qmvsr3<- function(quantile,n1,n2,n3,p) { #=================================================================== #The name of this function is the concatenation of: # "Quantiles of the MultiVariate Studentized Range Distribution # for the case of 3 groups". # quantile = 0.8,0.825,0.85,...,0.925,0.95,0.975,0.99,0.999 # p = 1,2,3,4,5 (dimension) # n1,n2,n3 = arbitrary group sizes between 4 and 100 # (e.g. n1=8, n2=13, and n3=21). #==================================================================== # author: Otto Schwalb # e-mail: schwalb@stat.rice.edu # 7/11/97: The purpose of this function is to allow anyone to # easily find quantiles of the multivariate studentized range # for the case of 1-way MANOVA with 3 groups without having to # know much about the theoretical details. # The quantiles given by this code are off by no more than 0.0151 # in the worst case, but generally are a great deal more accurate # than that. Currently, the equations are applicable for the # following situations (more work is in progress): # quantiles: 0.8,0.825,0.85,...,0.925,0.95,0.975,0.99,0.999 # dimensions: 1,2,3,4,5 # group sizes: arbitrary group sizes between 4 and 100 # Please notice that all quantiles are not available (there are only # the 10 possibilities listed above). This is in contrast to # the convention in Splus where quantiles are available for any # possible choice of alpha. n<- c(rep(0,3)) temp<- c(rep(0,3)) vary<- c(rep(0,29)) temp<- sort(c(n1,n2,n3)) coeff<- c(rep(0,29)) n[1]<- temp[1] n[2]<- temp[2] n[3]<- temp[3] if (n[3] > 4*n[1]) { stop("Although it is theoretically feasible to have the largest group more than 4 times the size of the smaller group, this possibility was not considered to be a reasonable one when we developed our equations. Thus quantiles from our function are only valid when the largest group is no more than 4 times the size of the smallest group.") } vary[1]<- 1 vary[2]<-n[1] vary[3]<-n[2] vary[4]<-n[3] vary[5]<-n[1]*n[2] vary[6]<-n[2]*n[3] vary[7]<-n[1]*n[3] vary[8]<-n[1]*n[2]*n[3] vary[9]<-n[1]^2 vary[10]<-n[2]^2 vary[11]<-n[3]^2 vary[12]<-n[1]^2*n[2]^2 vary[13]<-n[1]^2*n[3]^2 vary[14]<-n[2]^2*n[3]^2 vary[15]<-(n[1]*n[2]*n[3])^2 vary[16]<-n[1]^3 vary[17]<-n[2]^3 vary[18]<-n[3]^3 vary[19]<-n[1]^3*n[2]^3 vary[20]<-n[1]^3*n[3]^3 vary[21]<-n[2]^3*n[3]^3 vary[22]<-(n[1]*n[2]*n[3])^3 vary[23]<-n[1]^4 vary[24]<-n[2]^4 vary[25]<-n[3]^4 vary[26]<-n[1]^4*n[2]^4 vary[27]<-n[1]^4*n[3]^4 vary[28]<-n[2]^4*n[3]^4 vary[29]<-(n[1]*n[2]*n[3])^4 if (p == 1) { if (quantile==0.800) { coeff[1]<- 2.9214778742964498 coeff[2]<- -1.5903755610617600 coeff[3]<- 1.1251531466735201 coeff[4]<- 3.9852782834556102 coeff[5]<- 18.6345392451415002 coeff[6]<- 42.9837903183196985 coeff[7]<- 22.6876152457780016 coeff[8]<- -186.4139329389840043 coeff[9]<- 3.6884615292768199 coeff[10]<- -38.2250429979291013 coeff[11]<- -104.7482726656700009 coeff[12]<- -118.2510432029509957 coeff[13]<- 67.3614493025770997 coeff[14]<- -455.9235364125179899 coeff[15]<- 19116.8786558889987646 coeff[16]<- -38.3393212955455027 coeff[17]<- 165.9873171869749910 coeff[18]<- 674.7516336199560101 coeff[19]<- 56.1141972160329985 coeff[20]<- -10366.7951710158995411 coeff[21]<- -8914.2780497498206387 coeff[22]<- -691224.0167888570576906 coeff[23]<- 86.2434793597818015 coeff[24]<- -249.8271563862770108 coeff[25]<- -1540.3839946696500647 coeff[26]<- 1870.9039223253100772 coeff[27]<- 132371.2814369550033007 coeff[28]<- 242684.5410618160094600 coeff[29]<- -15581889.7061569001525640 } if (quantile==0.825) { coeff[1]<- 3.1651158879678198 coeff[2]<- -1.6434385824803399 coeff[3]<- 1.2895746408420301 coeff[4]<- 4.3310708583078803 coeff[5]<- 21.0050683815920003 coeff[6]<- 49.5302474363069010 coeff[7]<- 25.2567439407756993 coeff[8]<- -210.0989203796800098 coeff[9]<- 3.1214930972772401 coeff[10]<- -44.0793344266120002 coeff[11]<- -115.1034138079830029 coeff[12]<- -126.5449485222760018 coeff[13]<- 75.4684259919552005 coeff[14]<- -543.8694544738999639 coeff[15]<- 20689.0282354185983422 coeff[16]<- -38.9021840384242026 coeff[17]<- 194.5826285053549896 coeff[18]<- 739.7310184261190216 coeff[19]<- -114.6305937997980067 coeff[20]<- -10750.0040903322005761 coeff[21]<- -6920.0571719256404322 coeff[22]<- -843033.1723251759540290 coeff[23]<- 90.0075993241055983 coeff[24]<- -301.4631430057489752 coeff[25]<- -1713.7362953517599635 coeff[26]<- 4841.1459439160798865 coeff[27]<- 142202.7871010270027909 coeff[28]<- 228957.6227098979870789 coeff[29]<- -10475889.5673213005065918 } if (quantile==0.850) { coeff[1]<- 3.4458411887126399 coeff[2]<- -1.7019095726379900 coeff[3]<- 1.5120713691062799 coeff[4]<- 4.8561535679625196 coeff[5]<- 23.5202002365920002 coeff[6]<- 52.5774338649676025 coeff[7]<- 28.2668617536645002 coeff[8]<- -200.1098659122089884 coeff[9]<- 1.8460095760073001 coeff[10]<- -49.2418753040239991 coeff[11]<- -127.6935793398690038 coeff[12]<- -219.4519475341670045 coeff[13]<- -29.9870742668931989 coeff[14]<- -656.9039473134730542 coeff[15]<- 21775.2244569829999818 coeff[16]<- -33.6033180351836975 coeff[17]<- 221.5053719044850027 coeff[18]<- 827.1403133101730418 coeff[19]<- 1428.0880476444999658 coeff[20]<- -9008.9384751357702044 coeff[21]<- -6464.0430602652104426 coeff[22]<- -941595.0590631919912994 coeff[23]<- 82.5125038735856009 coeff[24]<- -347.8739792843559826 coeff[25]<- -1904.0484088676400916 coeff[26]<- -5101.8762730811004076 coeff[27]<- 127811.4037925720040221 coeff[28]<- 237725.1475660520081874 coeff[29]<- -7126475.5348636200651526 } if (quantile==0.875) { coeff[1]<- 3.7802066516736001 coeff[2]<- -1.7832780293115300 coeff[3]<- 1.6915318293622801 coeff[4]<- 5.3565545242128900 coeff[5]<- 25.3112626811895005 coeff[6]<- 60.1765082118289030 coeff[7]<- 34.6354405991150998 coeff[8]<- -247.3736886353399882 coeff[9]<- 1.2369642329874699 coeff[10]<- -52.9121032033572973 coeff[11]<- -143.4605717212380114 coeff[12]<- -167.6664806179369975 coeff[13]<- -61.8344983787854972 coeff[14]<- -531.4095293830119999 coeff[15]<- 25145.4615967091995117 coeff[16]<- -35.6776238360609028 coeff[17]<- 227.4794439790549916 coeff[18]<- 921.1239895660979755 coeff[19]<- 339.6757582973389731 coeff[20]<- -9741.7880530844504392 coeff[21]<- -14330.8876683241996943 coeff[22]<- -930270.6861864930251613 coeff[23]<- 89.4378656047417024 coeff[24]<- -346.5736138890870279 coeff[25]<- -2136.2131386982900949 coeff[26]<- 1234.3793892191799841 coeff[27]<- 144028.4649374680011533 coeff[28]<- 353469.3796419720165431 coeff[29]<- -20516683.7294389009475708 } if (quantile==0.900) { coeff[1]<- 4.1908267485764403 