dd.plot: Distance-Distance Plot

In mvoutlier: Multivariate Outlier Detection Based on Robust Methods

Description

The function dd.plot plots the classical mahalanobis distance of the data against the robust mahalanobis distance based on the mcd estimator. Different symbols (see function symbol.plot) and colours (see function color.plot) are used depending on the mahalanobis and euclidean distance of the observations (see Filzmoser et al., 2005).

Usage

dd.plot(x, quan=1/2, alpha=0.025, ...)

Arguments

x	matrix or data frame containing the data
quan	amount of observations which are used for mcd estimations. has to be between 0.5 and 1, default ist 0.5
alpha	amount of observations used for calculating the adjusted quantile (see function arw).
...	additional graphical parameters

Value

outliers	boolean vector of outliers
md.cla	mahalanobis distances of the observations based on classical estimators of location and scatter.
md.rob	mahalanobis distances of the observations based on robust estimators of location and scatter (mcd).

Author(s)

Moritz Gschwandtner <[e-mail]>
Peter Filzmoser <[e-mail]> http://cstat.tuwien.ac.at/filz/

References

P. Filzmoser, R.G. Garrett, and C. Reimann. Multivariate outlier detection in exploration geochemistry. Computers & Geosciences, 31:579-587, 2005.

See Also

symbol.plot, color.plot, arw, covPlot

Examples

# create data:
x <- cbind(rnorm(100), rnorm(100))
y <- cbind(rnorm(10, 3, 1), rnorm(10, 3, 1))
z <- rbind(x,y)
# execute:
dd.plot(z)
#
# Identify multivariate outliers for Co-Cu-Ni in humus layer of Kola data:
data(humus)
dd.plot(log(humus[,c("Co","Cu","Ni")]))

Example output

Loading required package: sgeostat
sROC 0.1-2 loaded
$outliers
  [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
 [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
 [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
 [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
 [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
 [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
 [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
 [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
 [97] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
[109]  TRUE  TRUE

$md.cla
  [1] 0.4432025 0.9881565 0.6823629 1.4106289 0.1905189 0.8951713 0.2223790
  [8] 0.9762006 0.9363338 0.8876320 0.5941308 1.0680861 1.2156934 0.6272335
 [15] 0.3459745 1.7438273 0.9144810 1.1703263 1.2930003 0.9096121 1.4748210
 [22] 1.1044471 1.5745557 1.1779907 0.4544073 0.3423597 1.4804047 0.9136061
 [29] 0.7689915 1.2345624 2.1449831 1.2985204 1.3376150 1.5054055 1.2669586
 [36] 2.0080874 2.8887666 2.1082587 0.7722900 2.0479418 0.6054277 0.8730633
 [43] 1.5352195 1.6227390 2.2490550 0.7767417 0.7619187 1.2291690 1.0271122
 [50] 0.3458976 0.5347576 0.8066637 1.3559122 0.1633154 1.0911933 0.8242747
 [57] 1.9008766 1.4673593 0.4674110 1.5696131 1.2779679 1.2172565 0.6940711
 [64] 0.8175654 1.2746275 0.6552624 1.3835653 0.2175131 0.7383950 0.9567036
 [71] 1.2229289 1.7491603 0.8069161 0.8825892 0.8677005 0.6184539 0.9896925
 [78] 0.6143067 1.0412634 1.1362311 1.7277396 0.9334942 1.3443582 0.5495323
 [85] 1.6463650 1.1358345 0.4440303 1.5981258 0.4731260 1.4258970 0.8015577
 [92] 1.7240093 1.5774039 0.4608714 2.1261761 0.2860461 0.5375851 1.3414517
 [99] 0.8020635 0.6496104 1.9456646 2.6322985 1.9972819 2.5945425 3.2087123
[106] 2.1971338 2.8454278 3.7524292 2.5791835 3.1864101

