Kernel Density EstimationTheory and Application in Discriminant AnalysisThomas LedlUniversitt Wien

IntroductionTheoryAspects of ApplicationSimulation StudySummaryContents:

Introduction

Introduction25 observations:Which distribution?

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Kernel density estimator model:

Question 1:Which choice of K(.) and h is the best for a descriptive purpose?

IntroductionClassification:

Diagramm2

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0.01325020880.0155490720.01798918850.02060092240.02342768470.02650966190.02986394490.03346616910.03723842870.04104645180.04470664650.04800158160.05070133970.05258794680.05348027270.05325689410.05187423920.04937717120.04589954590.0416535610.03690880950.03196425280.02711800540.02264018610.01875294970.01561955090.01334172590.01196271390.01147255340.01181306080.01288174520.0145360340.01660061180.01888064460.02118193750.02333610010.02522563210.02680183890.02808875930.02916923260.03015424260.03114222020.0321791080.03323102240.03417857960.0348360240.03499101820.03445472740.0331087280.03093632060.02803058180.02457826270.02082516380.01703286740.0134376580.01022026170.00749087840.00528943030.00359743590.00235617550.0014858957

0.0110230460.01300592340.01515880050.01752774750.02017189220.02314719110.02648593340.03017660820.03414890740.03826748470.04233620170.0461126310.04933104650.05173111980.0530888890.05324607790.05213356160.04978497790.04633752890.04201902240.03712283990.03197508590.02689983110.02218850860.01807805730.01473979760.01227812090.01073582750.01010205150.01031938710.0112887520.01287290310.01490138410.01718019670.01950824890.02169994470.02361004090.02515442230.02631992780.02715840160.02776439960.02824116350.02866377840.02905016060.02934883840.02944774250.02920192170.02847236370.02716486290.02525816350.02281418940.01996868560.01690612240.01382650910.01091286750.00830657980.0060945760.00430864220.00293420260.00192440480.0012152951

0.00887377330.01055592720.012436660.01457618880.01704712830.01991832910.02323398050.0269921830.03112774310.03550333780.03991170730.04408961540.04774239750.05057623010.05233391980.05282910810.05197350890.04979238930.04642512970.04211025150.03715727830.03191046520.0267109840.0218641050.01761623080.01414382250.01155316140.00988745160.00913670690.00924643260.01012304930.01163657240.01362327540.01589204270.01823732950.02045923950.02238796480.02390697060.02496809350.02559293190.02585843990.02586943040.02572509530.0254889890.02517121490.02472792280.02407787160.02313059610.02181740560.02011606830.01806254860.01574749750.01329976960.01086256030.00856895920.00652276020.00478794550.00338738880.00230896080.00151592950.0009584156

0.00693453520.00834778280.00998539360.01191922960.01423231990.01700277580.02028272360.02407610270.02832005780.03287446680.03752295070.04198679310.04595093280.04909897690.05115234860.05190755940.05126543790.0492471390.04599386110.04175010730.03683344140.03159628320.02638665830.02151458460.01722896870.01370699920.01105487660.0093161980.00848314360.00850608090.00929911020.01074174250.0126793770.01492659010.01727685150.01952014580.021466740.02297218420.02395684330.02441373660.02440131320.02402217730.02339319170.02261521180.02175085120.02081605890.01978684050.01861776360.01726556680.01571027490.01396778190.0120911410.01016148720.00827238270.0065126260.00495209630.00363350770.0025707990.00175303910.0011516670.0007286898

0.00528402640.0064682620.00789733710.00965154540.01182068350.01448808940.0177096610.02149143710.02577042560.03040347270.03516795170.0397760870.04390218640.04721945380.04944093060.0503579430.04986950270.047997490.04488491140.04077761370.03599289350.03088080970.02578511950.02101034370.01679961030.01332508670.01068973270.00893661680.00806082440.00801938120.0087364630.01010386530.01197933780.01418700330.01652400390.01877563580.0207380790.02224449190.0231880060.02353501310.02332434830.02265192140.02164467930.02043095640.01911514010.0177628740.01639942280.01501966530.01360492460.01214047660.01062832980.00909220240.00757451910.00612767980.00480311760.00364159260.00266708190.00188509950.00128489190.0008440970.0005342287

0.00394951250.00494515550.00619873710.00779534810.00982765040.01238014660.0155085910.01921792180.02344333430.0280393820.03278107140.03737887870.04150687370.04484030640.04709678190.04807408750.04767809910.04593593580.04299224030.03908956940.03453672980.02967091960.02482033440.02027330740.0162581940.01293550960.0104009150.00869527910.00781686980.00773107350.00837482980.00965564150.01144772150.01358961920.01588784450.01812936260.0201028120.02162489570.02256583650.02286712480.02254639920.02168776420.02041999020.01888843290.01722797350.01554340640.01390091650.01233068690.01083754220.00941481890.00805671570.0067658740.00555513490.00444444280.00345511680.00260396030.00189909930.0013384320.00091057630.00059752190.0003779531

