083763503 0.000922829 0.0696644

### 0.00064578 0.0568556 0.00044732 0.045582551 0.000306705 0.035930124 0.000208159 0.027865109 0.000139842 0.021274633 9.29928E-05 0.015998559 6.12113E-05 0.011855066 3.98826E-05 0.008659501 2.5722E-05 0.00623718 1.64209E-05 0.004431121 1.03767E-05 0.003105833 6.49066E-06 0.00214822 4.01874E-06 0.001466568 2.46298E-06 0.000988385 1.49417E-06 0.000657689

### Absolute values

0.000579917 2.92858E-05 0.0008687 8.77387E-05 0.001284552 0.00012974 0.001874696 0.000189344 0.002699714 0.000272671 0.003835413 0.000387377 0.005374035 0.000542778 0.007424283 0.000749853 0.010109452 0.001021055 0.013562852 0.001369848 0.017919633 0.001809883 0.023304116 0.002353716 0.029811945 0.003011006 0.037486681 0.003786155 0.0462911 0.004675401 0.056074278 0.005663502 0.066536639 0.006720201 0.077196417 0.007796838 0.087362307 0.008823593 0.09611827 0.009707945 0.102327303 0.010335058 0.104661137 0.010570775 0.101662098 0.010267872 0.091841411 0.009275983 0.073814986 0.007455314 0.046473228 0.004693796 0.00917585 0.000926761 0.03804338 0.003842381 0.094282831 0.009522566 0.1576157 0.015919186 0.224997187 0.022724716 0.292263436 0.029518607 0.354244929 0.035778738 0.405008262 0.040905835 0.438227575 0.044260985 0.447671321 0.045214803 0.427773224 0.043205096 0.374240219 0.037798262 

# 

#  

2 4 2 

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

      

1 

## ( )2 () () 2 M

i

i 

## xf a f x f b

 

##  

      

# 

### 0.284637455 0.028748383 0.158883344 0.016047218 0.000411873 4.15991E-05 0.18782147 0.018969969 0.395231257 0.039918357 0.612237125 0.06183595 0.8267965 0.083506447 1.026088455 0.103634934 1.197509618 0.120948471 1.329712319 0.134300944 1.413580947 0.142771676 1.443044227 0.145747467 1.415635461 0.142979182 1.33273831 0.134606569 1.199489353 0.121148425 1.024346204 0.103458967 0.818366595 0.082655026 0.594274668 0.060021741 0.365412073 0.036906619 0.144680625 0.014612743 0.056420378 0.005698458 0.228574626 0.023086037 0.365184292 0.036883613 0.462628185 0.046725447 0.520241996 0.052544442 0.540049159 0.054544965 0.526293985 0.053155692 0.484843542 0.048969198 0.422530427 0.042675573 0.346505441 0.03499705 0.263658786 0.026629537 0.180152901 0.018195443 0.101092161 0.010210308 0.030336761 0.003064013 0.029547598 0.002984307 0.07722465 0.00779969 0.112435203 0.011355955 0.135788687 0.013714657 0.148528978 0.015001427 0.152300952 0.015382396 0.148938347 0.015042773 0.140286733 0.01416896 0.128068772 0.012934946 0.113793105 0.011493104 0.098703708 0.009969074 0.083763503 0.008460114 0.0696644 0.007036104

### 0.0568556 0.005742416 0.045582551 0.004603838 0.035930124 0.003628943 0.027865109 0.002814376 0.021274633 0.002148738 0.015998559 0.001615854 0.011855066 0.001197362 0.008659501 0.00087461 0.00623718 0.000629955 0.004431121 0.000447543 0.003105833 0.000313689 0.00214822 0.00021697 0.001466568 0.000148123 0.000988385 9.98269E-05 0.000657689 3.32133E-05

### Cumulative normalization

2.92858E-05 1.10037E-05 0.000117025 4.39703E-05 0.000246764 9.27182E-05 0.000436108 0.000163862 0.00070878 0.000266314 0.001096156 0.000411865 0.001638934 0.000615806 0.002388786 0.000897553 0.003409841 0.0012812 0.004779689 0.001795901 0.006589572 0.002475939 0.008943288 0.003360314 0.011954294 0.004491657 0.015740449 0.005914251 0.02041585 0.007670967 0.026079352 0.009798948 0.032799553 0.012323968 0.040596391 0.01525352 0.049419984 0.01856886 0.059127929 0.022216484 0.069462986 0.026099735 0.080033761 0.030071555 0.090301633 0.033929562 0.099577616 0.037414882 0.107032929 0.04021611 0.111726725 0.041979738 0.112653486 0.042327955 0.116495868 0.043771676 0.126018434 0.047349645 0.141937619 0.053331054 0.164662335 0.061869545 0.194180942 0.072960745 0.22995968 0.0864041 0.270865514 0.101773889 0.3151265 0.118404328 0.360341303 0.135393152 0.403546399 0.151626856 0.441344661 0.165829018 

## ( )2 () () f a f x f b        

### 0.470093044 0.176630817 0.486140262 0.182660332 0.486181861 0.182675963 0.505151829 0.18980366 0.545070186 0.204802419 0.606906136 0.228036403 0.690412582 0.25941277 0.794047516 0.298352131 0.914995988 0.34379681 1.049296932 0.394258492 1.192068608 0.447902931 1.337816075 0.502665482 1.480795256 0.556387888 1.615401825 0.606964404 1.73655025 0.652484212 1.840009217 0.691357457 1.922664243 0.722413915 1.982685984 0.744966236 2.019592604 0.758833376 2.034205347 0.764323908 2.039903805 0.766465023 2.062989842 0.775139275 2.099873456 0.788997772 2.146598902 0.806554198 2.199143344 0.826297029 2.253688309 0.846791529 2.306844002 0.866764029 2.355813199 0.885163513 2.398488772 0.901198257 2.433485822 0.914347903 2.460115359 0.924353576 2.478310802 0.931190256 2.488521111 0.935026635 2.491585124 0.936177895 2.494569431 0.937299206 2.502369121 0.940229829 2.513725076 0.944496669 2.527439734 0.949649758 2.54244116 0.955286332 2.557823556 0.96106605 2.572866329 0.966718159 2.58703529 0.972041945 2.599970236 0.976902069 2.611463339 0.98122044 2.621432414 0.984966179 2.629892527 0.988144947 2.636928632 0.990788664

### 2.642671047 0.992946295 2.647274885 0.994676122 2.650903828 0.996039646 2.653718204 0.997097108 2.655866942 0.997904466 2.657482796 0.9985116 2.658680158 0.998961492 2.659554767 0.999290114 2.660184722 0.999526811 2.660632266 0.999694969 2.660945955 0.999812833 2.661162925 0.999894357 2.661311048 0.999950012 2.661410875 0.999987521 2.661444089 1

132.8984354