$md.rob
  [1] 0.5092839 0.8169744 0.5541385 1.5714413 0.3468056 0.8645935 0.5303601
  [8] 0.9172182 0.8764926 0.8442223 0.4559037 1.0201728 1.5207694 0.4872518
 [15] 0.1238489 1.5402164 0.8695925 1.2391708 1.1152878 0.8009491 1.6344986
 [22] 1.0143098 1.3601893 1.3755019 0.2652088 0.8169081 1.5363425 0.8071001
 [29] 0.6000130 1.2329109 1.9043920 1.2464558 1.2595102 1.2952714 1.3674307
 [36] 1.9070548 2.5699164 2.4724283 0.6873027 1.8600622 0.6017682 1.3420506
 [43] 1.4564333 1.5822218 2.1925817 0.6910706 0.9314847 1.3253362 1.7335074
 [50] 0.2178625 0.7368413 0.8423969 1.6641885 0.5266922 1.1021069 0.7748860
 [57] 1.7532168 1.3971112 0.7850928 1.9927593 1.1532915 1.9992519 0.9619829
 [64] 0.7017547 1.2668953 0.5466920 1.5031275 0.6406350 0.5799129 0.8413437
 [71] 1.8947180 1.8254095 0.9023536 0.9079450 0.7431007 0.4875425 0.8891024
 [78] 0.6167246 1.4331940 1.0804756 1.9663520 0.8972337 1.4296792 1.0846680
 [85] 1.9623071 0.9833581 0.6561895 1.6475966 0.2999328 1.2734877 0.6710661
 [92] 1.4884224 1.4779650 0.2723049 1.9200125 0.6901665 0.7326068 1.1801081
 [99] 0.6962078 0.6287393 3.0090334 3.9476198 3.0753808 3.6147528 4.7322106
[106] 3.3330079 3.7546170 5.0946849 3.8323804 4.2050143

$outliers
    1     2     3     4     5     6     7     8     9    10    11    12    13 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
   14    15    16    17    18    19    20    21    22    23    24    25    26 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
   27    28    29    30    31    32    33    34    35    36    37    38    39 
FALSE  TRUE  TRUE FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE 
   40    41    42    43    44    45    46    47    48    49    50    51    52 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE 
   53    54    55    56    57    58    59    60    61    62    63    64    65 
 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
   66    67    68    69    70    71    72    73    74    75    76    77    78 
FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE 
   79    80    81    82    83    84    85    86    87    88    89    90    91 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE  TRUE FALSE 
   92    93    94    95    96    97    98    99   100   101   102   103   104 
 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  105   106   107   108   109   110   111   112   113   114   115   116   117 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE FALSE 
  118   119   120   121   122   123   124   125   126   127   128   129   130 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE 
  131   132   133   134   135   136   137   138   139   140   141   142   143 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  144   145   146   147   148   149   150   151   152   153   154   155   156 
 TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE  TRUE 
  157   158   159   160   161   162   163   164   165   166   167   168   169 
FALSE FALSE FALSE FALSE  TRUE  TRUE FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE 
  170   171   172   173   174   175   176   177   178   179   180   181   182 
 TRUE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE 
  183   184   185   186   187   188   189   190   191   192   193   194   195 
FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  196   197   198   199   200   201   202   203   204   205   206   207   208 
FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  209   210   211   212   213   214   215   216   217   218   219   220   221 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  222   223   224   225   226   227   228   229   230   231   232   233   234 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE 
  235   236   237   238   239   240   241   242   243   244   245   246   247 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  248   249   250   251   252   253   254   255   256   257   258   259   260 
FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE 
  261   262   263   264   265   266   267   268   269   270   271   272   273 
FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  274   275   276   277   278   279   280   281   282   283   284   285   286 
FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  287   288   289   290   291   292   293   294   295   296   297   298   299 
FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE 
  300   301   302   303   304   305   306   307   308   309   310   311   312 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE 
  313   314   315   316   317   318   319   320   321   322   323   324   325 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  326   327   328   329   330   331   332   333   334   335   336   337   338 
 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE 
  339   340   341   342   343   344   345   346   347   348   349   350   351 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  352   353   354   355   356   357   358   359   360   361   362   363   364 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  365   366   367   368   369   370   371   372   373   374   375   376   377 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  378   379   380   381   382   383   384   385   386   387   388   389   390 
 TRUE FALSE  TRUE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  391   392   393   394   395   396   397   398   399   400   401   402   403 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  404   405   406   407   408   409   410   411   412   413   414   415   416 
FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  417   418   419   420   421   422   423   424   425   426   427   428   429 
FALSE FALSE FALSE  TRUE FALSE FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE FALSE 
  430   431   432   433   434   435   436   437   438   439   440   441   442 
FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  443   444   445   446   447   448   449   450   451   452   453   454   455 
FALSE  TRUE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE 
  456   457   458   459   460   461   462   463   464   465   466   467   468 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE 
  469   470   471   472   473   474   475   476   477   478   479   480   481 
FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE 
  482   483   484   485   486   487   488   489   490   491   492   493   494 
FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE 
  495   496   497   498   499   500   501   502   503   504   505   506   507 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  508   509   510   511   512   513   514   515   516   517   518   519   520 
FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  521   522   523   524   525   526   527   528   529   530   531   532   533 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  534   535   536   537   538   539   540   541   542   543   544   545   546 
FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE 
  547   548   549   550   551   552   553   554   555   556   557   558   559 
FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE 
  560   561   562   563   564   565   566   567   568   569   570   571   572 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE 
  573   574   575   576   577   578   579   580   581   582   583   584   585 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  586   587   588   589   590   591   592   593   594   595   596   597   598 
 TRUE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  599   600   601   602   603   604   605   606   607   608   609   610   611 
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE 
  612   613   614   615   616   617 
FALSE  TRUE FALSE FALSE FALSE FALSE 