0.00291720190.00375978650.00486467940.00631803430.0082115510.01062716270.01361718910.01718317880.02125794150.02569560360.03027361090.03470850170.03868441570.04189039080.04406032570.04500863210.04465529410.04303608620.0402965470.03667130930.03245291520.02795587420.02348216980.01929366420.01559502020.01252823240.01017717380.00857839430.00773332030.00761736510.00818318830.00935795580.01103714930.01307934090.01530669980.0175145810.01949070090.02104103090.02201678190.02233574770.02199231750.02105339090.01964128440.01790818820.01600869730.01407681980.01221188160.01047473170.00889269440.00746974780.00619786350.0050662130.00406649680.00319431070.00244767720.00182437080.00131950560.00092427270.00062604540.00040954410.0002585085

0.00214673730.00286412860.00383900940.00515508070.00689964010.00914893650.01194944320.01529812040.01912598350.02328961060.02757429070.03171037930.03540154830.03836075580.04034775410.04120136650.04086076180.03937220550.03688064380.03360828370.02982450180.02581261840.02183919690.01813060180.01485976120.0121437270.01005018960.00860915280.00782504360.00768494070.00816031260.00920220620.01073246970.01263548350.0147553410.01690220210.01886891220.02045570550.0214979460.02189038730.02160191480.02067707680.01922417540.01739315050.01534884880.01324586960.01120998860.0093287560.00765114690.006193980.00495175390.0039066550.00303646350.00231939320.00173606910.00126954720.00090446480.00062618370.00042038550.00027318780.0001716023

0.00158574870.00219778030.003053780.00423197860.00581247120.00786352640.01042434510.01348716970.01698279540.02077378950.02465876860.02838896070.03169547670.03432301590.03606395370.03678645130.03645146340.03511588910.03292192570.03007525390.0268164880.0233911550.02002329380.01689670160.01414608660.01185818180.01008065780.00883493880.00812827780.0079609620.0083262490.00920314580.01054472280.01226651820.01424012290.01629598550.01823706290.01986182010.02099217330.02150018530.02132726480.0204913510.01908057860.01723528360.01512290820.01291163940.01074821310.00874354390.00696739690.00545101560.00419508180.00317988680.00237502640.00174692370.00126358940.00089690180.00062315070.00042266360.00027914680.00017909820.000111401

0.00118156490.00170142170.00244436440.0034808420.00488175730.00670600660.00898503980.01170712630.01480503420.01815100650.02156194660.02481568650.02767657240.02992613840.03139312960.03197706810.03166093930.03051095650.02866404560.02630599820.02364473980.02088368880.01819978740.01572961110.01356518380.01175901840.01033583060.00930683310.00868195320.00847598720.00870652480.00938399580.01049672640.01199570730.0137843320.01571743370.01761173280.01926684920.02049311910.02114040820.02112154210.02042509560.01911481260.01731615090.01519342590.01292294360.0106678710.0085594560.00668705960.00509705420.00379868820.00277396640.00198853810.00140127830.00097129510.00066210190.00044339610.00029120240.00018714210.00011739860.0000717152

0.00088872240.00132519420.00195849210.0028497940.00405969540.00563720750.00760634120.00995270240.01261339520.01547362570.01837245240.0211182330.02351191460.02537413840.02657088490.02703249280.02676231470.02583356870.02437543420.02255150670.02053498930.01848533160.01653049920.01475779530.01321434650.01191626380.01086348560.01005589730.00950593640.00924375780.00931301520.00975790880.01060467920.01184248770.0134091590.01518639520.01700700470.01867387620.01998753160.02077682380.02092631620.02039443110.01921850950.01750598040.01541405720.01312286230.01080796260.00861775710.00665930710.00499371560.00363984380.00258361170.00178962880.00121232670.0008047560.00052431910.00033561680.00021110360.00013039920.00007899080.0000468327

0.00067229690.00103209360.00155940240.00230547650.00332032770.00464332710.00629191950.0082505780.01046284130.01282930440.01521355130.01745631450.01939603320.02089211470.02184619440.02221690020.02202500760.02134799360.02030526160.01903716660.01768208620.0163560310.01513871090.01406866760.01314820170.01235665680.01166858990.01107200530.0105815980.01024305150.01012663440.01031109410.01086140840.0118056760.01311689280.01470450160.01641860820.01806706330.01944272770.02035581130.02066476560.02029926790.01927046380.01766651680.01563491750.01335597460.01101361720.00876963430.00674590580.00501665290.00361011740.00251712140.00170308360.00112025690.00071788470.00044916790.00027499160.00016504560.00009724070.00005627490.0000319816

0.00050799520.0007975530.00122458730.00183052860.00265524450.0037292850.00506471070.00664630620.00842555140.01031970650.01221757710.01399204970.0155176960.01669017620.01744336020.01776033580.01767571440.017268540.01664712730.01592884650.01521892230.0145925790.01408431690.0136867790.01335969560.01304709080.01269879850.01229096580.01184013150.01140680250.01108693250.01099267190.01122640740.01185378890.01288180850.01424706730.01581737950.01740723040.01880475580.0198053780.02024555440.02002976570.01914514960.01766090060.01571307010.01347874880.01114581070.00888484670.00682859070.00506160990.00362019430.0025001060.00166866770.00107767310.00067446890.00040980760.00024224070.0001396210.00007864890.00004339050.0000234846

