#############################################################
##                        mmtbx.xtriage                    ##
##                                                         ##
##      P.H. Zwart, R.W. Grosse-Kunstleve & P.D. Adams     ##
##                                                         ##
#############################################################
Date 2006-07-11 Time 13:57:29 PDT -0700


##-------------------------------------------##
## WARNING:                                  ##
## Number of residues unspecified            ##
##-------------------------------------------##


Effective parameters: 
scaling.input {
  parameters {
    asu_contents {
      n_residues = None
      n_bases = None
      n_copies_per_asu = None
    }
    misc_twin_parameters {
      missing_symmetry {
        tanh_location = 0.08
        tanh_slope = 50
      }
      twinning_with_ncs {
        perform_analyses = True
        n_bins = 7
      }
      twin_test_cuts {
        low_resolution = 10
        high_resolution = None
        isigi_cut = 3
        completeness_cut = 0.85
      }
    }
    reporting {
      verbose = 1
      log = "logfile.log"
      ccp4_style_graphs = True
    }
  }
  xray_data {
    file_name = "/net/cci/phzwart/HCN2i029x133_rigid_refmac1.mtz"
    obs_labels = "F,SIGF"
    calc_labels = FC
    unit_cell = 94.73400116 94.73400116 124.0469971 90 90 90
    space_group = "I 4"
    high_resolution = 4.5
    low_resolution = None
  }
}


Symmetry, cell and reflection file content summary

Miller array info: /net/cci/phzwart/HCN2i029x133_rigid_refmac1.mtz:F,SIGF
Observation type: xray.amplitude
Type of data: double, size=3272
Type of sigmas: double, size=3272
Number of Miller indices: 3272
Anomalous flag: False
Unit cell: (94.734, 94.734, 124.047, 90, 90, 90)
Space group: I 4 (No. 79)
Systematic absences: 0
Centric reflections: 170
Resolution range: 40.0925 4.50444
Completeness in resolution range: 0.996649
Completeness with d_max=infinity: 0.995134

##----------------------------------------------------##
##                    Basic statistics                ##
##----------------------------------------------------##


Matthews coefficient and Solvent content statistics

Number of residues unknown, assuming 50% solvent content

----------------------------------------------------------------
|              Best guess :  509  residues in the asu          |
----------------------------------------------------------------


Completeness and data strength analyses 

  The following table lists the completeness in various resolution
  ranges, after applying a I/sigI cut. Miller indices for which
  individual I/sigI values are larger than the value specified in
  the top row of the table, are retained, while other intensities
  are discarded. The resulting completeness profiles are an indication
  of the strength of the data.

----------------------------------------------------------------------------------------
| Res. Range   | I/sigI>1  | I/sigI>2  | I/sigI>3  | I/sigI>5  | I/sigI>10 | I/sigI>15 |
----------------------------------------------------------------------------------------
| 40.09 -11.04 | 96.6%     | 96.6%     | 96.1%     | 95.7%     | 95.3%     | 95.3%     |
| 11.04 - 8.79 | 99.1%     | 99.1%     | 98.2%     | 98.2%     | 97.7%     | 97.3%     |
|  8.79 - 7.69 | 100.0%    | 100.0%    | 100.0%    | 100.0%    | 99.1%     | 98.6%     |
|  7.69 - 6.99 | 100.0%    | 99.5%     | 99.5%     | 98.6%     | 97.7%     | 96.8%     |
|  6.99 - 6.49 | 99.5%     | 98.6%     | 98.6%     | 98.1%     | 97.1%     | 96.2%     |
|  6.49 - 6.11 | 100.0%    | 100.0%    | 100.0%    | 99.6%     | 98.2%     | 96.1%     |
|  6.11 - 5.80 | 99.1%     | 98.6%     | 98.6%     | 97.7%     | 95.4%     | 94.4%     |
|  5.80 - 5.55 | 99.5%     | 99.5%     | 99.5%     | 99.0%     | 97.1%     | 95.6%     |
|  5.55 - 5.34 | 100.0%    | 100.0%    | 100.0%    | 98.7%     | 97.8%     | 96.0%     |
|  5.34 - 5.16 | 100.0%    | 99.6%     | 99.6%     | 99.6%     | 98.7%     | 97.8%     |
|  5.16 - 4.99 | 100.0%    | 99.5%     | 99.5%     | 99.1%     | 97.6%     | 95.3%     |
|  4.99 - 4.85 | 100.0%    | 99.5%     | 99.1%     | 99.1%     | 99.1%     | 98.1%     |
|  4.85 - 4.72 | 100.0%    | 99.5%     | 99.5%     | 99.5%     | 97.6%     | 97.2%     |
|  4.72 - 4.61 | 100.0%    | 100.0%    | 100.0%    | 100.0%    | 100.0%    | 99.5%     |
----------------------------------------------------------------------------------------