coeff[2]<- -1.8891885893129501 coeff[3]<- 2.0271896825260698 coeff[4]<- 5.9114221132126001 coeff[5]<- 27.4020150834791991 coeff[6]<- 63.9777912941137998 coeff[7]<- 39.5809946112487978 coeff[8]<- -230.8555764200339979 coeff[9]<- 1.0329409364621400 coeff[10]<- -58.8674250337712976 coeff[11]<- -154.0457370804899995 coeff[12]<- -218.5212294723910134 coeff[13]<- -286.0519178329279839 coeff[14]<- -622.4058376388760507 coeff[15]<- 25472.4328906966002251 coeff[16]<- -39.7594578852085974 coeff[17]<- 256.9128139195590279 coeff[18]<- 976.2203739940149489 coeff[19]<- 746.1852205080040221 coeff[20]<- -4407.1715312828901006 coeff[21]<- -13768.0605053265007882 coeff[22]<- -999246.7326157799689099 coeff[23]<- 103.9036644143800032 coeff[24]<- -403.2376803238349794 coeff[25]<- -2224.4087042866899537 coeff[26]<- 1572.5687089071500395 coeff[27]<- 92482.8160458912025206 coeff[28]<- 360313.1126986810122617 coeff[29]<- -17766473.4127523005008698 } if (quantile==0.925) { coeff[1]<- 4.7189769723843797 coeff[2]<- -1.8717564170961600 coeff[3]<- 2.4633931220026302 coeff[4]<- 6.7115876210770198 coeff[5]<- 31.9690295920586003 coeff[6]<- 77.8992189351474025 coeff[7]<- 44.7349900641795983 coeff[8]<- -228.8377170430520096 coeff[9]<- -1.0092921079014201 coeff[10]<- -71.5562043648445041 coeff[11]<- -175.4656627111839953 coeff[12]<- -299.2316661461030094 coeff[13]<- -325.0414500383719769 coeff[14]<- -1256.1079913804999251 coeff[15]<- 31592.8245751130998542 coeff[16]<- -39.0202239395768018 coeff[17]<- 323.6613197522179917 coeff[18]<- 1109.1946764139199786 coeff[19]<- 914.3029783202639464 coeff[20]<- -7359.3028054876504029 coeff[21]<- -590.3924195522739637 coeff[22]<- -1533363.9107433799654245 coeff[23]<- 113.7973123348010063 coeff[24]<- -522.7709252753279543 coeff[25]<- -2448.0217245922799520 coeff[26]<- 5898.8044903119898663 coeff[27]<- 122936.7172843690059381 coeff[28]<- 221741.5005789250135422 coeff[29]<- 7600714.0347049701958895 } if (quantile==0.950) { coeff[1]<- 5.4659090491614899 coeff[2]<- -1.8025078876584000 coeff[3]<- 2.8744428344448001 coeff[4]<- 8.1595674047009403 coeff[5]<- 38.6018061763804994 coeff[6]<- 95.7922667215195958 coeff[7]<- 57.3609328022184997 coeff[8]<- -284.8913205199430081 coeff[9]<- -5.6009502062466998 coeff[10]<- -81.4522395282885014 coeff[11]<- -216.9325433097039877 coeff[12]<- -335.6667815140310154 coeff[13]<- -398.4029223537269786 coeff[14]<- -1673.9524611327599359 coeff[15]<- 44930.5326648943009786 coeff[16]<- -29.5228763001153993 coeff[17]<- 356.0155045386479742 coeff[18]<- 1428.7157733186099904 coeff[19]<- 420.7255390105140123 coeff[20]<- -14379.7801947840998764 coeff[21]<- 1703.3406243169599747 coeff[22]<- -2298445.7707911501638591 coeff[23]<- 112.6570138319780057 coeff[24]<- -562.7209905878349900 coeff[25]<- -3296.3264271758898758 coeff[26]<- 10739.2051266894995933 coeff[27]<- 236391.7839820600056555 coeff[28]<- 291614.0611340589821339 coeff[29]<- 9854457.1787078194320202 } if (quantile==0.975) { coeff[1]<- 6.7504890302857596 coeff[2]<- -1.5869176986222100 coeff[3]<- 3.9667207560724398 coeff[4]<- 10.1120437490310007 coeff[5]<- 50.2081908511823016 coeff[6]<- 119.8012090480179950 coeff[7]<- 74.8041136366893937 coeff[8]<- -287.0073389146809859 coeff[9]<- -12.7230294339835996 coeff[10]<- -102.2755007771380065 coeff[11]<- -248.8487312617180010 coeff[12]<- -585.5990461713239483 coeff[13]<- -784.9379261427659458 coeff[14]<- -1566.0560614368800998 coeff[15]<- 51079.3100325659033842 coeff[16]<- -12.8766499708571001 coeff[17]<- 431.6274335914329754 coeff[18]<- 1463.6646018289900439 coeff[19]<- 3751.8675515664099294 coeff[20]<- -4250.6398348805896603 coeff[21]<- -19043.3867128636993584 coeff[22]<- -2116249.7147826300933957 coeff[23]<- 101.9055650092190035 coeff[24]<- -662.4389766982819765 coeff[25]<- -2885.4295664551600566 coeff[26]<- -11398.5018347556997469 coeff[27]<- 58946.6288898331986275 coeff[28]<- 428486.1272759070270695 coeff[29]<- 18344205.1901342011988163 } if (quantile==0.990) { coeff[1]<- 8.4494905132192102 coeff[2]<- -1.0900189037900700 coeff[3]<- 6.3305763252471197 coeff[4]<- 13.5996482043591005 coeff[5]<- 66.7056959917507015 coeff[6]<- 192.2690243703449937 coeff[7]<- 122.4631767285140000 coeff[8]<- -249.4424741480590058 coeff[9]<- -29.9878604195710992 coeff[10]<- -159.3685932057209982 coeff[11]<- -378.4956007295280074 coeff[12]<- -901.4273149419079800 coeff[13]<- -2783.5878540525400240 coeff[14]<- -3767.1057599308701356 coeff[15]<- 81642.9079526067071129 coeff[16]<- 42.9357210187022034 coeff[17]<- 695.6402403122540363 coeff[18]<- 2389.5117675315100314 coeff[19]<- 5020.3861304908195962 coeff[20]<- 39407.7207366881993948 coeff[21]<- 13699.8674774794999394 coeff[22]<- -5519478.9313614703714848 coeff[23]<- 40.9046284316439994 coeff[24]<- -1096.7700155048898978 coeff[25]<- -5236.3505118723496707 coeff[26]<- -7189.1451578593596423 coeff[27]<- -290802.1177719580009580 coeff[28]<- 300307.3014301629737020 coeff[29]<- 144502697.5196619927883148 } if (quantile==0.999) { coeff[1]<- 12.7327332405000995 coeff[2]<- 2.1968957493005199 coeff[3]<- 12.2395640571533004 coeff[4]<- 25.9901804178018985 coeff[5]<- 98.2557768200529011 coeff[6]<- 522.0616903773959621 coeff[7]<- 236.6208617289300093 coeff[8]<- -340.2242581463449937 coeff[9]<- -83.6286874359886951 coeff[10]<- -315.2715869671300197 coeff[11]<- -823.1055385652980476 coeff[12]<- -808.1067608400389872 coeff[13]<- -5424.1348310563298583 coeff[14]<- -19986.9840880793017277 coeff[15]<- 317635.3456940680043772 coeff[16]<- 215.7133649047329982 coeff[17]<- 1403.4733589121999557 coeff[18]<- 5874.5093218964102562 coeff[19]<- -25943.4785635082007502 coeff[20]<- 38235.6189887490982073 coeff[21]<- 375775.1405527779716067 coeff[22]<- -30774684.7651046998798847 coeff[23]<- -156.8830503352789947 coeff[24]<- -1984.4866389298399554 coeff[25]<- -14149.5820564309997280 coeff[26]<- 267709.4236759460181929 coeff[27]<- 81154.7314393125998322 coeff[28]<- -2649200.5529320701025426 coeff[29]<- 1080195321.0816400051116943 } } if (p == 2) { if (quantile==0.800) { coeff[1]<- 4.9178712487693801 coeff[2]<- -1.8330691903616201 coeff[3]<- 2.8500219034199499 coeff[4]<- 7.7615935358383403 coeff[5]<- 35.2988928029092008 coeff[6]<- 101.7881406029640061 coeff[7]<- 51.6751822526149027 coeff[8]<- -283.5155036544260270 coeff[9]<- -2.9805468146803999 coeff[10]<- -83.5024833914664981 coeff[11]<- -206.6967931189280137 coeff[12]<- -293.7062344120070065 coeff[13]<- -312.4713152105670133 coeff[14]<- -1872.0373345268399135 coeff[15]<- 45203.6132007621999946 coeff[16]<- -32.3523378221773967 coeff[17]<- 