$md.cla
        1         2         3         4         5         6         7         8 
0.3623207 1.3427365 0.9019713 1.4801477 2.5484440 1.3791393 1.1157676 1.9727053 
        9        10        11        12        13        14        15        16 
0.6357517 1.4248657 1.1081916 1.4975390 1.2879212 1.5896654 1.7103639 0.4736188 
       17        18        19        20        21        22        23        24 
0.3995875 1.0597866 1.0840518 1.2096110 1.4702443 0.9691355 0.9078219 1.8294046 
       25        26        27        28        29        30        31        32 
1.2632915 1.2442798 1.1052344 7.2803688 2.0185866 1.0943531 2.0378761 1.2422806 
       33        34        35        36        37        38        39        40 
1.4137861 2.4409894 6.1280200 1.9525059 1.8237934 1.5119856 1.6491823 1.4809594 
       41        42        43        44        45        46        47        48 
2.0108462 1.8813003 2.3144678 0.7584250 1.0649156 1.1076255 1.4615938 1.9021875 
       49        50        51        52        53        54        55        56 
2.2350935 1.3329851 2.3185189 1.2208283 2.6194314 0.9588428 1.4827813 0.8997260 
       57        58        59        60        61        62        63        64 
0.3923821 0.6658703 1.4432144 1.2967434 0.9645358 0.7278884 1.9332546 1.5934825 
       65        66        67        68        69        70        71        72 
1.0112903 1.8318620 6.4784200 0.5168628 0.6331380 2.4857753 1.1176104 1.8814817 
       73        74        75        76        77        78        79        80 
1.0826968 1.4883955 8.1102408 0.9387955 0.4383638 0.7090629 1.1825851 0.6914837 
       81        82        83        84        85        86        87        88 
0.5451754 0.5552732 1.9325179 1.6602476 1.4391960 1.2082589 5.0678015 1.4669949 
       89        90        91        92        93        94        95        96 
1.1830552 4.8581131 1.0036170 1.7825760 1.1836317 0.7589057 1.9543266 1.8427682 
       97        98        99       100       101       102       103       104 
1.2184834 1.0080599 1.0139170 0.8994097 0.9229644 1.6377812 1.8729061 1.6000179 
      105       106       107       108       109       110       111       112 
1.0642410 1.2102382 2.0787510 0.8976364 1.0426907 1.7469944 1.5030112 0.6657359 
      113       114       115       116       117       118       119       120 
1.4063147 1.4762825 3.2261747 3.8889519 1.3038205 1.1700572 1.3672607 1.6644732 
      121       122       123       124       125       126       127       128 
1.0194456 1.7168240 0.6118774 0.2762271 0.7740757 3.4402104 1.7994165 1.0488209 
      129       130       131       132       133       134       135       136 
1.3854366 2.0797644 1.7638694 1.0815671 2.2611215 1.5133246 1.5907311 1.5730376 
      137       138       139       140       141       142       143       144 
0.8586014 0.6582427 0.9675227 0.9947266 1.2879022 1.3907767 2.5763017 2.6904333 
      145       146       147       148       149       150       151       152 
2.3145861 0.6855843 0.8323490 1.2061274 1.4155318 1.4004155 1.2009916 1.4661342 
      153       154       155       156       157       158       159       160 
1.0259998 2.4938882 0.8229071 2.1463644 1.1351679 1.0605643 1.0309887 1.1188688 
      161       162       163       164       165       166       167       168 
2.9412666 2.8442966 1.1257200 2.7643096 1.0938150 1.5074675 1.5143780 3.1413978 
      169       170       171       172       173       174       175       176 
1.5894038 2.2414730 1.6550564 0.7471523 4.0370984 0.8620847 1.3773870 1.1894853 
      177       178       179       180       181       182       183       184 
0.9712279 3.0946946 0.6577061 0.9802150 0.9887477 1.3069910 0.7270269 1.2487889 
      185       186       187       188       189       190       191       192 
1.1400928 0.4947073 1.0491278 4.9257030 1.2485222 1.9590479 1.5107254 2.7892572 
      193       194       195       196       197       198       199       200 
1.4792679 2.1525016 0.3370758 1.1686737 2.3222713 0.6250914 1.1748540 1.3363145 
      201       202       203       204       205       206       207       208 