0.00038030350.00060681550.00094209270.00141844890.00206658090.00290940170.00395485170.00518916440.00657250490.0080388530.00950132970.01086293710.01203120250.0129339320.01353262780.01383034470.0138718230.01373536080.01351767560.0133145650.01320122970.01321647970.01335458030.01356718070.01377569560.01389202610.01384320790.01359414850.01316262190.01262227330.01209216420.01171460630.01162579190.01192537080.01265136330.01376573480.01515392020.01663896910.01800818080.01904753530.01957740050.01948241320.01872944310.01737010220.01552781130.01337300190.0110925790.00886054730.00681559530.00504893760.00360276360.00247715570.00164195440.00104989980.00064818470.00038682350.0002234690.00012519190.00006815290.0000361360.0000187062

0.00027990410.00045158570.00070619390.00106804370.00155996480.00219858060.00298888460.00391928210.00495859660.0060564870.00714816620.00816333250.00903803080.00972713490.01021460090.01051880540.01069113280.01080733250.01095272760.01120382240.01160995560.01217912980.0128718170.01360524590.0142685160.01474621630.01494573920.01482197610.01439316220.01374343810.01301077420.01236235590.01196241160.01193905870.01235682860.01320030420.0143721560.01570625180.01699377340.01801776930.01858972430.01858102380.01794302020.01671180510.01499727560.0129597140.01077982310.00862914730.0066468780.00492664340.00351391490.00241210120.00159389930.00101421880.00062174320.00036743020.00020950220.00011537860.00006145850.00003171710.0000158903

0.00020122960.0003270150.00051371330.00077897390.00113919690.00160606080.00218259080.00285966550.00361409470.00440935330.00519962280.00593702660.006581020.00710807410.00751934210.00784407670.00813721290.00847062790.00891894850.00954216840.01036849120.0113814480.01251513120.01366015370.01468070490.01544025650.01583082420.01579910440.01536293690.01461352820.013702180.012813930.01213347060.01181025270.01192960230.01249526490.0134265380.01457053150.01572746410.01668453090.01725212840.01729551660.01675572250.01565571890.01409123090.01220906730.01017859650.00816307230.0062967310.0046713240.0033328890.00228703590.00150950770.000958460.00058558270.00034436480.0001950110.00010640660.00005598740.0000284360.0000139594

0.0001406160.00022955760.00036159340.000549080.00080339940.0011325070.00153820380.00201379190.00254295230.00310063330.00365641850.00418026660.00464980710.00505773090.00541742120.00576497460.00615621810.00665819440.00733577190.00823535310.00936885820.01070191390.01215010280.01358595240.01485709150.01581308590.01633571960.01636584330.01592008120.01509278530.0140420890.01296268780.0120509650.01146953380.01131803560.0116154520.01229684590.01322485110.01421374150.01506175190.01558575960.01565182370.01519574870.01422988760.01283546470.01114300740.00930605610.00747440520.00577245870.00428622880.00305984120.0021000370.00138570320.00087913470.00053632450.00031466960.00017759610.00009644890.00005042280.00002539010.0000123234

-3

-2,9

-2,8

-2,7

-2,6

-2,5

-2,4

-2,3

-2,2

-2,1

-2

-1,9

-1,8

-1,7

-1,6

-1,5

-1,4

-1,3

-1,2

-1,1

-1

-0,9

-0,8

-0,7

-0,6

-0,5

-0,4

-0,3

-0,2

-0,1

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

1,2

1,3

1,4

1,5

1,6

1,7

1,8

1,9

2

2,1

2,2

2,3

2,4

2,5

2,6

2,7

2,8

2,9

3

Tabelle1

Gruppe1:

m0.1325025204

-0.29832318660.85380196680sigma=1010

0101

Sigma=Daten:

-2.8269278118-1.37181666310.1591549431

1.42707689040.236782954-0.94724100560.98183056961

0.2367829541.0502721842-0.87719172371.3221521183-3-2.9-2.8-2.7-2.6-2.5-2.4-2.3-2.2-2.1-2-1.9-1.8-1.7-1.6-1.5-1.4-1.3-1.2-1.1-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50.60.70.80.911.11.21.31.41.51.61.71.81.922.12.22.32.42.52.62.72.82.93-3-2.9-2.8-2.7-2.6-2.5-2.4-2.3-2.2-2.1-2-1.9-1.8-1.7-1.6-1.5-1.4-1.3-1.2-1.1-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50.60.70.80.911.11.21.31.41.51.61.71.81.922.12.22.32.42.52.62.72.82.93