387.2808110619749868 coeff[18]<- 1336.8345100316701064 coeff[19]<- -647.0933990082929768 coeff[20]<- -12044.8648755242993502 coeff[21]<- 6877.6483059199499621 coeff[22]<- -2534187.4953171000815928 coeff[23]<- 102.6362904617469951 coeff[24]<- -651.0718751601129952 coeff[25]<- -3108.1104083437398913 coeff[26]<- 24235.4284554205005406 coeff[27]<- 220137.6085391720116604 coeff[28]<- 283776.0553886889829300 coeff[29]<- 11580919.5456281006336212 } if (quantile==0.825) { coeff[1]<- 5.2164739636957203 coeff[2]<- -1.8347123374486101 coeff[3]<- 3.1825123572888301 coeff[4]<- 8.3339873957902704 coeff[5]<- 37.7283743977811028 coeff[6]<- 110.4786788712240053 coeff[7]<- 56.9496908111590017 coeff[8]<- -280.1850478373880264 coeff[9]<- -4.6331561651713402 coeff[10]<- -91.8557749953372991 coeff[11]<- -222.9995281114510135 coeff[12]<- -349.1438209731840061 coeff[13]<- -494.0256147154969995 coeff[14]<- -2117.4665269998499753 coeff[15]<- 49489.0570823755988386 coeff[16]<- -27.9116543237127992 coeff[17]<- 433.3170841049540059 coeff[18]<- 1441.3241671310599941 coeff[19]<- -516.9136351770680449 coeff[20]<- -8984.6049777236694354 coeff[21]<- 8413.7042794702992978 coeff[22]<- -2897315.0673056300729513 coeff[23]<- 100.1601850987260036 coeff[24]<- -737.2193080949330124 coeff[25]<- -3332.3067447194098349 coeff[26]<- 27308.1330862335016718 coeff[27]<- 199868.2313900270091835 coeff[28]<- 299864.8578231999999844 coeff[29]<- 20700864.3378026001155376 } if (quantile==0.850) { coeff[1]<- 5.5568615332367397 coeff[2]<- -1.7652666289434000 coeff[3]<- 3.5518324504417400 coeff[4]<- 8.9277560518309205 coeff[5]<- 42.6981757542691014 coeff[6]<- 123.4907594863509956 coeff[7]<- 63.4995504019763004 coeff[8]<- -334.9988446134519791 coeff[9]<- -7.9859358119367201 coeff[10]<- -102.4756643927340036 coeff[11]<- -241.5271745635249943 coeff[12]<- -371.9274562329339915 coeff[13]<- -492.9592328288699719 coeff[14]<- -2072.4986937305798165 coeff[15]<- 53648.7993058154024766 coeff[16]<- -16.5873658166923015 coeff[17]<- 478.6497007823169838 coeff[18]<- 1551.1055572560399014 coeff[19]<- -604.4449767448810462 coeff[20]<- -10271.0774313903002621 coeff[21]<- -820.6602128403279721 coeff[22]<- -2775970.2462657499127090 coeff[23]<- 84.0602541054875019 coeff[24]<- -808.4864050427249822 coeff[25]<- -3587.6023772362500495 coeff[26]<- 28396.7367615168986958 coeff[27]<- 217022.3147568590065930 coeff[28]<- 444676.4221005589934066 coeff[29]<- -287671.0314561870181933 } if (quantile==0.875) { coeff[1]<- 5.9546159739152102 coeff[2]<- -1.7142199619784999 coeff[3]<- 4.0193273453291702 coeff[4]<- 9.8003206493142301 coeff[5]<- 45.8657518850776000 coeff[6]<- 143.0640648819230023 coeff[7]<- 70.4892327305314979 coeff[8]<- -373.7969972801340077 coeff[9]<- -10.2797820662273995 coeff[10]<- -116.0103241864880061 coeff[11]<- -271.0435708735240041 coeff[12]<- -382.0120054715550282 coeff[13]<- -486.1856670475049782 coeff[14]<- -2642.6697264228200766 coeff[15]<- 61281.0973732389029465 coeff[16]<- -10.5281435571501998 coeff[17]<- 556.0052726649339547 coeff[18]<- 1756.7068356942199898 coeff[19]<- -1475.2478702582300230 coeff[20]<- -13709.5192956542996399 coeff[21]<- 10514.4111677926994162 coeff[22]<- -3434978.6053186599165201 coeff[23]<- 76.6859165077958949 coeff[24]<- -970.9485045046250207 coeff[25]<- -4101.1270284399197408 coeff[26]<- 42198.3980696474027354 coeff[27]<- 274714.4619735180167481 coeff[28]<- 376701.5761785790091380 coeff[29]<- 16465204.0734116006642580 } if (quantile==0.900) { coeff[1]<- 6.4365845928810703 coeff[2]<- -1.5550612879452901 coeff[3]<- 4.5714451159671698 coeff[4]<- 10.5691323974754994 coeff[5]<- 52.2937078203243004 coeff[6]<- 156.9184605119810101 coeff[7]<- 80.2093598599668951 coeff[8]<- -419.2786562292490089 coeff[9]<- -15.6306224645863008 coeff[10]<- -127.8320849549120055 coeff[11]<- -289.5766197575629803 coeff[12]<- -499.6723218035160130 coeff[13]<- -579.6425124166879641 coeff[14]<- -2537.8404184541300310 coeff[15]<- 67534.2803041067963932 coeff[16]<- 9.5394719106105992 coeff[17]<- 603.9945421983350116 coeff[18]<- 1827.3370229375800591 coeff[19]<- 570.9730364938809544 coeff[20]<- -12660.4636833292006486 coeff[21]<- -1396.1689494108300096 coeff[22]<- -3469423.9864986999891698 coeff[23]<- 46.9807264348229978 coeff[24]<- -1040.8466317030699884 coeff[25]<- -4149.3897064890998081 coeff[26]<- 24809.1686166770996351 coeff[27]<- 249799.9268549369880930 coeff[28]<- 500725.3825259759905748 coeff[29]<- 11314703.9006996005773544 } if (quantile==0.925) { coeff[1]<- 7.0550598500213200 coeff[2]<- -1.5263085445411300 coeff[3]<- 5.2938981427157099 coeff[4]<- 11.6040801817360997 coeff[5]<- 54.4949931104312029 coeff[6]<- 185.6022685188779917 coeff[7]<- 92.0243405353232049 coeff[8]<- -447.7364868657310240 coeff[9]<- -16.0376339686944007 coeff[10]<- -142.8807364629460039 coeff[11]<- -324.1027644032209878 coeff[12]<- -380.9699066047990073 coeff[13]<- -643.2523487563449862 coeff[14]<- -3707.6728646805900098 coeff[15]<- 80801.2269816506013740 coeff[16]<- -6.1580912198527500 coeff[17]<- 668.2828053553040490 coeff[18]<- 2045.4666799694700785 coeff[19]<- -3586.5975119032200382 coeff[20]<- -17622.7354612023009395 coeff[21]<- 31897.7739459686999908 coeff[22]<- -5066078.5289501603692770 coeff[23]<- 88.1666769539216943 coeff[24]<- -1146.9521046850099992 coeff[25]<- -4658.6643426964901664 coeff[26]<- 61720.0860211640974740 coeff[27]<- 354415.7022285570274107 coeff[28]<- 153506.1813497359980829 coeff[29]<- 76366526.5043188035488129 } if (quantile==0.950) { coeff[1]<- 7.9111065895720598 coeff[2]<- -1.4557012283117301 coeff[3]<- 6.4396512617128598 coeff[4]<- 13.5893512561424998 coeff[5]<- 63.3146293204431032 coeff[6]<- 228.6068894828160012 coeff[7]<- 111.9325054815089970 coeff[8]<- -556.2151525502499680 coeff[9]<- -20.2175627129214988 coeff[10]<- -170.4108929953289930 coeff[11]<- -384.6405029915439968 coeff[12]<- -344.7266622313640028 coeff[13]<- -786.2279047945550019 coeff[14]<- -4210.5106158431499352 coeff[15]<- 97084.7403061968943803 coeff[16]<- -5.3359987361678902 coeff[17]<- 782.8135453269979962 coeff[18]<- 2416.0868850928000029 coeff[19]<- -5552.5021432181201817 coeff[20]<- -19286.2167818287016416 coeff[21]<- 29423.9483639930003847 coeff[22]<- -5777895.0211850898340344 coeff[23]<- 100.4013430445299946 coeff[24]<- -1334.1517486134900992 coeff[25]<- -5541.9503191525300281 coeff[26]<- 75415.1001122643065173 coeff[27]<- 400864.1310128810000606 coeff[28]<- 316227.2610995200229809 coeff[29]<- 66674690.9867174029350281 } if (quantile==0.975) { coeff[1]<- 9.3543425459392502 coeff[2]<- -0.9624518186911700 