Maximum likelihood isotropic Wilson scaling 
ML estimate of overall B value of /net/cci/phzwart/HCN2i029x133_rigid_refmac1.mtz:F,SIGF:
43.16 A**(-2)
Estimated -log of scale factor of /net/cci/phzwart/HCN2i029x133_rigid_refmac1.mtz:F,SIGF:
 0.93


Maximum likelihood anisotropic Wilson scaling 
ML estimate of overall B_cart value of /net/cci/phzwart/HCN2i029x133_rigid_refmac1.mtz:F,SIGF:
45.14,  0.00,  0.00
       45.14,  0.00
              38.81
Equivalent representation as U_cif: 
 0.57, -0.00, -0.00
        0.57,  0.00
               0.49

ML estimate of  -log of scale factor of /net/cci/phzwart/HCN2i029x133_rigid_refmac1.mtz:F,SIGF:
 0.93
Correcting for anisotropy in the data

Some basic intensity statistics follow.



Low resolution completeness analyses 

 The following table shows the completeness
 of the data to 5 Angstrom.
unused:         - 40.0938 [  0/5  ] 0.000
bin  1: 40.0938 - 10.7104 [243/251] 0.968
bin  2: 10.7104 -  8.5281 [235/237] 0.992
bin  3:  8.5281 -  7.4579 [247/247] 1.000
bin  4:  7.4579 -  6.7796 [232/232] 1.000
bin  5:  6.7796 -  6.2957 [248/248] 1.000
bin  6:  6.2957 -  5.9257 [250/250] 1.000
bin  7:  5.9257 -  5.6298 [218/219] 0.995
bin  8:  5.6298 -  5.3853 [240/240] 1.000
bin  9:  5.3853 -  5.1785 [244/244] 1.000
bin 10:  5.1785 -  5.0001 [237/237] 1.000
unused:  5.0001 -         [  0/0  ]



Mean intensity analyses 
 Analyses of the mean intensity. 
 Inspired by: Morris et al. (2004). J. Synch. Rad.11, 56-59.
 The following resolution shells are worrisome: 
------------------------------------------------
| d_spacing | z_score | compl. | <Iobs>/<Iexp> |
------------------------------------------------
     None
------------------------------------------------

Possible outliers 
  Inspired by: Read, Acta Cryst. (1999). D55, 1759-1764

 Acentric reflections:

-----------------------------------------------------------------
| d_space |      H     K     L |  |E|  | p(wilson) | p(extreme) |
-----------------------------------------------------------------
|   8.709 |      0,    2,   14 |  3.20 |  3.61e-05 |   9.98e-02 |
|   6.112 |      3,   10,   15 |  3.34 |  1.43e-05 |   4.07e-02 |
|   6.112 |     10,    3,   15 |  3.38 |  1.10e-05 |   3.15e-02 |
-----------------------------------------------------------------

 p(wilson)  : 1-(1-exp[-|E|^2]) 
 p(extreme) : 1-(1-exp[-|E|^2])^(n_acentrics)
 p(wilson) is the probability that an E-value of the specified
 value would be observed when it would selected at random from
 the given data set.
 p(extreme) is the probability that the largest |E| value is 
 larger or equal then the observed largest |E| value.

 Both measures can be used for outlier detection. p(extreme)
 takes into account the size of the dataset.


 Centric reflections:

            None 


Ice ring related problems

 The following statistics were obtained from ice-ring 
 insensitive resolution ranges 
  mean bin z_score      : 1.29
      ( rms deviation   : 0.77 )
  mean bin completeness : 1.00
     ( rms deviation   : 0.00 )

 The following table shows the z-scores 
 and completeness in ice-ring sensitive areas.
 Large z-scores and high completeness in these 
 resolution ranges might be a reason to re-assess
 your data processsing if ice rings were present.