1.20876848091.3045556696-30.00027983940.00034452460.00042140240.00051208140.00061822480.00074151360.0008836030.00104606950.00123035170.00143768350.00166902430.0019249850.00220575550.00251103480.00283996770.00319109270.00356230220.00395082160.0043532080.00476537130.00518262050.00559973390.0060110550.00641060990.00679224470.00714977910.007477170.00776867970.00801904230.00822362170.00837855390.00848086880.00852858440.00852077090.00845758070.00834024380.00817102740.00795316370.00769074660.00738860440.00705215180.00668722940.00629993570.00589645980.00548291990.00506521390.00464888710.00423902080.00384014320.00345616620.00309034630.00274526970.00242285930.00212440210.00185059150.00160158410.00137706440.00117631620.00099829580.00084170470.0007050592-30.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.010.010.010.010.020.020.020.020.020.020.020.020.010.010.010.010.010.000.000.000.000.000.000.000.000.000.000.000.00

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0.83470808931.2205217697-2.80.0004167980.00051292640.00062711860.00076174520.0009192530.0011021120.00131274910.00155347070.0018263740.00213324980.00247547780.00285391920.00326880980.00371965750.0042051510.00472308270.0052702940.00584264460.00643501290.007041330.00765464950.00826725330.00887079440.00945647130.01001523250.01053800230.01101592250.01144059960.01180434870.01210042430.01232322850.01246848630.01253338240.0125166520.01241862160.01224119850.01198780910.01166328860.01127372810.01082628410.01032896040.00979037070.00921949180.00862541830.00801712530.00740325160.00679190620.00619050640.00560565030.00504302540.00450735370.0040023720.00353084450.00309460390.00269461590.00233106290.00200344050.00171066220.00145116690.00122302630.0010240463-2.80.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.010.010.010.010.020.020.020.020.030.030.020.020.020.020.020.010.010.010.010.000.000.000.000.000.000.000.000.000.000.001

0.7279639603-0.1641188441-0.26599082051.1741068445-2.70.00050314630.00061905990.00075672190.00091897840.00110876530.00132904370.00158272050.00187255480.00220105140.00257034340.00298206730.00343723370.0039360990.00447804340.00506146110.00568366990.00634084460.00702798310.00773890720.00846630470.00920181460.00993615580.01065929880.01136067690.01202943170.01265468510.0132258290.01373282210.01416648190.01451876110.01478299530.01495411250.01502879560.01500558890.01488494510.01466921120.0143625520.01397081670.01350135340.01296277980.01236472080.01171752290.0110319590.0103189330.00958919790.00885309440.00812032180.00739974430.00669923970.00602559090.00538442220.00478017610.00421613020.00369444720.00321625330.00278173880.00239027450.00204053730.00173063960.0014582570.0012207502-2.70.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.010.010.010.010.020.020.020.030.030.030.030.030.030.020.020.020.010.010.010.010.010.010.000.000.000.000.000.000.000.000.002

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0.47534513210.9678266249-2.40.00084730760.00104185290.0012727320.001544660.00186249080.00223110860.00265529410.00313956780.00368801280.00430407980.00499037910.00574846770.00657863780.00747971730.00844889140.00948155560.01057121220.01170941830.01288579380.01408809790.01530237630.01651318020.0177038570.01885690420.01995437950.02097835290.02191138740.0227370280.02344028270.0240080740.02442964340.02469688980.02480462860.02475075910.02453633240.02416551740.02364546610.0229860840.02219971660.02130076490.0203052480.01923032950.0180938290.01691373680.015707750.01449284760.01328491560.01209843520.01094623920.00983934060.00878683320.00779586130.00687165190.00601760290.00523541650.00452526760.00388599860.00331532670.00281005840.00236629950.0019796544-2.40.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.010.010.010.010.020.020.030.030.030.040.040.040.040.040.030.030.030.020.020.020.020.010.010.010.010.010.010.010.000.000.000.005

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Gruppe2:1.14412614492.763464752-2.20.00115648430.00142142170.00173568730.0021056460.00253784190.00303884880.00361508860.00427261870.00501689090.00585248760.00678284170.00780994880.00893408370.0101535330.01146435630.01286019330.0143321270.01586861880.01745552590.01907620920.0207117380.0223411920.02394205730.02549070940.02696296860.02833471310.02958252650.03068435750.03162016520.03237252420.03292716380.03327341770.03340456570.03331805010.03301555890.03250297090.03179016580.03089070760.02982141520.02860183990.02725367180.02580010080.02426515730.02267306070.02104759690.019411550.01778620290.01619092260.01464283880.01315661890.01174434060.01041545650.00917684320.00803292370.00698585070.00603573670.00518091670.00441822930.00374330510.00315084860.0026349063-2.20.000.000.000.000.000.000.000.000.000.000.000.000.000.000.010.010.010.010.010.010.010.010.000.000.000.000.000.000.000.010.010.010.020.020.020.030.030.040.040.040.040.040.040.040.040.030.030.030.030.020.020.020.020.010.010.010.010.010.000.000.007