coeff[3]<- 8.3687023544499102 coeff[4]<- 16.9550808489263005 coeff[5]<- 74.9332012077949940 coeff[6]<- 310.5273317197519987 coeff[7]<- 138.2399031177519930 coeff[8]<- -567.8614473529760289 coeff[9]<- -28.6599894081586015 coeff[10]<- -215.3890443611340118 coeff[11]<- -481.7140002568380055 coeff[12]<- -543.4460600207969492 coeff[13]<- -743.5843986247469957 coeff[14]<- -7489.7461715438703322 coeff[15]<- 125934.1186382150044665 coeff[16]<- 4.4622112678811696 coeff[17]<- 1003.4699655792700241 coeff[18]<- 2966.9329619038799137 coeff[19]<- -4065.2608041855501142 coeff[20]<- -33361.4970795932022156 coeff[21]<- 120525.7309820990049047 coeff[22]<- -9154104.7384600397199392 coeff[23]<- 100.7917864506659953 coeff[24]<- -1767.4589848658699793 coeff[25]<- -6536.7758093277998341 coeff[26]<- 78920.8984494172036648 coeff[27]<- 574901.9361481709638610 coeff[28]<- -707373.9231434300309047 coeff[29]<- 236437741.1506760120391846 } if (quantile==0.990) { coeff[1]<- 11.2266376765802001 coeff[2]<- 0.2120157377692100 coeff[3]<- 11.7416387912590992 coeff[4]<- 21.3510389127132001 coeff[5]<- 88.0332720868915999 coeff[6]<- 458.7601345287289973 coeff[7]<- 194.3144532744589981 coeff[8]<- -764.4728057226800502 coeff[9]<- -46.6823089007898986 coeff[10]<- -296.2981997682369979 coeff[11]<- -649.0815086541009578 coeff[12]<- -64.4362100536673950 coeff[13]<- -937.4147767752280060 coeff[14]<- -12604.8786587231006706 coeff[15]<- 201515.7278613270027563 coeff[16]<- 32.5551966081853976 coeff[17]<- 1382.5539641466000376 coeff[18]<- 4126.2680415808099497 coeff[19]<- -21742.9674626724990958 coeff[20]<- -59704.9260606793031911 coeff[21]<- 247624.6706558259902522 coeff[22]<- -16942341.7654023990035057 coeff[23]<- 88.3757308980190004 coeff[24]<- -2494.1494908140898588 coeff[25]<- -9632.7566755610805558 coeff[26]<- 244348.5027007060125470 coeff[27]<- 1096950.3273887899704278 coeff[28]<- -1695208.3412938099354506 coeff[29]<- 480267297.4833670258522034 } if (quantile==0.999) { coeff[1]<- 15.8300012178784009 coeff[2]<- 5.4867271096418797 coeff[3]<- 16.7500391979085990 coeff[4]<- 40.1412327025612967 coeff[5]<- 146.5979164525830072 coeff[6]<- 613.9547200017060504 coeff[7]<- 307.7819263326520058 coeff[8]<- 40.8101641960486035 coeff[9]<- -123.5893764000859960 coeff[10]<- -331.6202728122499934 coeff[11]<- -910.4258884235349569 coeff[12]<- -1681.9633712691299934 coeff[13]<- -3832.0924156766300257 coeff[14]<- -8450.1506989001100010 coeff[15]<- 75486.2925130038056523 coeff[16]<- 297.5005736405910284 coeff[17]<- 965.1000853638629451 coeff[18]<- 4497.7185396501399737 coeff[19]<- 18870.0502044210006716 coeff[20]<- 63510.7605487913970137 coeff[21]<- 267816.7480845450190827 coeff[22]<- -10364142.5806058999150991 coeff[23]<- -360.4931430248209949 coeff[24]<- -1195.3374041039398890 coeff[25]<- -8845.8875228539800446 coeff[26]<- -106367.1882842540071579 coeff[27]<- -310986.1891370139783248 coeff[28]<- -4386921.4670786503702402 coeff[29]<- 926274544.3754529953002930 } } if (p == 3) { if (quantile==0.800) { coeff[1]<- 6.6221315422890896 coeff[2]<- -1.5163708969960701 coeff[3]<- 4.6956044533463599 coeff[4]<- 12.4982848301545992 coeff[5]<- 49.7889776043793972 coeff[6]<- 167.9669050736939937 coeff[7]<- 88.6283746548339053 coeff[8]<- -284.9878251119559991 coeff[9]<- -14.9851382586316006 coeff[10]<- -121.7793155186260066 coeff[11]<- -327.1942372013210161 coeff[12]<- -476.5413404023029784 coeff[13]<- -923.8225280163750313 coeff[14]<- -3591.0830967828901521 coeff[15]<- 69946.8667610395932570 coeff[16]<- -6.6258907427691103 coeff[17]<- 525.5801300533310041 coeff[18]<- 2085.3075532648199442 coeff[19]<- -366.5922692864419901 coeff[20]<- -9849.8438985470002081 coeff[21]<- 40611.8062658034978085 coeff[22]<- -4976566.6248417198657990 coeff[23]<- 84.0029215770196060 coeff[24]<- -841.1125142551890121 coeff[25]<- -4828.9518388245096503 coeff[26]<- 30656.3897403457012842 coeff[27]<- 291932.3040484929806553 coeff[28]<- 53250.3299043301012716 coeff[29]<- 91208459.2188325971364975 } if (quantile==0.825) { coeff[1]<- 6.9597249150584402 coeff[2]<- -1.4710417516168799 coeff[3]<- 5.0336370150799103 coeff[4]<- 13.4176455388075002 coeff[5]<- 54.9653645181969992 coeff[6]<- 183.0536575171099969 coeff[7]<- 95.5904417187953044 coeff[8]<- -299.9483815953410044 coeff[9]<- -17.8414263647862015 coeff[10]<- -131.9518405973570054 coeff[11]<- -352.8865376665820008 coeff[12]<- -559.6657192277340300 coeff[13]<- -1020.9491424639400066 coeff[14]<- -3930.4967971988598947 coeff[15]<- 77177.1851678178936709 coeff[16]<- 0.3909219641768100 coeff[17]<- 566.8761108328869796 coeff[18]<- 2257.1309936320499219 coeff[19]<- 188.8918733796899971 coeff[20]<- -9985.2905293180192530 coeff[21]<- 42060.9906411638003192 coeff[22]<- -5383920.5136073995381594 coeff[23]<- 78.2369257382707985 coeff[24]<- -894.0660099926980138 coeff[25]<- -5237.0232346237899037 coeff[26]<- 27985.6558599583004252 coeff[27]<- 304161.6684825890115462 coeff[28]<- 102142.7438120639999397 coeff[29]<- 93160366.5646062940359116 } if (quantile==0.850) { coeff[1]<- 7.3425910953429598 coeff[2]<- -1.3943039278164100 coeff[3]<- 5.4975003698544800 coeff[4]<- 14.3646557365358998 coeff[5]<- 58.1539428055845988 coeff[6]<- 198.5838769574909861 coeff[7]<- 108.3887705912860042 coeff[8]<- -342.7803668681970066 coeff[9]<- -21.7265184329202015 coeff[10]<- -140.4178652002989907 coeff[11]<- -381.7942661035349943 coeff[12]<- -479.8526879726049970 coeff[13]<- -1302.1855760084499707 coeff[14]<- -3963.0867177813001945 coeff[15]<- 84916.9902374458033592 coeff[16]<- 11.8488614671628998 coeff[17]<- 586.9683729342599463 coeff[18]<- 2437.5198552960700908 coeff[19]<- -2369.4085528771702229 coeff[20]<- -5093.6830940460904458 coeff[21]<- 36762.4849211363034556 coeff[22]<- -5823156.5226197196170688 coeff[23]<- 63.4657708252012966 coeff[24]<- -909.9618738957390178 coeff[25]<- -5650.5644964269004049 coeff[26]<- 48039.7056304422003450 coeff[27]<- 271308.3255403389921412 coeff[28]<- 181410.6959088270086795 coeff[29]<- 101706265.1367170065641403 } if (quantile==0.875) { coeff[1]<- 7.7866264891636101 coeff[2]<- -1.2792575439872600 coeff[3]<- 6.0538966230356097 coeff[4]<- 15.6475612850657999 coeff[5]<- 61.3017497482225977 coeff[6]<- 218.7485258784249993 coeff[7]<- 116.8022630113340057 coeff[8]<- -304.1493164217229719 coeff[9]<- -24.2264856634030004 coeff[10]<- -152.7753785348689917 coeff[11]<- -416.6880320089809970 coeff[12]<- -570.2138742148549682 coeff[13]<- -1525.4365957479099052 coeff[14]<- -4656.5062953663100416 coeff[15]<- 88236.8173439865058754 coeff[16]<- 14.2029543815531003 coeff[17]<- 