------------------------------------------------
| d_spacing | z_score | compl. | Rel. Ice int. |
------------------------------------------------
------------------------------------------------

 Abnormalities in mean intensity or completeness at
 resolution ranges with a relative ice ring intensity
 lower then 0.10 will be ignored.

 No ice ring related problems detected.
 If ice rings were present, the data does not look
 worse at ice ring related d_spacings as compared
 to the rest of the data set 




Basic analyses completed

##----------------------------------------------------##
##                   Twinning Analyses                ##
##----------------------------------------------------##



Using data between 10.00 to 4.61 Angstrom.

Determining possible twin laws.

The following twin laws have been found:

-------------------------------------------------------------------------------
| Type | Axis   | R metric (%) | delta (le Page) | delta (Lebedev) | Twin law |
-------------------------------------------------------------------------------
|   M  | 2-fold | 0.000        | 0.000           | 0.000           | -k,-h,-l |
-------------------------------------------------------------------------------
M:  Merohedral twin law
PM: Pseudomerohedral twin law

  1 merohedral twin operators found
  0 pseudo-merohedral twin operators found
In total,   1 twin operator were found


Number of centrics  : 132
Number of acentrics : 2609

 Largest patterson peak with length larger then 15 Angstrom 

 Frac. coord.        :   0.000    0.000    0.175
 Distance to origin  :  21.684
 Height (origin=100) :   6.773
 p_value(height)     :   5.442e-01

   The reported p_value has the following meaning: 
     The probability that a peak of the specified height 
     or larger is found in a Patterson function of a 
     macro molecule that does not have any translational
     pseudo symmetry is equal to  5.442e-01 
     p_values smaller then 0.05 might indicate 
     weak translation pseudo symmetry, or the self vector of 
     a large anomalous scatterer such as Hg, whereas values 
     smaller then 1e-3 are a very strong indication for 
     the presence of translational pseudo symmetry.



Wilson ratio and moments 

Acentric reflections 
   <I^2>/<I>^2    :2.101   (untwinned: 2.000; perfect twin 1.500)
   <F>^2/<F^2>    :0.779   (untwinned: 0.785; perfect twin 0.885)
   <|E^2 - 1|>    :0.750   (untwinned: 0.736; perfect twin 0.541)


Centric reflections 
   <I^2>/<I>^2    :2.857   (untwinned: 3.000; perfect twin 2.000)
   <F>^2/<F^2>    :0.655   (untwinned: 0.637; perfect twin 0.785)
   <|E^2 - 1|>    :0.836   (untwinned: 0.968; perfect twin 0.736)



NZ test (0<=z<1) to detect twinning and possible translational NCS


-----------------------------------------------
|  Z  | Nac_obs | Nac_theo | Nc_obs | Nc_theo |
-----------------------------------------------
| 0.0 |   0.000 |    0.000 |  0.000 |   0.000 |
| 0.1 |   0.097 |    0.095 |  0.235 |   0.248 |
| 0.2 |   0.182 |    0.181 |  0.379 |   0.345 |
| 0.3 |   0.257 |    0.259 |  0.508 |   0.419 |
| 0.4 |   0.331 |    0.330 |  0.530 |   0.474 |
| 0.5 |   0.393 |    0.394 |  0.583 |   0.520 |
| 0.6 |   0.453 |    0.451 |  0.614 |   0.561 |
| 0.7 |   0.504 |    0.503 |  0.644 |   0.597 |
| 0.8 |   0.555 |    0.551 |  0.689 |   0.629 |
| 0.9 |   0.601 |    0.593 |  0.712 |   0.657 |
| 1.0 |   0.640 |    0.632 |  0.758 |   0.683 |
-----------------------------------------------
| Maximum deviation acentric      :  0.008    |
| Maximum deviation centric       :  0.089    |
|                                             |
| <NZ(obs)-NZ(twinned)>_acentric  : +0.002    |
| <NZ(obs)-NZ(twinned)>_centric   : +0.047    |
-----------------------------------------------


 L test for acentric data

 using difference vectors (dh,dk,dl) of the form: 
(2hp,2kp,2lp)
  where hp, kp, and lp are random signed integers such that 
  2 <= |dh| + |dk| + |dl| <= 8 

  Mean |L|   :0.492  (untwinned: 0.500; perfect twin: 0.375)
  Mean  L^2  :0.326  (untwinned: 0.333; perfect twin: 0.200)

  The distribution of |L| values indicates a twin fraction of
  0.00. Note that this estimate is not as reliable as obtained
  via a Britton plot or H-test if twin laws are available. 