3.0689671 1.6357854 0.6356513 0.6226265 2.1892724 1.1595550 0.6181859 1.6292794 
      209       210       211       212       213       214       215       216 
1.7502055 2.2136909 1.3596497 1.1697859 1.2184481 1.0297483 1.8372214 0.9312437 
      217       218       219       220       221       222       223       224 
1.0105244 0.6883889 0.9404472 1.3316360 1.8034817 0.7202928 0.6412639 1.2970213 
      225       226       227       228       229       230       231       232 
0.3942373 1.2078291 1.8138361 1.2521496 1.2071466 0.2130095 1.2092567 2.6283631 
      233       234       235       236       237       238       239       240 
1.1459642 1.4372631 1.6872660 1.1943187 2.3411227 2.3213879 0.6520546 1.9692345 
      241       242       243       244       245       246       247       248 
2.7076477 1.5196776 1.2335312 1.3859607 0.9529427 1.5225775 1.4896778 2.5718141 
      249       250       251       252       253       254       255       256 
1.9464287 1.3863665 0.4216605 0.8844680 3.1763510 1.6665618 0.5722788 1.7942002 
      257       258       259       260       261       262       263       264 
2.4283121 2.1756895 1.7153284 0.8774250 2.0872174 1.9158182 1.7723397 1.4472753 
      265       266       267       268       269       270       271       272 
0.7091057 0.3385974 1.5970948 0.6053790 0.9729533 1.6512554 0.9834902 1.1853626 
      273       274       275       276       277       278       279       280 
1.3391553 1.3479663 1.5001159 2.1892192 2.3033843 1.5190371 1.4603211 0.9222581 
      281       282       283       284       285       286       287       288 
2.2957182 1.2761273 1.2839665 1.5727168 1.1784947 0.6313632 1.2992746 1.1070289 
      289       290       291       292       293       294       295       296 
2.3316787 2.3938241 1.0634361 1.7961362 1.1479620 1.4313766 0.8432543 1.5723885 
      297       298       299       300       301       302       303       304 
3.1219461 1.0645483 1.8707983 1.7811093 2.2240422 0.7687703 1.5679274 1.9236644 
      305       306       307       308       309       310       311       312 
1.4898235 1.2003878 1.0605676 1.3258979 0.7957580 1.1759930 3.0913084 1.4486283 
      313       314       315       316       317       318       319       320 
1.0937188 1.5294522 0.6083143 1.7498780 1.7561164 1.9856681 1.2350174 1.2924058 
      321       322       323       324       325       326       327       328 
1.1355580 0.5756602 0.5574843 1.4630480 1.9783987 2.1904075 2.3488528 1.0598769 
      329       330       331       332       333       334       335       336 
1.9917922 1.2486734 0.6949118 1.1719126 1.5394805 3.2004597 1.7490444 0.7384061 
      337       338       339       340       341       342       343       344 
0.7387298 0.9990854 1.0114742 1.1322517 1.1907152 1.0948516 1.6679946 1.5376928 
      345       346       347       348       349       350       351       352 
0.6499208 0.8591305 0.6496303 0.8562123 1.7197470 1.0916626 1.0202389 1.1853378 
      353       354       355       356       357       358       359       360 
1.1581789 0.9750803 0.6032155 1.1910510 1.3086362 0.8606225 1.5802585 1.6064388 
      361       362       363       364       365       366       367       368 
0.5182000 1.6656212 1.7960806 1.0610587 1.2186149 1.1012444 0.9873544 1.4128919 
      369       370       371       372       373       374       375       376 
1.3617481 1.1219024 1.3779119 0.9987614 1.2751416 0.8708766 1.0624274 2.2900094 
      377       378       379       380       381       382       383       384 
1.4370114 2.2738871 1.1406625 1.8390990 1.6769587 1.3067522 3.4630708 0.8825421 
      385       386       387       388       389       390       391       392 
1.8059080 1.3219496 0.8305232 0.8368240 1.5186085 2.3898244 1.2448444 1.2396900 
      393       394       395       396       397       398       399       400 
0.4578502 1.7407970 1.6451102 1.2814453 1.3585781 1.0670542 1.8713187 1.3321466 
      401       402       403       404       405       406       407       408 
0.3209244 1.4656669 1.5597816 0.9132879 0.8908078 1.2768860 0.8163388 1.5138029 
      409       410       411       412       413       414       415       416 