639.8900260752139957 coeff[18]<- 2661.7652128856398122 coeff[19]<- -1529.6416592934899654 coeff[20]<- -2656.2103307331499309 coeff[21]<- 49496.8972507846992812 coeff[22]<- -6140623.0037937397137284 coeff[23]<- 68.6314669131759985 coeff[24]<- -988.2514400070899683 coeff[25]<- -6144.8494813706902278 coeff[26]<- 44326.5707180406025145 coeff[27]<- 273185.4260998059762642 coeff[28]<- 107903.6954631929984316 coeff[29]<- 109213359.8693110048770905 } if (quantile==0.900) { coeff[1]<- 8.3204219910806607 coeff[2]<- -1.1286403165715000 coeff[3]<- 6.8388876514006203 coeff[4]<- 17.1659831715365989 coeff[5]<- 64.3340852373244019 coeff[6]<- 245.9107251136730099 coeff[7]<- 128.4165548037599933 coeff[8]<- -276.5653171698889992 coeff[9]<- -27.0431859421547003 coeff[10]<- -169.4076689597899872 coeff[11]<- -461.3407415967760130 coeff[12]<- -589.3603902563679640 coeff[13]<- -1739.4698643180799991 coeff[14]<- -5830.5604417806398487 coeff[15]<- 99361.9696079337008996 coeff[16]<- 14.3354462161839002 coeff[17]<- 719.3361784313440239 coeff[18]<- 2979.3118812615798561 coeff[19]<- -2991.5218026850197930 coeff[20]<- -2866.1800497125100264 coeff[21]<- 80103.5144240280933445 coeff[22]<- -7661714.3303832802921534 coeff[23]<- 78.3196315137739987 coeff[24]<- -1135.0843280421900090 coeff[25]<- -6957.2616579987497971 coeff[26]<- 63727.2942658491010661 coeff[27]<- 318432.6293936740257777 coeff[28]<- -147129.4478545429883525 coeff[29]<- 169878075.7429729998111725 } if (quantile==0.925) { coeff[1]<- 8.9970212131657696 coeff[2]<- -0.7850879674097200 coeff[3]<- 7.8102586145068500 coeff[4]<- 19.0318000647564993 coeff[5]<- 70.4434675610766021 coeff[6]<- 274.7695827156119890 coeff[7]<- 147.8862649714320128 coeff[8]<- -210.2857770236680039 coeff[9]<- -35.9203805929279980 coeff[10]<- -189.0366063559239933 coeff[11]<- -514.1583555508609606 coeff[12]<- -747.6041534551650329 coeff[13]<- -2431.0749267984701874 coeff[14]<- -7056.8631841009901109 coeff[15]<- 114121.2518065570038743 coeff[16]<- 45.8823349922522965 coeff[17]<- 808.5764125124619568 coeff[18]<- 3349.9876257107998754 coeff[19]<- -2728.2110153293701842 coeff[20]<- 7832.0937608808799268 coeff[21]<- 108205.8460079969954677 coeff[22]<- -9432317.4973048605024815 coeff[23]<- 36.1990122272056993 coeff[24]<- -1288.0026674273399294 coeff[25]<- -7863.9120784835004088 coeff[26]<- 73747.8363163804024225 coeff[27]<- 270769.4261182579793967 coeff[28]<- -367093.7569911389728077 coeff[29]<- 236457004.6811519861221313 } if (quantile==0.950) { coeff[1]<- 9.9317726213135398 coeff[2]<- -0.3095397151541600 coeff[3]<- 8.9748486618305900 coeff[4]<- 21.9393542067712985 coeff[5]<- 83.8507608491378988 coeff[6]<- 330.1954081739489766 coeff[7]<- 174.5017157918939859 coeff[8]<- -242.0966181342110133 coeff[9]<- -46.8165222398042005 coeff[10]<- -219.9100933450150137 coeff[11]<- -598.5494879887800153 coeff[12]<- -878.0730872466390338 coeff[13]<- -2875.1553657950798879 coeff[14]<- -8317.2108306208592694 coeff[15]<- 140618.5299820349900983 coeff[16]<- 71.7833920631261009 coeff[17]<- 928.5718607192020499 coeff[18]<- 3897.3588113586502004 coeff[19]<- -3510.4282546925001043 coeff[20]<- 8284.3404410161692795 coeff[21]<- 127989.3565134800010128 coeff[22]<- -11607597.2412567995488644 coeff[23]<- 15.9656575065659005 coeff[24]<- -1484.5679029075599829 coeff[25]<- -9130.0252678040396859 coeff[26]<- 90288.9839210755017120 coeff[27]<- 334760.3714535139733925 coeff[28]<- -485810.7896627539885230 coeff[29]<- 305096710.7001330256462097 } if (quantile==0.975) { coeff[1]<- 11.4948076752340995 coeff[2]<- 0.6500071390569599 coeff[3]<- 11.0509841602448997 coeff[4]<- 27.0559496688665995 coeff[5]<- 111.2619621548480069 coeff[6]<- 428.8899596872739721 coeff[7]<- 229.0646335084830127 coeff[8]<- -418.9485911680069989 coeff[9]<- -70.0414600547312034 coeff[10]<- -272.0412078532140185 coeff[11]<- -749.3544360312580466 coeff[12]<- -1170.7143483122799807 coeff[13]<- -3134.6336636768601238 coeff[14]<- -9659.8994413440996141 coeff[15]<- 201237.8487618550134357 coeff[16]<- 137.5703997764240114 coeff[17]<- 1117.2876422507499683 coeff[18]<- 4875.5705578782999510 coeff[19]<- -2754.6403773724700841 coeff[20]<- -11015.5277578378008911 coeff[21]<- 125001.6599985710054170 coeff[22]<- -15157297.2050318997353315 coeff[23]<- -64.9616052428434045 coeff[24]<- -1736.0334708099799172 coeff[25]<- -11596.5033850715008157 coeff[26]<- 84439.2328219712944701 coeff[27]<- 699888.7890095609473065 coeff[28]<- -118344.1983721019933000 coeff[29]<- 335072329.3069310188293457 } if (quantile==0.990) { coeff[1]<- 13.5005496180811999 coeff[2]<- 2.0102571965674199 coeff[3]<- 14.9311239669064992 coeff[4]<- 34.5175808683930967 coeff[5]<- 137.2604470751840040 coeff[6]<- 569.4639117788369731 coeff[7]<- 293.3381096035399764 coeff[8]<- -234.9670900243150129 coeff[9]<- -94.7302704503499058 coeff[10]<- -356.3214906763220142 coeff[11]<- -953.0945948211359564 coeff[12]<- -1637.7910281474601106 coeff[13]<- -4222.9402243627700955 coeff[14]<- -14834.8745183512000949 coeff[15]<- 281654.0826297720195726 coeff[16]<- 190.8773714803409973 coeff[17]<- 1481.7924656724198940 coeff[18]<- 6224.9434748599896920 coeff[19]<- -3630.6862916798800143 coeff[20]<- -25131.3851144311993266 coeff[21]<- 267193.8640562089858577 coeff[22]<- -24251144.3904719017446041 coeff[23]<- -107.9605805402899961 coeff[24]<- -2371.5677422897801989 coeff[25]<- -15008.0391207058000873 coeff[26]<- 123595.4675037179986248 coeff[27]<- 1213140.7776256098877639 coeff[28]<- -1410096.0551406599115580 coeff[29]<- 668223606.6380430459976196 } if (quantile==0.999) { coeff[1]<- 18.3268715591755011 coeff[2]<- 9.8214303937666294 coeff[3]<- 27.1688740893320997 coeff[4]<- 58.8660724698641999 coeff[5]<- 189.1299877281290094 coeff[6]<- 907.8637204583419589 coeff[7]<- 452.8506609626459749 coeff[8]<- 3756.3991795758602166 coeff[9]<- -220.7777216181719950 coeff[10]<- -640.5372136410160238 coeff[11]<- -1558.5537834128399481 coeff[12]<- -7658.4252091000398650 coeff[13]<- -18411.4168039350988693 coeff[14]<- -42936.1834940995031502 coeff[15]<- 230095.9214869709976483 coeff[16]<- 660.4564270458920419 coeff[17]<- 3067.0975035314500019 coeff[18]<- 10247.0192040179008472 coeff[19]<- 86556.3246977149974555 coeff[20]<- 325695.7439906040090136 coeff[21]<- 1202116.9709408499766141 coeff[22]<- -40901132.0663323029875755 coeff[23]<- -686.5246853403670002 coeff[24]<- -5452.1581429857997136 coeff[25]<- -22594.5411659995988884 coeff[26]<- -372898.9067170950002037 coeff[27]<- -1869203.6503424800466746 coeff[28]<- -11990151.7095769997686148 coeff[29]<- 