---------------------------------------------
 Analysing possible twin law :  -k,-h,-l
---------------------------------------------


Results of the H-test on a-centric data: 

 (Only 50.0% of the strongest twin pairs were used)

mean |H| : 0.033   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.003   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.467
Estimation of twin fraction via cum. dist. of H: 0.470



Britton analyses

  Extrapolation performed on  0.47 < alpha < 0.495 
  Estimated twin fraction: 0.446
  Correlation: 0.9877

R vs R statistic:
  R_abs_twin = <|I1-I2|>/<|I1+I2|>
  Lebedev, Vagin, Murshudov. Acta Cryst. (2006). D62, 83-95

   R_abs_twin observed data   : 0.038
   R_abs_twin calculated data : 0.291

  R_sq_twin = <(I1-I2)^2>/<(I1+I2)^2>
   R_sq_twin observed data    : 0.002
   R_sq_twin calculated data  : 0.091



Maximum Likelihood twin fraction determination
    Zwart, Read, Grosse-Kunstleve & Adams, to be published.


   The estimated twin fraction is equal to 0.392


Estimation of twin fraction, while taking into account the
effects of possible NCS parallel to the twin axis.
    Zwart, Read, Grosse-Kunstleve & Adams, to be published.

  A parameters D_ncs will be estimated as a function of resolution,
  together with a global twin fraction.
  D_ncs is an estimate of the correlation coefficient between
  untwinned, error-free, twin related, normalized intensities.
  Large values (0.95) could indicate an incorrect point group.
  Value of D_ncs larger than say, 0.5, could indicate the presence
  of NCS. The twin fraction should be smaller or similar to other
  estimates given elsewhere.

  The refinement can take some time. 
  For numerical stability issues, D_ncs is limited between 0 and 0.95.
  The twin fraction is allowed to vary between 0 and 0.45.
  Refinement cycle numbers are printed out to keep you entertained.

. . . .   5  . . . .  10  . . . .  15  . . . .  20  . . . .  25  . . . .  30 
. . . .  35  . . . .  40  . . . .  45  . . . .  50  . . . .  55  . . . .  60 
. . . .  65  . . . .  70  . . . .  75  . . . .  80  . . . .  85  . . . .  90 
. . . .  95  . . . . 100  . . . . 105  . .

  Cycle : 107
  -----------
  Log[likelihood]:       18359.617
  twin fraction: 0.363
  D_ncs in resolution ranges: 
     9.9721 -- 7.5529 :: 0.950
     7.5529 -- 6.5047 :: 0.950
     6.5047 -- 5.8693 :: 0.950
     5.8693 -- 5.4264 :: 0.950
     5.4264 -- 5.0927 :: 0.927
     5.0927 -- 4.8284 :: 0.924
     4.8284 -- 4.6117 :: 0.920

 The correlation of the calculated F^2 should be similar to 
 the estimated values. 

 Observed correlation between twin related, untwinned calculated F^2
 in resolutiuon ranges, as well as ewstimates D_ncs^2 values:
 Bin    d_max     d_min     CC_obs   D_ncs^2 
  1)    9.9721 -- 7.5529 ::  0.725    0.902
  2)    7.5529 -- 6.5047 ::  0.701    0.902
  3)    6.5047 -- 5.8693 ::  0.543    0.902
  4)    5.8693 -- 5.4264 ::  0.698    0.902
  5)    5.4264 -- 5.0927 ::  0.639    0.858
  6)    5.0927 -- 4.8284 ::  0.655    0.855
  7)    4.8284 -- 4.6117 ::  0.671    0.847


Exploring higher metric symmetry

The point group of data as dictated by the space group is I 4
  the point group in the niggli setting is Hall:  I 4 (x+y,y+z,x+z)
The point group of the lattice is Hall:  I 4 2 (x+y,y+z,x+z)
A summary of R values for various possible point groups follow.