2.3956947 2.0137028 1.0000114 2.3403033 1.4906863 1.4350967 1.2573198 0.6621689 
      417       418       419       420       421       422       423       424 
1.0820732 1.2574121 2.2553120 3.1749256 0.9029815 1.5875024 2.7721226 1.0002018 
      425       426       427       428       429       430       431       432 
1.8997699 1.2088676 0.9707929 1.9734029 1.7504116 0.9200724 2.5512832 1.1424932 
      433       434       435       436       437       438       439       440 
0.7115774 1.3779526 2.6098974 1.7761705 1.4888656 1.9216423 1.1814082 1.0653046 
      441       442       443       444       445       446       447       448 
0.5580092 1.6063558 1.7892824 3.5641662 1.3913593 1.3746512 1.6490890 3.1234389 
      449       450       451       452       453       454       455       456 
5.8361831 1.3093003 2.7974955 0.8502091 1.5724170 1.5206864 1.2873216 1.1557226 
      457       458       459       460       461       462       463       464 
1.3333426 0.9072252 1.1902246 1.3480392 1.6429375 1.6238576 1.2959975 0.9276111 
      465       466       467       468       469       470       471       472 
1.5241656 1.0013453 1.3846433 2.2945758 0.9511519 2.1846408 1.0442698 2.3438730 
      473       474       475       476       477       478       479       480 
3.2283930 1.4479804 0.7013240 2.3878820 1.8351698 4.4976836 1.7232081 2.3205041 
      481       482       483       484       485       486       487       488 
1.2794334 1.1064016 2.0166388 0.7041893 0.3426514 1.3246500 1.7816500 1.3673275 
      489       490       491       492       493       494       495       496 
2.0776838 1.4199509 1.1746506 2.9549461 1.7720041 1.8468879 1.5833168 0.9606594 
      497       498       499       500       501       502       503       504 
1.0758470 0.7004447 1.2843223 1.5860967 0.9606803 0.8463996 2.3220340 1.0063604 
      505       506       507       508       509       510       511       512 
1.1515059 1.9143812 0.5074576 1.6556885 1.7344029 1.6747050 0.7447150 1.5620714 
      513       514       515       516       517       518       519       520 
1.0575338 1.1488344 2.6239020 2.0989322 1.2507544 1.4061137 1.7902845 1.7709452 
      521       522       523       524       525       526       527       528 
2.9421642 1.4007780 1.4271771 2.0302191 2.1153040 1.3268044 1.2018648 1.6013877 
      529       530       531       532       533       534       535       536 
1.3451750 0.8373890 1.6978615 0.8265035 1.8485227 1.9940265 2.1278987 1.4086882 
      537       538       539       540       541       542       543       544 
0.9189577 0.8304974 1.2864598 1.4175603 0.8431932 1.9500016 2.1251242 1.8031198 
      545       546       547       548       549       550       551       552 
1.2590720 0.8831174 1.2280417 2.5899843 0.6314217 1.8524424 0.6150484 0.3584750 
      553       554       555       556       557       558       559       560 
1.6085431 0.9956101 1.6117474 3.5151906 2.0487338 0.7749227 0.6274150 0.8355697 
      561       562       563       564       565       566       567       568 
1.0786298 1.7411018 0.4906674 2.6252737 1.3677226 1.5366723 3.5328688 0.7582178 
      569       570       571       572       573       574       575       576 
0.6977958 1.2539023 1.5988474 1.4212347 2.4098431 1.4142812 1.4925063 2.1873075 
      577       578       579       580       581       582       583       584 
1.3148773 0.8129942 0.7238400 1.2089854 1.1198984 1.4445592 1.3775671 1.2811768 
      585       586       587       588       589       590       591       592 
1.4102205 2.6587405 1.6791047 1.5216927 2.3633527 1.2598590 0.8718319 1.1875779 
      593       594       595       596       597       598       599       600 
0.7134186 1.5520270 1.5148988 1.7599266 2.0813601 1.0825052 1.3039979 0.9723184 
      601       602       603       604       605       606       607       608 
1.7058535 0.6835378 0.3293645 1.0243275 1.4425593 0.5988055 1.4472846 1.2175101 
      609       610       611       612       613       614       615       616 
1.2437418 1.9363634 1.3113474 1.2685444 4.1433957 2.6830922 1.7140629 1.5040575 
      617 
2.0263173 