2336250998.9633998870849609 } } if (p == 4) { if (quantile==0.800) { coeff[1]<- 8.1929730993336296 coeff[2]<- -0.8120735361360700 coeff[3]<- 6.8094012237304300 coeff[4]<- 17.9969639161752006 coeff[5]<- 69.4792508157501061 coeff[6]<- 267.3008315503259951 coeff[7]<- 135.6327268464629867 coeff[8]<- -198.9787403524389902 coeff[9]<- -33.2144409313298965 coeff[10]<- -175.6405276901950003 coeff[11]<- -490.6367512985369785 coeff[12]<- -885.6199944159529878 coeff[13]<- -2122.3040106376902258 coeff[14]<- -6449.9961965880302159 coeff[15]<- 109190.0846437269938178 coeff[16]<- 38.4291016744626006 coeff[17]<- 717.0943924127119544 coeff[18]<- 3162.3628897896101080 coeff[19]<- 3457.5145479550201344 coeff[20]<- 3243.6144495339999594 coeff[21]<- 82022.1136614776041824 coeff[22]<- -7953121.4142840104177594 coeff[23]<- 48.1813084384516017 coeff[24]<- -1034.8630220042900874 coeff[25]<- -7203.7486370149499635 coeff[26]<- -6743.4127543977101595 coeff[27]<- 239196.2674309060093947 coeff[28]<- -173525.5503557990014087 coeff[29]<- 194014481.3652969896793365 } if (quantile==0.825) { coeff[1]<- 8.5613686864019503 coeff[2]<- -0.6884997206188600 coeff[3]<- 7.3535191722927902 coeff[4]<- 19.0421144658856001 coeff[5]<- 72.9850679447812070 coeff[6]<- 287.3347171547849825 coeff[7]<- 146.9930287072889996 coeff[8]<- -199.8394049853069987 coeff[9]<- -36.9387127458658000 coeff[10]<- -187.1119560040199872 coeff[11]<- -522.5521561587810311 coeff[12]<- -884.8440707300450185 coeff[13]<- -2406.9447692054700383 coeff[14]<- -6945.1021369762402173 coeff[15]<- 118860.8847058310057037 coeff[16]<- 47.6336496777269005 coeff[17]<- 757.2350620031810422 coeff[18]<- 3371.5048360364999098 coeff[19]<- 2026.3532184513799166 coeff[20]<- 6906.7801663536001797 coeff[21]<- 88688.3257243752013892 coeff[22]<- -8673987.6865539904683828 coeff[23]<- 39.9750880493267999 coeff[24]<- -1080.0468690879999940 coeff[25]<- -7686.1914882541495899 coeff[26]<- 5001.0239066049898611 coeff[27]<- 230120.5290865220013075 coeff[28]<- -198813.2704282240010798 coeff[29]<- 214566119.8536480069160461 } if (quantile==0.850) { coeff[1]<- 8.9799372461057398 coeff[2]<- -0.5681924044081600 coeff[3]<- 7.8461696049611600 coeff[4]<- 20.2554485723639992 coeff[5]<- 76.8555794089218978 coeff[6]<- 316.4675248906930278 coeff[7]<- 157.3278161869550047 coeff[8]<- -240.3268453543379906 coeff[9]<- -39.0604450583342029 coeff[10]<- -199.1527021401319928 coeff[11]<- -559.7555741515619729 coeff[12]<- -839.7193793070759966 coeff[13]<- -2319.1369118687498485 coeff[14]<- -7652.6250904222697500 coeff[15]<- 131590.7328101499879267 coeff[16]<- 43.9151400430670975 coeff[17]<- 797.4842209955769476 coeff[18]<- 3598.6883820793300401 coeff[19]<- 204.5930487019809902 coeff[20]<- -336.3029184098369910 coeff[21]<- 102887.8556702969945036 coeff[22]<- -9570348.5564272291958332 coeff[23]<- 54.0035181103190993 coeff[24]<- -1140.5635978108500694 coeff[25]<- -8205.5717486216708494 coeff[26]<- 19122.9517677596995782 coeff[27]<- 321341.3218014399753883 coeff[28]<- -302356.6876116620260291 coeff[29]<- 240106292.0094049870967865 } if (quantile==0.875) { coeff[1]<- 9.4609015050970999 coeff[2]<- -0.3762722372259600 coeff[3]<- 8.6288538828813302 coeff[4]<- 21.8932384258978985 coeff[5]<- 84.6365407313583944 coeff[6]<- 355.7618266445119843 coeff[7]<- 171.9351444009990075 coeff[8]<- -295.2805907110139856 coeff[9]<- -44.1423677277829967 coeff[10]<- -222.1195067572460005 coeff[11]<- -616.2395661716740278 coeff[12]<- -870.8560365813569888 coeff[13]<- -2346.7871609832800459 coeff[14]<- -8545.4262254250097612 coeff[15]<- 149401.2074950920068659 coeff[16]<- 51.4892023476155032 coeff[17]<- 896.4007933583440035 coeff[18]<- 3980.9642666764698333 coeff[19]<- -1114.1994940105200840 coeff[20]<- -7500.1729134414599685 coeff[21]<- 115142.8048171819973504 coeff[22]<- -10691750.3511693999171257 coeff[23]<- 55.8385276236003989 coeff[24]<- -1298.7341299300298942 coeff[25]<- -9150.9090619995604357 coeff[26]<- 32043.7329085819983447 coeff[27]<- 444592.4003067419980653 coeff[28]<- -318435.6776168060023338 coeff[29]<- 258410734.7733669877052307 } if (quantile==0.900) { coeff[1]<- 10.0364409213570998 coeff[2]<- 0.0022220662479900 coeff[3]<- 9.5077877611002393 coeff[4]<- 23.9443047054143996 coeff[5]<- 88.2853168156282067 coeff[6]<- 379.2146245311240023 coeff[7]<- 187.2623549711370003 coeff[8]<- -165.7662336410969885 coeff[9]<- -50.8213239076114007 coeff[10]<- -235.9838886553160080 coeff[11]<- -665.7296381464490196 coeff[12]<- -1049.1208940547298880 coeff[13]<- -2930.1054873380999197 coeff[14]<- -9457.7314141859496885 coeff[15]<- 152318.6391322679992300 coeff[16]<- 69.6684754448638017 coeff[17]<- 944.4032012375739669 coeff[18]<- 4309.0234164594203321 coeff[19]<- 1030.8148853377399519 coeff[20]<- 1927.4615895290498884 coeff[21]<- 134933.2824177659931593 coeff[22]<- -10987898.2107775006443262 coeff[23]<- 38.3227141607269033 coeff[24]<- -1360.5824251680999168 coeff[25]<- -9915.7225771606608760 coeff[26]<- 18002.6923498834985367 coeff[27]<- 398447.0611601870041341 coeff[28]<- -459867.1470027070026845 coeff[29]<- 273358936.5618169903755188 } if (quantile==0.925) { coeff[1]<- 10.7637305982078004 coeff[2]<- 0.5599840341253900 coeff[3]<- 10.6219245997386000 coeff[4]<- 26.3390199755821008 coeff[5]<- 95.5152656185652944 coeff[6]<- 415.6443130228490190 coeff[7]<- 209.1199677823190086 coeff[8]<- -59.6001617386480973 coeff[9]<- -60.5217616804738014 coeff[10]<- -257.0398399992560030 coeff[11]<- -727.1021297075069469 coeff[12]<- -1208.9974775249800132 coeff[13]<- -3592.9054602949199761 coeff[14]<- -10551.2339049946003797 coeff[15]<- 160244.8008512450032867 coeff[16]<- 94.7832561544955041 coeff[17]<- 1016.4671412471800522 coeff[18]<- 4714.4175409565395967 coeff[19]<- 2610.7746254380899700 coeff[20]<- 13298.4492927775008866 coeff[21]<- 166680.5697704390040599 coeff[22]<- -12201922.4164818990975618 coeff[23]<- 11.6458760674412005 coeff[24]<- -1470.6775225535800473 coeff[25]<- -11014.9949748035996890 coeff[26]<- 9965.6765476255804970 coeff[27]<- 364280.8391739029902965 coeff[28]<- -710443.1630431769881397 coeff[29]<- 327481329.8754540085792542 } if (quantile==0.950) { coeff[1]<- 11.7629220255548006 coeff[2]<- 1.2547736557763300 coeff[3]<- 12.0519652556113002 coeff[4]<- 30.3911857608163984 coeff[5]<- 108.2813546102970008 coeff[6]<- 487.4485887436280223 coeff[7]<- 227.0152972483309952 coeff[8]<- 93.7278990246104939 coeff[9]<- -69.5662053127345956 coeff[10]<- -293.4204086462839882 coeff[11]<- -829.7561194589060278 coeff[12]<- -1638.0139125339298971 coeff[13]<- -3565.5953775731600217 