-------------------------------------------------------------------------------------------------
| Point group                | mean R_used | max R_used | mean R_unused | min R_unused | choice |
-------------------------------------------------------------------------------------------------
| Hall:  I 4 (x+y,y+z,x+z)   | None        | None       | 0.038         | 0.038        |        |
| Hall:  I 4 2 (x+y,y+z,x+z) | 0.038       | 0.038      | None          | None         | <---   |
-------------------------------------------------------------------------------------------------

R_used: mean and maximum R value for symmetry operators *used* in this point group
R_unused: mean and minimum R value for symmetry operators *not used* in this point group
 The likely point group of the data is:  Hall:  I 4 2 (x+y,y+z,x+z)

Possible space groups in this point groups are:
   Unit cell: (94.734, 94.734, 124.047, 90, 90, 90)
   Space group: I 4 2 2 (No. 97)

   Unit cell: (94.734, 94.734, 124.047, 90, 90, 90)
   Space group: I 41 2 2 (No. 98)

Note that this analyses does not take into account the effects of twinning.
If the data is (allmost) perfectly twinned, the symmetry will appear to be
higher than it actually is.





-------------------------------------------------------------------------------
Twinning and intensity statistics summary (acentric data):

Statistics independent of twin laws
  - <I^2>/<I>^2 : 2.101
  - <F>^2/<F^2> : 0.779
  - <|E^2-1|>   : 0.750
  - 
, <L^2>: 0.492, 0.326
       Multivariate Z score L-test: 1.555 
       The multivariate Z score is a quality measure of the given
       spread in intensities. Good to reasonable data is expected
       to have a Z score lower than 3.5. 
       Large values can indicate twinning, but small values do not
       neccesarily exclude it. 


Statistics depending on twin laws
-----------------------------------------------------------------------------------
| Operator | type | R_abs obs. | R_abs calc. | Britton alpha | H alpha | ML alpha |
-----------------------------------------------------------------------------------
| -k,-h,-l |   M  | 0.038      | 0.291       | 0.446         | 0.470   | 0.392    |
-----------------------------------------------------------------------------------

Patterson analyses
  - Largest peak height   : 6.773
   (correpsonding p value : 5.442e-01)


The largest off-origin peak in the Patterson function is 6.77% of the 
height of the origin peak. No significant pseudotranslation is detected.

The results of the L-test indicate that the intensity statistics
behave as expected. No twinning is suspected.
The symmetry of the lattice and intensity however suggests that the
input space group is too low. See the relevant sections of the log
file for more details on your choice of space groups.
As the symmetry is suspected to be incorrect, it is advicable to reconsider data processing.
 

-------------------------------------------------------------------------------


$TABLE: Intensity plots:
$GRAPHS
:Intensity plots 
:A:1,2,3,4:
$$
1/resol^2   <I>_smooth_approximation   <I>_via_binning   <I>_expected   $$ 
$$
0.010050   403460.006026   435403.760483   417700.152528
0.014050   321340.592788   325135.722182   328279.362825
0.018050   258197.847659   256877.177324   241251.925353
0.022050   178737.878416   174752.140991   207142.463420
0.026050   176446.174805   187539.376325   207292.287235
0.030050   204903.382394   203879.963356   228367.744827
0.034050   311155.880665   311066.280752   277685.285832
0.038050   319030.292690   315080.818287   355869.005029
0.042050   453427.795290   452970.635383   444094.664482
0.046050   483132.406868   481336.420035   516273.167233
0.049285   587331.536692   653429.219737   551452.061985
$$


$TABLE: Z scores and completeness:
$GRAPHS
:Data sanity and completeness check 
:A:1,2,3:
$$
1/resol^2   Z_score   Completeness   $$ 
$$
0.010050   0.385773   0.988827
0.014050   0.110890   1.000000
0.018050   0.783773   1.000000
0.022050   2.652776   1.000000
0.026050   1.538257   1.000000
0.030050   1.769339   0.996795
0.034050   1.756384   1.000000
0.038050   2.058986   1.000000
0.042050   0.323224   1.000000
0.046050   1.195961   1.000000
0.049285   1.669128   1.000000
$$


$TABLE: <I/sigma_I>:
$GRAPHS
:Signal to noise 
:N:1,2:
$$
1/resol^2   <I/sigma_I>;_Signal_to_noise   $$ 
$$
0.002622   53.597566
0.006622   59.107721
0.010622   58.509939
0.014622   56.882841
0.018622   54.735040
0.022622   51.534593
0.026622   51.112260
0.030622   50.648913
0.034622   54.235279
0.038622   52.385708
0.042622   55.470816
0.046622   53.825529
0.050622   56.615295
$$