$md.rob
         1          2          3          4          5          6          7 
 0.4602194  1.3973494  1.1636417  1.7352235  2.8164906  2.4517078  1.1200700 
         8          9         10         11         12         13         14 
 2.0755511  0.6247366  1.5959892  1.2373649  1.7019460  1.3083892  1.7964380 
        15         16         17         18         19         20         21 
 2.3208262  0.3734383  0.4487657  1.1244396  1.4630872  1.2758394  1.9353261 
        22         23         24         25         26         27         28 
 0.9396214  0.7936344  2.1628645  1.2636405  1.0908268  1.8158094 13.8490280 
        29         30         31         32         33         34         35 
 3.3303407  1.1273784  4.0008704  1.3558759  1.4202871  2.5293541 11.9346478 
        36         37         38         39         40         41         42 
 1.9998243  1.6687063  1.3155714  2.4851081  1.8312073  1.9422655  1.7536023 
        43         44         45         46         47         48         49 
 2.9379822  0.8520008  1.0866537  1.3918708  1.5816692  3.0181160  4.4481082 
        50         51         52         53         54         55         56 
 1.3351993  4.4452483  1.2168759  3.2563552  0.9851833  1.7750248  0.9211538 
        57         58         59         60         61         62         63 
 0.2371133  0.6386769  1.4399977  1.8725814  2.0565318  0.8232257  2.5408833 
        64         65         66         67         68         69         70 
 2.4966108  1.1840401  1.8855070 12.6680176  0.6890968  0.5557419  2.5340699 
        71         72         73         74         75         76         77 
 1.0700598  1.7641389  1.3003610  1.6060778 15.2392011  1.1652222  0.3560650 
        78         79         80         81         82         83         84 
 0.6707300  1.1727390  0.5984193  0.8463743  1.3641184  3.0544655  2.6567842 
        85         86         87         88         89         90         91 
 1.4186762  1.1401883 10.0214176  1.3887622  1.2950368  6.2789248  1.3153399 
        92         93         94         95         96         97         98 
 3.6600637  1.1183176  0.9952256  2.3879273  2.1820730  1.1958631  0.9346077 
        99        100        101        102        103        104        105 
 0.9651647  1.0569102  0.9553037  1.5746630  1.7700184  1.7082193  1.1189664 
       106        107        108        109        110        111        112 
 1.4467803  2.3053172  0.8198044  1.0200710  1.6362495  1.5128819  0.6161416 
       113        114        115        116        117        118        119 
 1.2600653  1.6999574  6.3117975  7.8293855  2.1665257  1.1477009  1.2165766 
       120        121        122        123        124        125        126 
 2.4400055  1.5716128  1.5873141  0.4951257  0.3766258  0.7294083  3.4028598 
       127        128        129        130        131        132        133 
 1.8878027  1.3985081  1.3754663  1.9896254  1.5644419  1.0841446  2.3267285 
       134        135        136        137        138        139        140 
 1.3921676  1.9140772  1.5206459  1.0372990  0.6496428  0.7904720  0.9206830 
       141        142        143        144        145        146        147 
 1.3059183  1.3402678  2.8326399  5.0743400  4.5423375  0.6284530  0.9719789 
       148        149        150        151        152        153        154 
 2.0849259  1.5518495  1.4319364  1.2612213  1.5247174  0.9373864  3.2858917 
       155        156        157        158        159        160        161 
 0.7780677  3.9323626  0.9489541  1.1347990  1.1542975  1.0847353  5.9512309 
       162        163        164        165        166        167        168 
 3.1980140  1.6149164  5.6325756  1.4726724  1.4660060  1.3280172  3.1214708 
       169        170        171        172        173        174        175 
 2.4882618  4.2363927  1.7520211  0.5914037  7.8998599  0.7719461  1.3662231 
       176        177        178        179        180        181        182 
 1.2827268  1.0130245  4.1153775  0.6049512  1.1832261  0.9308539  1.9334947 
       183        184        185        186        187        188        189 
 0.6491232  1.2343267  1.0833062  0.4096501  1.3972013  6.2086110  1.2670281 
       190        191        192        193        194        195        196 
 2.0667626  1.7267587  2.7000109  1.4684488  2.3108442  1.0772746  1.0924933 
       197        198        199        200        201        202        203 
 4.6056233  1.0066986  1.0356381  1.3067702  3.4511352  1.4649821  0.5577533 
       204        205        206        207        208        209        210 