coeff[14]<- -13255.0854373993006448 coeff[15]<- 179922.6933054580003954 coeff[16]<- 107.0184640898490045 coeff[17]<- 1168.4842572665399985 coeff[18]<- 5404.0333993631302292 coeff[19]<- 8874.9684261419697577 coeff[20]<- -3407.0583366512100838 coeff[21]<- 239599.3167835889908019 coeff[22]<- -14326824.4670646991580725 coeff[23]<- 10.3541483377600994 coeff[24]<- -1726.7566798261700569 coeff[25]<- -12804.6128510172002279 coeff[26]<- -32717.2064044342987472 coeff[27]<- 672472.3558527800487354 coeff[28]<- -1365919.5439110300503671 coeff[29]<- 418728011.0834810137748718 } if (quantile==0.975) { coeff[1]<- 13.4220337711119004 coeff[2]<- 2.2597880655591598 coeff[3]<- 14.7350489818549004 coeff[4]<- 37.5116649079118005 coeff[5]<- 133.0467418980940124 coeff[6]<- 613.4971627739020050 coeff[7]<- 289.2075119270689925 coeff[8]<- 114.0142065016080011 coeff[9]<- -90.7448631208596055 coeff[10]<- -350.5970318567419781 coeff[11]<- -1027.3515387127099530 coeff[12]<- -1980.6510117474599610 coeff[13]<- -4230.0007102632698661 coeff[14]<- -15439.1360069117999956 coeff[15]<- 241345.9027065259870142 coeff[16]<- 148.9455073550890063 coeff[17]<- 1341.4469672891800656 coeff[18]<- 6653.8466773215695866 coeff[19]<- 11201.7394306767000671 coeff[20]<- -11072.5894336350993399 coeff[21]<- 256039.1342215790064074 coeff[22]<- -17394614.6384611018002033 coeff[23]<- -22.3399576614051014 coeff[24]<- -1937.3091461115600396 coeff[25]<- -15707.4197651756003324 coeff[26]<- -61765.5476192607020494 coeff[27]<- 846219.5865110900485888 coeff[28]<- -1126950.5718561098910868 coeff[29]<- 473442522.9795250296592712 } if (quantile==0.990) { coeff[1]<- 15.5317145674901003 coeff[2]<- 4.8811876167005996 coeff[3]<- 18.9487619313297984 coeff[4]<- 46.6626709881405972 coeff[5]<- 180.6823374610870019 coeff[6]<- 848.5979315612360097 coeff[7]<- 351.1745312329770172 coeff[8]<- 232.8992188372070018 coeff[9]<- -130.7860046536769971 coeff[10]<- -483.0042603488309965 coeff[11]<- -1295.4459930733100919 coeff[12]<- -2879.0264147555199088 coeff[13]<- -3426.9465860521299874 coeff[14]<- -23347.7263425599012407 coeff[15]<- 347883.4490004170220345 coeff[16]<- 252.3907097402739907 coeff[17]<- 1969.7163792034800736 coeff[18]<- 8335.5645774589902430 coeff[19]<- 15960.9896656664004695 coeff[20]<- -71760.7046971030067652 coeff[21]<- 470788.4816198340267874 coeff[22]<- -26860822.0969482995569706 coeff[23]<- -165.5173040634219888 coeff[24]<- -3082.7165135670597920 coeff[25]<- -20076.9256034389982233 coeff[26]<- -59240.2483100919998833 coeff[27]<- 1817194.6373834300320596 coeff[28]<- -2798344.3245773399248719 coeff[29]<- 803615117.6278860569000244 } if (quantile==0.999) { coeff[1]<- 20.6259047261607016 coeff[2]<- 12.5821337540845004 coeff[3]<- 29.9148638952460004 coeff[4]<- 74.0097959898280067 coeff[5]<- 270.6134317783329948 coeff[6]<- 1582.5042235126600190 coeff[7]<- 696.9519172667189650 coeff[8]<- 343.1248571051269778 coeff[9]<- -282.1576396187360274 coeff[10]<- -777.2251288024059477 coeff[11]<- -2274.5459865132597770 coeff[12]<- -3082.1027362894101316 coeff[13]<- -8556.0657162021198019 coeff[14]<- -43974.4343440945012844 coeff[15]<- 928620.7722860029898584 coeff[16]<- 749.4460408632950248 coeff[17]<- 2995.0875632223801404 coeff[18]<- 14772.0755539503006730 coeff[19]<- -24294.4955457487994863 coeff[20]<- -134949.0630039770039730 coeff[21]<- 1060748.7703480699565262 coeff[22]<- -80216481.2087040990591049 coeff[23]<- -902.9500638559740082 coeff[24]<- -4644.3543096757803141 coeff[25]<- -35893.0467099201996461 coeff[26]<- 223181.5750296520127449 coeff[27]<- 4334831.9154024999588728 coeff[28]<- -9579563.7097634300589561 coeff[29]<- 3356549022.4093999862670898 } } if (p == 5) { if (quantile==0.800) { coeff[1]<- 9.6790128632729697 coeff[2]<- 0.0525981109476300 coeff[3]<- 9.4501894730200409 coeff[4]<- 24.6621892582725017 coeff[5]<- 94.3539511635679986 coeff[6]<- 377.9920047023970255 coeff[7]<- 188.4536610693050136 coeff[8]<- -108.5899326080830036 coeff[9]<- -55.6985189171588004 coeff[10]<- -241.7344970048100095 coeff[11]<- -674.2436830617150463 coeff[12]<- -1345.9805586366198895 coeff[13]<- -2972.0011550600302144 coeff[14]<- -9505.3649610814500193 coeff[15]<- 158066.8044782899960410 coeff[16]<- 101.9143564704949938 coeff[17]<- 1012.0494216911199601 coeff[18]<- 4420.4573383117203775 coeff[19]<- 5759.7465950213900214 coeff[20]<- 3231.8035856528099430 coeff[21]<- 161232.1437297759985086 coeff[22]<- -12566624.8784187994897366 coeff[23]<- -30.9661057888596005 coeff[24]<- -1592.7511849145000724 coeff[25]<- -10554.3215942878996429 coeff[26]<- 2164.7889258739801335 coeff[27]<- 468467.4569902109797113 coeff[28]<- -745253.3639600520255044 coeff[29]<- 362044024.2048060297966003 } if (quantile==0.825) { coeff[1]<- 10.0732486445419003 coeff[2]<- 0.2855574336420900 coeff[3]<- 10.1588808504852999 coeff[4]<- 25.9860630664051016 coeff[5]<- 99.7112847215469031 coeff[6]<- 402.4416544731869863 coeff[7]<- 202.1173475409050013 coeff[8]<- -72.8295558849373066 coeff[9]<- -61.6636969931239989 coeff[10]<- -257.7195772414769976 coeff[11]<- -713.0556066989259989 coeff[12]<- -1439.0304882036400613 coeff[13]<- -3335.3685147406899887 coeff[14]<- -10191.4179690065993782 coeff[15]<- 167394.6017614029988181 coeff[16]<- 120.5089919552050048 coeff[17]<- 1078.8054889882700991 coeff[18]<- 4683.2689830166700631 coeff[19]<- 6067.2991060869399007 coeff[20]<- 7742.4814028137197965 coeff[21]<- 178555.4528796130034607 coeff[22]<- -13532391.8693646006286144 coeff[23]<- -56.0435053140481969 coeff[24]<- -1709.6834255812100309 coeff[25]<- -11244.4166427615000430 coeff[26]<- 4900.9297875980100798 coeff[27]<- 483276.0203889510012232 coeff[28]<- -877544.0838236600393429 coeff[29]<- 401024307.3962659835815430 } if (quantile==0.850) { coeff[1]<- 10.5144880787931996 coeff[2]<- 0.5780266320271200 coeff[3]<- 11.0649678971798995 coeff[4]<- 27.8351947709505012 coeff[5]<- 104.0921865199180019 coeff[6]<- 432.2567321925810120 coeff[7]<- 218.4064936569110102 coeff[8]<- 1.9282595454517999 coeff[9]<- -68.2452519583100070 coeff[10]<- -277.9322073801560009 coeff[11]<- -771.3027977516990177 coeff[12]<- -1536.3223156276299051 coeff[13]<- -3888.0787671243901968 coeff[14]<- -11509.4030741206006496 coeff[15]<- 183266.8539014119887725 coeff[16]<- 139.8920447164589973 coeff[17]<- 1177.8471718699299799 coeff[18]<- 5150.4154152322298614 coeff[19]<- 5343.7692367258296144 coeff[20]<- 13083.2033810667999205 coeff[21]<- 211955.0442447650129907 coeff[22]<- -15405187.2558475006371737 coeff[23]<- -77.0547566647621949 coeff[24]<- -1895.5051650137399974 coeff[25]<- -12559.0972298489996319 