$TABLE: NZ test:
$GRAPHS
:NZ test, acentric and centric data 
:A:1,2,3,4,5:
$$
z   Acentric_observed   Acentric_untwinned   Centric_observed   Centric_untwinned   $$ 
$$
0.000000   0.000000   0.000000   0.000000   0.000000
0.100000   0.097355   0.095200   0.234848   0.248100
0.200000   0.182445   0.181300   0.378788   0.345300
0.300000   0.256803   0.259200   0.507576   0.418700
0.400000   0.330778   0.329700   0.530303   0.473800
0.500000   0.393254   0.393500   0.583333   0.520500
0.600000   0.453047   0.451200   0.613636   0.561400
0.700000   0.504025   0.503400   0.643939   0.597200
0.800000   0.554619   0.550700   0.689394   0.628900
0.900000   0.601380   0.593400   0.712121   0.657200
1.000000   0.640475   0.632100   0.757576   0.683300
$$


$TABLE: L test,acentric data:
$GRAPHS
:L test, acentric data 
:A:1,2,3,4:
$$
|l|   Observed   Acentric_theory   Acentric_theory,_perfect_twin   $$ 
$$
0.000000   0.002371   0.000000   0.000000
0.020000   0.029872   0.020000   0.029996
0.040000   0.054528   0.040000   0.059968
0.060000   0.073495   0.060000   0.089892
0.080000   0.096254   0.080000   0.119744
0.100000   0.114746   0.100000   0.149500
0.120000   0.134661   0.120000   0.179136
0.140000   0.150782   0.140000   0.208628
0.160000   0.167378   0.160000   0.237952
0.180000   0.188715   0.180000   0.267084
0.200000   0.209104   0.200000   0.296000
0.220000   0.229967   0.220000   0.324676
0.240000   0.252252   0.240000   0.353088
0.260000   0.273115   0.260000   0.381212
0.280000   0.292082   0.280000   0.409024
0.300000   0.308203   0.300000   0.436500
0.320000   0.324324   0.320000   0.463616
0.340000   0.347558   0.340000   0.490348
0.360000   0.368421   0.360000   0.516672
0.380000   0.386439   0.380000   0.542564
0.400000   0.407776   0.400000   0.568000
0.420000   0.425794   0.420000   0.592956
0.440000   0.446183   0.440000   0.617408
0.460000   0.464675   0.460000   0.641332
0.480000   0.490280   0.480000   0.664704
0.500000   0.508298   0.500000   0.687500
0.520000   0.526790   0.520000   0.709696
0.540000   0.543860   0.540000   0.731268
0.560000   0.564248   0.560000   0.752192
0.580000   0.583215   0.580000   0.772444
0.600000   0.600759   0.600000   0.792000
0.620000   0.621622   0.620000   0.810836
0.640000   0.643907   0.640000   0.828928
0.660000   0.665244   0.660000   0.846252
0.680000   0.686581   0.680000   0.862784
0.700000   0.703651   0.700000   0.878500
0.720000   0.722617   0.720000   0.893376
0.740000   0.745377   0.740000   0.907388
0.760000   0.764343   0.760000   0.920512
0.780000   0.787577   0.780000   0.932724
0.800000   0.807018   0.800000   0.944000
0.820000   0.829777   0.820000   0.954316
0.840000   0.850640   0.840000   0.963648
0.860000   0.869606   0.860000   0.971972
0.880000   0.889047   0.880000   0.979264
0.900000   0.910858   0.900000   0.985500
0.920000   0.930773   0.920000   0.990656
0.940000   0.948791   0.940000   0.994708
0.960000   0.965861   0.960000   0.997632
0.980000   0.982930   0.980000   0.999404
$$