 0.5894031  2.0901272  1.1598878  0.5254893  2.1164486  1.9024627  2.0347487 
       211        212        213        214        215        216        217 
 1.7583235  0.9750909  1.2827062  1.0106934  1.7875257  1.0710065  1.0955217 
       218        219        220        221        222        223        224 
 0.6778925  1.0644333  1.1589018  1.7666356  0.7298410  0.5640001  1.5750401 
       225        226        227        228        229        230        231 
 0.3555526  1.5107430  1.5662272  1.8932494  1.0659261  0.5648292  1.5862593 
       232        233        234        235        236        237        238 
 3.5709442  1.2048376  1.3434069  2.0180299  1.3859769  2.2880569  2.5021659 
       239        240        241        242        243        244        245 
 1.1763913  2.2300211  2.6885352  2.3835096  1.1597543  1.3635506  0.8908689 
       246        247        248        249        250        251        252 
 2.0407836  1.7025184  2.5353214  3.1007702  1.8587129  0.3373269  0.9815151 
       253        254        255        256        257        258        259 
 3.3531341  1.5871258  0.9420154  1.8135090  4.8569805  4.1799208  1.5868639 
       260        261        262        263        264        265        266 
 0.8169975  2.3479667  3.5042220  2.9642508  1.3860644  1.0206780  0.4367310 
       267        268        269        270        271        272        273 
 1.4942386  0.9753386  1.1917754  1.9057141  1.0646794  1.3196493  1.4034911 
       274        275        276        277        278        279        280 
 1.8136175  1.8489798  3.6007878  2.3216309  1.5634958  1.3482616  0.8716648 
       281        282        283        284        285        286        287 
 2.2269696  2.2539713  1.2542714  1.5885295  1.3902011  0.4800809  1.5257567 
       288        289        290        291        292        293        294 
 1.1077491  2.1933403  3.9351114  0.9889440  1.8276459  1.0016947  1.3172916 
       295        296        297        298        299        300        301 
 1.1065551  1.6553055  3.4413886  1.3957945  2.4974485  1.8970346  2.3295963 
       302        303        304        305        306        307        308 
 0.6549838  1.6002204  2.9642524  1.3184998  1.4601838  1.2925712  1.1725165 
       309        310        311        312        313        314        315 
 0.7990753  1.1627257  5.9095506  2.1707887  0.9093087  1.7453853  0.5340144 
       316        317        318        319        320        321        322 
 1.7145769  1.8755000  1.8822939  1.4770276  1.1780956  1.2629653  0.4404275 
       323        324        325        326        327        328        329 
 0.3858894  1.4073505  1.9450935  4.1358509  2.4317830  1.2551512  2.0399861 
       330        331        332        333        334        335        336 
 1.0950706  0.6301244  1.3341779  3.0279287  5.9070961  3.1331537  0.7207675 
       337        338        339        340        341        342        343 
 0.7249008  1.0017043  0.9926184  1.1056256  1.6554001  0.9872052  2.2706654 
       344        345        346        347        348        349        350 
 2.2968910  1.0732197  1.0611215  0.5613778  0.9750927  2.1415555  1.1085438 
       351        352        353        354        355        356        357 
 0.9855751  1.6773321  1.1823476  0.8454616  0.8478753  1.3305976  1.1325613 
       358        359        360        361        362        363        364 
 0.9580395  1.4840076  1.7844863  0.4856484  1.8776755  1.6858346  1.2611745 
       365        366        367        368        369        370        371 
 1.1749046  1.0566692  0.9375638  1.6861790  2.3292562  1.0558550  1.3971924 
       372        373        374        375        376        377        378 
 0.9326626  1.3363306  0.8334410  1.4863395  2.5028064  1.3461922  3.3096181 
       379        380        381        382        383        384        385 
 1.0968294  3.1989464  1.9981525  1.1197795  6.7031255  0.7977631  1.9231174 
       386        387        388        389        390        391        392 
 1.1387176  0.7794376  0.9723430  1.6687493  2.1876728  1.2708640  1.3056743 
       393        394        395        396        397        398        399 
 0.3892766  1.7197370  2.0450231  1.2421007  1.4002394  1.3896334  2.2202070 
       400        401        402        403        404        405        406 
 1.3891410  0.7124979  2.9878407  1.8985186  0.8952156  0.9617093  1.5777940 
       407        408        409        410        411        412        413 
 0.9883718  3.0210295  4.4623489  2.0282209  0.9611302  2.1658002  2.6544928 