m=-1.0697362995-0.5719160729-2.10.00133643940.00164225820.00200492890.00243176620.00293028590.00350803160.00417236540.00493022230.0057878330.00675042030.00782187680.00900443470.01029834080.01170155020.01320945410.01481465930.01650683450.01827263810.02009574160.02195695710.02383447540.02570421650.02754028770.02931554040.03100221080.03257262470.03399994190.03525891330.03632662080.03718316950.03781230410.03820192150.03834445780.03823713330.03788204170.03728608270.03646073930.03542170890.03418840810.03278336870.03123155480.02955962780.027795190.02596603650.02409944310.02222151580.02035662060.0185269110.01675196190.01504851570.01343033930.01190818660.0104898580.00918034320.00798203360.00689498810.00591723490.0050450960.00427351650.00359638910.0030068605-2.10.000.000.000.000.000.000.000.000.000.000.000.000.010.010.010.010.010.010.010.010.010.010.010.010.000.000.000.000.000.010.010.010.020.020.030.030.040.040.040.050.050.050.050.040.040.040.040.030.030.030.030.020.020.020.020.010.010.010.010.000.008

-0.2075551038-0.5583080477-1.49065726872.2267514649-20.00153320040.00188364950.00229914620.00278803630.00335888840.00402029620.00478063810.00564779610.00662883910.00772967580.00895468690.01030634950.01178486610.0133878170.01510985210.01694244120.01887370190.02088832060.02296758260.02508952140.02722919480.02935908710.03144963630.03346987070.03538814290.03717293380.03879370280.04022174970.04143105690.04239907630.04310742760.04354247880.04369578240.04356434810.04315074010.04246299350.04151435490.04032285840.03891075490.03730382210.03553058310.03362146770.031607950.02952169720.02739375970.02525383230.02312960790.0210462430.01902594410.01708768320.01524703790.01351615310.0119038120.01041560120.00905415560.00781946240.00670920660.00571914050.00484345970.00407517210.0034064462-20.000.000.000.000.000.000.000.000.000.000.000.010.010.010.010.010.010.010.010.010.010.010.010.010.010.000.000.000.010.010.010.010.020.020.030.030.040.040.050.050.050.050.050.050.040.040.040.040.040.030.030.030.020.020.020.020.010.010.010.010.009

0.68642293631.7557787285-1.90.0017461790.00214485970.00261742570.00317332950.00382226940.00457396410.0054378790.00642290740.00753701030.00878682310.01017723940.0117109850.01338819990.01520604530.01715835710.01923536590.02142350540.02370532660.02605953620.028461170.03088190950.03329054250.03565356220.0379358930.04010172240.04211541350.04394246750.04555049930.04691018790.04799616430.04878779840.04926984980.04943295650.04927393670.04879589260.04800810920.04692575460.04556939450.04396434230.04213987390.04012834160.03796422350.03568314790.03332093110.03091266340.02849187640.02608981540.02373483910.02145195640.01926250870.01718399430.01523002870.01341042840.01173140190.0101958280.00880360240.00755202930.00643624020.00544961910.00458421930.003831157-1.90.000.000.000.000.000.000.000.000.000.000.010.010.010.010.010.010.010.010.010.010.010.010.010.010.010.010.000.000.010.010.010.010.020.020.030.030.040.040.050.050.050.050.050.050.050.050.040.040.040.040.030.030.030.020.020.020.010.010.010.010.0010

Sigma=0.97528982220.2540574567-1.80.00197432530.00242458730.00295816420.00358568440.0043180450.0051661570.00614063620.00725144340.0085074790.00991613970.01148285070.01321058750.01509940630.01714600480.01934333430.02168028890.02414149290.02670720920.02935338720.03205186230.03477071660.03747480170.04012641640.04268612550.04511369790.04736913410.04941374780.05121126130.05272887170.05393824540.05481639610.05534641230.05551799810.05532780620.05477954640.05388386550.05265800280.05112523920.04931416130.04725777590.04499251140.04255714860.0399917250.03733645510.03463070680.03191206870.02921553810.02657285090.02401196720.0215567190.01922661850.01703681810.01499820870.01311763760.01139822420.00983975060.00843910350.00719074460.00608718850.00511946950.0042775835-1.80.000.000.000.000.000.000.000.000.000.010.010.010.010.010.010.020.020.020.020.020.020.010.010.010.010.010.010.010.010.010.010.010.020.020.030.030.040.040.050.050.050.050.050.050.050.050.050.050.040.040.040.040.030.030.020.020.020.010.010.010.0011

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1.3923635497-0.26104446040.1249020443-0.2888358469-1.60.00246944350.00303135050.00369690730.00447926020.00539186920.00644818870.00766128220.00904337430.0106053470.01235619030.01430242310.01644750340.01879125040.02132930480.02405265670.02694726740.02999381730.03316760260.03643860560.03977175410.04312737970.04646187450.04972854040.05287860950.05586241020.05863064090.06113570750.06333307480.0651825780.06664964210.06770635590.06833235480.06851547350.06825213940.06754748810.06641519740.0648770450.06296221280.06070636580.05815054840.05533994520.05232255750.04914785090.04586542570.04252375970.03916906560.03584429940.03258834530.0294353940.02641452010.02354945860.02085856650.01835495470.01604676550.01393756880.01202684940.01031055510.00878167890.00743084820.00624690.005217423-1.60.000.000.000.000.000.000.000.000.010.010.010.010.020.020.020.020.020.020.020.020.020.020.020.010.010.010.010.010.010.010.010.010.020.020.030.030.040.040.040.050.050.050.050.050.050.050.050.050.050.050.040.040.040.030.030.020.020.010.010.010.0113