$TABLE: Britton plot for twin law -k,-h,-l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.000000   0.000000
0.019802   0.000000   0.000000
0.029703   0.000000   0.000000
0.039604   0.000000   0.000000
0.049505   0.000000   0.000000
0.059406   0.000000   0.000000
0.069307   0.000000   0.000000
0.079208   0.000383   0.000000
0.089109   0.000383   0.000000
0.099010   0.000383   0.000000
0.108911   0.000383   0.000000
0.118812   0.000383   0.000000
0.128713   0.000383   0.000000
0.138614   0.000383   0.000000
0.148515   0.000383   0.000000
0.158416   0.000383   0.000000
0.168317   0.000383   0.000000
0.178218   0.000383   0.000000
0.188119   0.000383   0.000000
0.198020   0.000383   0.000000
0.207921   0.000767   0.000000
0.217822   0.000767   0.000000
0.227723   0.000767   0.000000
0.237624   0.000767   0.000000
0.247525   0.000767   0.000000
0.257426   0.000767   0.000000
0.267327   0.000767   0.000000
0.277228   0.000767   0.000000
0.287129   0.000767   0.000000
0.297030   0.000767   0.000000
0.306931   0.000767   0.000000
0.316832   0.001150   0.000000
0.326733   0.001150   0.000000
0.336634   0.001150   0.000000
0.346535   0.001150   0.000000
0.356436   0.001150   0.000000
0.366337   0.002301   0.000000
0.376238   0.003451   0.000000
0.386139   0.007285   0.000000
0.396040   0.010353   0.000000
0.405941   0.016488   0.000000
0.415842   0.024923   0.000000
0.425743   0.034509   0.000000
0.435644   0.047163   0.000000
0.445545   0.065567   0.000000
0.455446   0.090107   0.055135
0.465347   0.119248   0.115183
0.475248   0.165261   0.175230
0.485149   0.241181   0.235278
$$


$TABLE: H test for possible twin law -k,-h,-l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.098926   0.000000
0.020000   0.504601   0.328197
0.040000   0.713190   0.656393
0.060000   0.814417   0.984590
0.080000   0.878834   1.000000
0.100000   0.935583   1.000000
0.120000   0.963190   1.000000
0.140000   0.981595   1.000000
0.160000   0.987730   1.000000
0.180000   0.992331   1.000000
0.200000   0.995399   1.000000
0.220000   0.996933   1.000000
0.240000   0.998466   1.000000
0.260000   0.998466   1.000000
0.280000   1.000000   1.000000
0.300000   1.000000   1.000000
0.320000   1.000000   1.000000
0.340000   1.000000   1.000000
0.360000   1.000000   1.000000
0.380000   1.000000   1.000000
0.400000   1.000000   1.000000
0.420000   1.000000   1.000000
0.440000   1.000000   1.000000
0.460000   1.000000   1.000000
0.480000   1.000000   1.000000
0.500000   1.000000   1.000000
0.520000   1.000000   1.000000
0.540000   1.000000   1.000000
0.560000   1.000000   1.000000
0.580000   1.000000   1.000000
0.600000   1.000000   1.000000
0.620000   1.000000   1.000000
0.640000   1.000000   1.000000
0.660000   1.000000   1.000000
0.680000   1.000000   1.000000
0.700000   1.000000   1.000000
0.720000   1.000000   1.000000
0.740000   1.000000   1.000000
0.760000   1.000000   1.000000
0.780000   1.000000   1.000000
0.800000   1.000000   1.000000
0.820000   1.000000   1.000000
0.840000   1.000000   1.000000
0.860000   1.000000   1.000000
0.880000   1.000000   1.000000
0.900000   1.000000   1.000000
0.920000   1.000000   1.000000
0.940000   1.000000   1.000000
0.960000   1.000000   1.000000
0.980000   1.000000   1.000000
$$


$TABLE: Likelihood based twin fraction estimation for possible twin law -k,-h,-l:
$GRAPHS
:Likelihood based twin fraction estimate 
:A:1,2:
$$
alpha   NLL_(acentric_data)   $$ 
$$
0.021739   5151.970186
0.043478   5030.714437
0.065217   4904.005607
0.086957   4783.635381
0.108696   4737.739426
0.130435   4646.783863
0.152174   4489.124506
0.173913   4321.353030
0.195652   4142.101999
0.217391   3949.660739
0.239130   3741.960863
0.260870   3516.369965
0.282609   3269.418630
0.304348   2996.654957
0.326087   2692.125440
0.347826   2347.709509
0.369565   1961.374670
0.391304   1588.847694
0.413043   1610.916469
0.434783   2794.619605
0.456522   7985.248870
0.478261   18055.012519
$$