       414        415        416        417        418        419        420 
 1.6901093  1.2863682  0.5145374  1.1214822  1.2413724  2.6834845  3.4657623 
       421        422        423        424        425        426        427 
 0.8438962  1.5231615  3.4747894  1.0156386  3.4898908  1.1999509  1.0065939 
       428        429        430        431        432        433        434 
 2.0484446  1.6238637  1.2567835  4.9074290  1.6105775  0.6433209  1.6257237 
       435        436        437        438        439        440        441 
 2.6633429  1.6431611  2.0340652  1.9849975  1.1895578  1.4782018  0.6912230 
       442        443        444        445        446        447        448 
 1.5219989  1.7928102  3.3740749  1.3902974  1.3878676  2.7360172  3.6504566 
       449        450        451        452        453        454        455 
 7.9547540  1.2938853  2.7834912  0.7820483  1.3938366  1.6144276  1.3948351 
       456        457        458        459        460        461        462 
 1.1496214  1.4206698  1.0014548  1.1544522  1.4166893  1.8513273  1.8445141 
       463        464        465        466        467        468        469 
 1.6266425  1.0583313  1.4174334  0.9115640  1.8401259  3.8582582  0.9794814 
       470        471        472        473        474        475        476 
 2.8773149  1.2573507  2.7174002  3.1655406  1.7931933  0.6354564  2.2023130 
       477        478        479        480        481        482        483 
 1.8119598  5.3341191  1.8185451  2.7281686  1.5592567  1.5734696  2.9199822 
       484        485        486        487        488        489        490 
 0.9925776  0.2860427  1.7161123  3.5437207  1.4430881  2.0096514  1.6007975 
       491        492        493        494        495        496        497 
 1.1283587  3.7822208  1.8213382  1.7551083  1.6667974  1.0748809  1.0670622 
       498        499        500        501        502        503        504 
 0.7167203  1.2373693  1.8447476  0.9456872  0.8664448  2.3728326  1.0429955 
       505        506        507        508        509        510        511 
 1.0822810  2.0147523  0.3368660  1.5107092  3.1011615  1.4706727  0.7008756 
       512        513        514        515        516        517        518 
 1.3735626  1.3278185  1.0267174  2.7582903  2.2061464  1.5294175  1.3217647 
       519        520        521        522        523        524        525 
 1.5611781  2.0609279  2.9179895  1.6551517  1.9789110  1.9263495  2.3659907 
       526        527        528        529        530        531        532 
 1.8385196  1.0469412  1.6780341  1.3424002  1.0497430  1.6909076  0.8877867 
       533        534        535        536        537        538        539 
 2.0349048  1.8645964  3.9054350  1.2903120  0.8333387  0.6533355  1.8329542 
       540        541        542        543        544        545        546 
 1.4929654  1.0430649  2.5120546  3.2763202  1.9585122  2.1843292  0.9339528 
       547        548        549        550        551        552        553 
 1.1223713  4.9184327  0.6359541  2.0856060  0.5357552  0.2827950  1.5245500 
       554        555        556        557        558        559        560 
 1.9903203  2.7287530  4.4280846  1.9201216  1.0830875  0.5798206  1.0970004 
       561        562        563        564        565        566        567 
 1.3283328  1.8147589  0.3857552  2.8533388  1.4088707  1.4284394  6.5526600 
       568        569        570        571        572        573        574 
 0.6608354  0.6867761  1.8267722  1.4628348  1.5335875  3.0183758  1.4588039 
       575        576        577        578        579        580        581 
 1.3919904  2.4510863  1.3132244  0.9470852  0.5838039  1.2260301  1.1152706 
       582        583        584        585        586        587        588 
 1.3800636  1.3448853  2.2723748  1.5027265  4.9320214  1.6306471  2.1281720 
       589        590        591        592        593        594        595 
 4.1701465  1.1986329  1.1805381  1.2204371  0.6761330  1.5376857  1.7206789 
       596        597        598        599        600        601        602 
 2.1706334  2.1729727  1.0065252  1.1762840  1.3250759  2.0833752  0.6474769 
       603        604        605        606        607        608        609 
 0.5901802  1.2860118  1.5467724  0.5165037  1.6200238  1.0283125  1.1558116 
       610        611        612        613        614        615        616 
 1.9063807  1.1662746  2.2062050  8.2751804  2.9361082  2.0555666  2.7478079 
       617 
 2.0275511 

mvoutlier documentation built on July 30, 2021, 9:09 a.m.