-0.26104446041.04793443420.71240947360.7294889909-1.50.00273180370.00335270660.00408796270.00495203410.00595971740.00712579020.00846458610.00998949990.01171243250.01364318550.01578882440.01815303040.02073546620.02353118520.02653011480.02971664570.03306935870.03656091770.04015815320.04382235430.04750977880.05117238280.05475875950.05821526670.06148731250.06452075780.06726338780.06966639610.07168582380.07328389540.07443019220.07510261590.07528809650.0749830150.07419332080.07293433880.07123027480.06911344140.06662323960.06380493980.06070831650.05738619170.05389294910.05028307440.04660977710.04292374030.03927203620.03569723760.0322367410.02892231010.02577983640.02282930360.02008493820.01755551870.0152448150.01315212670.01127288660.00959930120.00812099850.00682565870.0056996087-1.50.000.000.000.000.000.000.000.010.010.010.010.020.020.020.020.030.030.030.030.030.020.020.020.010.010.010.010.010.010.010.010.010.020.020.030.030.040.040.040.050.050.050.050.050.050.050.050.050.050.050.050.040.040.030.030.020.020.010.010.010.0114

-1.53014752871.6053619472-1.40.00300012980.0036812480.00448761330.00543501960.00653961420.00781751040.00928432080.01095461550.0128413140.01495502440.01730334680.0198901670.02271496510.02577217370.02905061650.03253306550.03619594750.04000923440.04393654090.04793545040.05195807970.05595188210.05986067880.0636258950.0671879670.07048787610.07346875480.07607750530.07826636710.0799943690.08122860370.08194526950.08213043390.08178048390.08090224320.07951275110.07763871270.07531564530.0725867590.06950162180.0661146650.06248359280.05866776110.0547265870.05071804960.04669733030.04271563730.03881924250.03504875160.0314386130.02801686470.02480510190.02181864770.01906689480.016553790.01427842290.01223568740.010416980.0088109070.00740397140.0061812197-1.40.000.000.000.000.000.000.010.010.010.010.010.020.020.020.030.030.030.030.030.030.030.020.020.020.010.010.010.010.010.010.010.020.020.020.030.030.040.040.040.050.050.050.050.050.050.050.050.050.050.050.040.040.040.030.030.020.020.010.010.010.0115

0.75338852690.18767195260.9178165783-3.360502549-1.30.00327092620.00401268210.00489062180.00592186830.0071239150.0085142040.01010961690.01192588660.01397693610.01627416120.01882567590.02163554660.02470304520.02802195590.03157997090.03535821520.03933093530.04346538610.04772194540.05205447440.05641093810.06073428270.06496356060.06903527570.07288491240.07644860020.07966485470.08247633010.08483151380.08668629380.08800533140.08876318130.08894510760.08854756030.08757829050.08605609940.08401023110.08147943920.07851076550.07515808770.07148049660.06754057120.06340262320.05913097680.05478834840.05043438090.04612437640.04190826210.03782980680.0339260990.03022727910.02675651310.0235301830.02055826330.01784484870.01538879620.0131844420.01122235980.00949012540.00797306030.0066549296-1.30.000.000.000.000.000.010.010.010.010.010.020.020.020.030.030.030.030.030.030.030.030.020.020.020.010.010.010.010.010.010.010.020.020.020.030.030.040.040.040.040.050.050.050.050.050.050.050.050.050.050.040.040.040.030.030.020.020.010.010.010.0116

0.18767195261.00100797280.3652485248-1.0581326276-1.20.00354031250.00434224750.00529118420.00640555140.00770416340.00920576280.0109284710.01288915230.01510270150.01758127030.02033345550.02336347620.02667037110.03024725630.03408067940.03815011310.04242762730.0468777750.05145772290.05611764880.06080141670.06544752990.06999034760.07436153910.07849173320.08231231130.08575728120.088765160.09128079330.09325703430.09465621280.09545132850.09562691810.09517955520.09411796130.09246272340.09024562970.08750865480.0843026380.08068571490.07672156740.07247756790.0680228910.06342666670.05875624330.05407561680.04944407680.04491510220.04053552870.03634499550.03237566720.02865221250.02519201630.02200559030.01909714510.0164652830.01410377210.01200236130.01014760220.0085236480.0071130016-1.20.000.000.000.000.010.010.010.010.010.020.020.020.030.030.030.040.040.040.040.030.030.030.020.020.020.010.010.010.010.010.020.020.020.030.030.030.030.040.040.040.040.040.040.050.050.050.050.050.040.040.040.040.030.030.020.020.020.010.010.010.0117

-0.9966834114-1.6376558304-1.10.00380410590.00466481630.00568305470.00687851110.00827127360.00988133580.01172800810.0138292360.01620083680.01885567280.02180278390.02504650870.02858563020.03241258550.03651278070.04086405610.04543634240.05019154740.05508370390.06005940350.06505852650.07001526880.07485944920.07951806870.08391707710.08798329110.09164639510.09484095090.09750833520.09959852630.10107166330.10189930980.10206536690.1015665940.1004127140.09862609810.09624104440.09330268280.08986555590.08599193630.08174995460.07721161580.07245078430.06754121530.06255470490.05755942110.05261846620.04778870710.04311989610.03865409060.03442536430.03045979370.02677569170.02338405210.02028916490.01748935930.01497783210.01274351830.01077196820.00904619840.007547489-1.10.000.000.000.010.010.010.010.010.020.020.020.030.030.030.040.040.040.040.040.040.030.030.020.020.020.010.010.010.010.020.020.020.020.030.030.030.030.040.040.040.040.040.040.040.040.040.040.040.040.040.040.030.030.030.020.020.020.010.010.010.0118

Gesamt-0.3600189302-0.0742276168-10.00405792240.00497501810.00605969730.00733284520.00881575340.01052959540.01249479860.01473031940.01725283230.0200758510.02320880910.02665612890.03041631740.03448113170.0388348580.043453750.04830567210.05334998810.05853772680.06381205180.06910904540.07435880610.07948684360.08441573850.08906702080.0933632060.09722991740.10059801380.10340563940.10560011030.10713955750.10799425540.10814757590.10759652710.10635184960.10443766890.10189071770.09875916340.09510109390.09098272740.08647642360.08165857890.0766074920.07140128050.06611592610.0608235130.05559071290.05047755560.04553650740.04081186570.03633946330.03214666310.02825261270.02466872280.02139932340.01844245560.01579075090.01343235460.01135185510.00953118420.0079504592-10.000.000.010.010.010.010.010.020.020.020.030.030.040.040.040.040.040.040.040.040.030.030.030.020.020.020.020.020.020.020.020.020.030.030.030.030.030.040.040.040.040.040.040.040.040.040.040.040.040.030.030.030.030.020.020.020.020.010.010.010.0119

1.3473663785-1.1198145583-0.90.00429729360.00526738340.0064144610.00776051840.0093279590.01113904230.01321522030.01557637120.0182399440.02122003230.02452640590.02816353140.03212962360.03641576980.04100517610.04587258320.05098389860.05629608780.06175735950.06730766910.0728795550.07839930320.08378842420.08896540740.09384770350.09835387090.10240580920.10593099690.10886464330.11115166640.11274841130.11362403650.1137615040.1131581310.11182567690.1097899620.10709003560.10377693030.09991205850.09556532090.09081300930.08573559010.08041545890.07493475250.06937329760.06380676540.05830508720.05293117050.04773994080.04277771510.03808190110.03368100070.02959488670.02583531170.0224066050.01930650850.01652710370.01405578460.01187623450.00996937110.0083142311-0.90.000.010.010.010.010.020.020.020.020.030.030.040.040.040.050.050.050.050.040.040.040.030.030.020.020.020.020.020.020.020.020.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.020.020.020.020.010.010.010.010.0120

m-1.33944695340.6143621906-0.80.00451779440.00553650050.00674077080.00815359440.00979837310.01169833820.01387585340.01635161150.01914373830.02226682340.0257309080.02954046230.03369339640.03818014950.04298290740.04807499860.05342051880.05897422620.06468174550.07048010460.07629861910.08206011940.08768250340.09308057690.09816813060.10286018580.1070753290.11073804690.11378096970.1161469290.11779074290.1186806510.11879933450.11814447720.11672884040.11457984930.11173870950.10825909320.10420545350.09965104110.0946757080.08936359090.08380076660.07807296990.07226345780.06645108950.06070868170.05510167840.04968716090.04451320510.03961857760.03503274930.03077619270.02686092060.02329121920.0200645250.0171723950.0146015240.01233476370.01035210840.0086316161-0.80.010.010.010.010.020.020.020.030.030.030.040.040.040.050.050.050.050.050.050.040.040.030.030.030.020.020.020.020.020.020.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.030.020.020.020.020.020.020.020.010.010.010.010.0121

-0.25293914520.14774695960.48117726690.0540088624-0.70.00471517750.00577718010.00703232760.00850447710.01021789560.01219665220.01446389110.01704099620.01994665810.02319586840.02679886860.03076009070.03507713320.03973982060.04472939680.05001790650.05556781340.06133190220.06725349990.07326704490.07929901450.08526920880.0910923710.09668010380.10194303030.1067931260.1111461410.11492401950.11805722070.12048684480.12216647350.12306364460.12316089530.12245632760.12096366970.11871183150.11574397320.11211612960.10789545140.10315814050.09798716730.09246986630.0866955060.08075292670.07472833150.06870330490.06275311690.05694535490.0513389090.0459833170.04091846040.03617458880.03177263630.02772478760.0240352440.02070113560.01771353070.01505849010.01271812390.01067161140.0088961538-0.70.010.010.010.020.020.020.030.030.030.040.040.050.050.050.050.050.050.050.050.050.040.040.030.030.030.020.020.020.020.030.030.030.030.030.040.040.030.030.030.030.030.030.020.020.020.020.020.020.020.020.020.020.020.020.010.010.010.010.010.010.0122

-1.2704504115-0.0112064552-0.60.00488550850.00598462050.00728330970.00880615390.01057813480.01262400770.01496755050.01763069960.0206325870.02398850350.02770881510.03179787390.03625296570.04106334520.0462094120.05166207990.05738239370.06332143730.06942057350.07561204050.08181991980.08796146810.09394879590.09969084950.10509564120.11007265470.11453533920.11840359850.12160617420.12408282680.12578621860.12668341820.12675695970.12600540770.12444340430.12210119420.11902365130.11526884880.11090623740.10601451150.10067925450.09499046080.0890400360.0829193690.0767170650.07051691420.06439615670.0584240860.05266101610.04715761930.04195462440.03708285240.03256355090.02840898450.02462322840.02120311190.01813925920.01541717550.01301833420.01092122470.0091023305-0.60.010.010.020.020.020.030.030.040.040.040.050.050.050.060.060.060.060.050.050.050.040.040.030.030.030.030.030.030.030.030.030.030.040.040.040.040.040.030.030.030.030.020.020.020.020.020.020.020.020.020.020.010.010.010.010.010.010.010.010.010.0123

1.709904609-0.6670317159-0.50.00502529610.00615456650.00748856510.0090524280.01087168550.01297161380.01537646380.01810857420.02118738580.02462837860.02844196490.03263237630.03719659060.04212334950.04739232220.05297346870.0588266560.06490157580.07113799990.07746640260.08380896080.09008092810.09619235950.10205014640.10756030280.11263042670.11717225050.12110418270.12435373770.12685975650.12857431890.12946426810.12951227660.12871740750.12709514470.12467689120.12150895850.11765109180.11317459630.10816014870.10269538470.09687236580.09078502450.08452668820.07818776890.07185369680.06560315750.05950667680.05362557740.04801131430.04270517810.03773834140.03313221030.02889903490.02504272580.02155982280.01844055990.01566997670.01322902770.01109565210.0092457696-0.50.010.020.020.020.030.030.040.040.050.050.050.060.060.060.060.060.060.060.050.050.050.040.040.030.030.030.030.030.030.030.040.040.040.040.040.040.040.030.030.030.020.020.020.020.020.010.010.010.010.010.010.010.010.010.010.010.010.010.010.020.0224

sigma-0.12490204430.4347051547-0.40.00513161040.00628345440.00764378720.00923812920.01109238180.01323216530.01568203260.01846456650.02159937630.02510201780.02898286970.0332460050.03788810430.04289746370.04825315160.05392437030.0598700760.06603890530.07236944650.07879088260.08522401860.09158268710.09777550860.10370796560.10928472790.11441215470.11900088290.12296840260.12624151810.12875859070.13047146840.13134701720.13136818760.13053456650.12886239040.12638401980.12314689750.11921203860.11465211840.10954924310.10399249750.09807537210.09189317350.08554051580.07910898430.0726850480.06634828230.06016994510.05421193080.04852610850.04315403250.03812699980.03346641630.02918442330.02528473180.0217636090.01861096150.01581146210.01334567620.01119114350.0093233863-0.40.010.020.020.030.030.040.040.050.050.060.060.060.060.060.060.060.060.060.060.050.050.040.040.040.030.030.030.030.040.040.040.040.040.040.040.040.040.030.030.030.020.020.020.010.010.010.010.010.010.010.010.010.010.010.010.010.010.010.010.020.0225

1.3756860721-0.0441743829-0.9399559531-0.093893166-0.30.00520218570.00636853610.0077456650.0093592950.01123551250.01340009790.01587772890.01869106820.02185975010.02539929090.02931995640.0336256260.03831270050.04336910710.04877345560.05449440320.06049028130.06670903160.07308849150.07955705330.0860347120.0924344920.09866423140.10462867960.11023184630.11537952520.11998190210.12395614660.12722888480.12973844940.13143681140.13229110860.13228470280.13141771920.12970704160.12718576650.12390213750.11991801050.11530691680.11015180910.10454258580.09857349850.09234054480.08593894610.07946080190.07299299660.06661542020.06039954670.0544073930.04869086420.04329147450.03824041550.03355893390.02925897030.02534400530.02181005660.01864677210.01583856610.01336575170.01120562920.0093334979-0.30.020.020.030.030.040.040.050.050.060.060.060.070.070.070.070.070.070.060.060.060.050.050.040.040.040.040.040.040.040.040.040.040.040.040.040.040.040.030.030.030.020.020.020.010.010.010.010.010.010.010.010.010.010.010.010.010.010.010.010.020.0226

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