coeff[26]<- 20270.2315584151001531 coeff[27]<- 530365.1854500169865787 coeff[28]<- -1095166.4623976000584662 coeff[29]<- 467542253.6861000061035156 } if (quantile==0.875) { coeff[1]<- 11.0307198282703993 coeff[2]<- 0.9596817625196500 coeff[3]<- 11.7917823591902007 coeff[4]<- 29.6324317203477996 coeff[5]<- 113.2279891092679946 coeff[6]<- 466.3067977360159944 coeff[7]<- 236.1084976663470059 coeff[8]<- 20.7671871462214988 coeff[9]<- -76.7769391489253934 coeff[10]<- -295.7324618596960022 coeff[11]<- -819.5206161705250452 coeff[12]<- -1689.2201834655900257 coeff[13]<- -4279.2431126367000616 coeff[14]<- -12021.5329040827000426 coeff[15]<- 195345.7226646750059444 coeff[16]<- 166.2718363308929952 coeff[17]<- 1232.2569822590301101 coeff[18]<- 5432.8381175338399771 coeff[19]<- 6978.0447004036295766 coeff[20]<- 20144.4026090437000676 coeff[21]<- 221512.9201153669855557 coeff[22]<- -16193874.1128666996955872 coeff[23]<- -112.8130185675999968 coeff[24]<- -1958.1036863085801087 coeff[25]<- -13204.2621787772004609 coeff[26]<- 7290.7503318703402329 coeff[27]<- 499418.0453133470145985 coeff[28]<- -1172935.2984470699448138 coeff[29]<- 505410896.6439869999885559 } if (quantile==0.900) { coeff[1]<- 11.6421387081238006 coeff[2]<- 1.5344591979532500 coeff[3]<- 12.8428341373727992 coeff[4]<- 32.2129779570450978 coeff[5]<- 120.0741905223080011 coeff[6]<- 511.0732852905400136 coeff[7]<- 256.2800025939139914 coeff[8]<- 160.0374868559360095 coeff[9]<- -87.5664315942383951 coeff[10]<- -320.0265744714459970 coeff[11]<- -894.3840173120449890 coeff[12]<- -1933.7668655656300416 coeff[13]<- -4999.4714510302201234 coeff[14]<- -14024.7714591754993307 coeff[15]<- 214060.1420570019981824 coeff[16]<- 203.9873318413930008 coeff[17]<- 1335.8861959089299489 coeff[18]<- 5986.7136796614304330 coeff[19]<- 9349.2919971294104471 coeff[20]<- 31080.3997820067997964 coeff[21]<- 274764.2257330699940212 coeff[22]<- -18464531.2200239002704620 coeff[23]<- -168.6133484256980068 coeff[24]<- -2125.3469871053798670 coeff[25]<- -14630.7611902996995923 coeff[26]<- -5404.9180353538904455 coeff[27]<- 480821.1560285799787380 coeff[28]<- -1633428.7939631000626832 coeff[29]<- 614293223.4394570589065552 } if (quantile==0.925) { coeff[1]<- 12.4132943817803998 coeff[2]<- 2.1366718878189102 coeff[3]<- 14.4505832779437000 coeff[4]<- 35.2215394652733025 coeff[5]<- 133.8528748763299916 coeff[6]<- 571.4820716002519703 coeff[7]<- 285.5414523429819837 coeff[8]<- 284.1835882415600167 coeff[9]<- -101.3159250662939996 coeff[10]<- -359.6769896395779824 coeff[11]<- -985.7711625019039730 coeff[12]<- -2334.9270715933198517 coeff[13]<- -5799.9489190763397346 coeff[14]<- -16210.8264240456992411 coeff[15]<- 238036.8062301629979629 coeff[16]<- 246.6051240117890018 coeff[17]<- 1519.1674025206900751 coeff[18]<- 6645.0003233762599848 coeff[19]<- 14486.2513967197992315 coeff[20]<- 43514.7369385014026193 coeff[21]<- 346614.1397025110200047 coeff[22]<- -21814990.3893244005739689 coeff[23]<- -226.1893808125969940 coeff[24]<- -2466.2787592958597997 coeff[25]<- -16509.6660916731998441 coeff[26]<- -33684.8368542375028483 coeff[27]<- 497417.8442978070233949 coeff[28]<- -2324221.9290342601016164 coeff[29]<- 791787626.0169019699096680 } if (quantile==0.950) { coeff[1]<- 13.4678449413757999 coeff[2]<- 3.0318860763097000 coeff[3]<- 16.5384056456621984 coeff[4]<- 39.9549971832636004 coeff[5]<- 147.3636521844630067 coeff[6]<- 654.4466123596449734 coeff[7]<- 337.4811117803359934 coeff[8]<- 413.5957218719499906 coeff[9]<- -120.7867327043250043 coeff[10]<- -401.3332135294559748 coeff[11]<- -1133.2935938400401028 coeff[12]<- -2482.0503087077599957 coeff[13]<- -7106.3827332625196505 coeff[14]<- -17933.2288693810005498 coeff[15]<- 269051.7478745370171964 coeff[16]<- 301.9386250763799922 coeff[17]<- 1639.6831923061899943 coeff[18]<- 7690.4181559878197731 coeff[19]<- 14041.3542763101995661 coeff[20]<- 62136.4383709104004083 coeff[21]<- 388686.7436344460002147 coeff[22]<- -23996918.8478320017457008 coeff[23]<- -300.4049308099590121 coeff[24]<- -2599.4701901772800738 coeff[25]<- -19427.4298080670996569 coeff[26]<- -37310.7991164292034227 coeff[27]<- 531745.5864395960234106 coeff[28]<- -2525649.5336393201723695 coeff[29]<- 883940352.5991430282592773 } if (quantile==0.975) { coeff[1]<- 15.2057315859906002 coeff[2]<- 5.1233339386760797 coeff[3]<- 19.8183806652860000 coeff[4]<- 48.3850622105628005 coeff[5]<- 177.1370441466949899 coeff[6]<- 806.6635217800289865 coeff[7]<- 446.8679118045660061 coeff[8]<- 614.3839946904679437 coeff[9]<- -169.0979823449220021 coeff[10]<- -474.6052659644889786 coeff[11]<- -1415.2683366428500449 coeff[12]<- -3013.1303338986899689 coeff[13]<- -10554.7242700602000696 coeff[14]<- -21075.0787741880994872 coeff[15]<- 354371.5558539759949781 coeff[16]<- 476.2722539445670122 coeff[17]<- 1895.2515406549900945 coeff[18]<- 9786.6349865636202594 coeff[19]<- 16874.4915434936010570 coeff[20]<- 125617.6924502220063005 coeff[21]<- 478248.5500408689840697 coeff[22]<- -32340475.5357724018394947 coeff[23]<- -557.3954625559630358 coeff[24]<- -3042.3872088026300844 coeff[25]<- -25353.9075414582985104 coeff[26]<- -49117.5469514555006754 coeff[27]<- 369178.3535266909748316 coeff[28]<- -3098671.5343909300863743 coeff[29]<- 1291513574.1315600872039795 } if (quantile==0.990) { coeff[1]<- 17.3741569654661987 coeff[2]<- 8.4545442003072502 coeff[3]<- 26.2327507123473005 coeff[4]<- 63.6246473591046993 coeff[5]<- 207.0801339883840058 coeff[6]<- 981.7805970698650526 coeff[7]<- 594.6346729513919627 coeff[8]<- 1967.6638693600200440 coeff[9]<- -245.6448856048880032 coeff[10]<- -609.7703406622109696 coeff[11]<- -1910.7058503029800249 coeff[12]<- -4964.0334968563201983 coeff[13]<- -18913.4608846941009688 coeff[14]<- -31604.0013149299011275 coeff[15]<- 509068.0723791859927587 coeff[16]<- 795.1757592745440206 coeff[17]<- 2606.8363093062898770 coeff[18]<- 14338.1948666692005645 coeff[19]<- 30534.3930940712016309 coeff[20]<- 269859.3216963299782947 coeff[21]<- 783170.3047914699418470 coeff[22]<- -54155294.7248459979891777 coeff[23]<- -1024.6953531443700740 coeff[24]<- -4442.1286030014998687 coeff[25]<- -39370.6693541791028110 coeff[26]<- -60098.6655900281984941 coeff[27]<- 161535.0769253789912909 coeff[28]<- -4935575.8922464195638895 coeff[29]<- 2331331543.8766198158264160 } if (quantile==0.999) { coeff[1]<- 22.5206803966993014 coeff[2]<- 22.3303470740649992 coeff[3]<- 42.7800406666542017 coeff[4]<- 101.0226663231960060 coeff[5]<- 428.5887269026259787 coeff[6]<- 1664.6382101954300197 coeff[7]<- 1067.7816607207000743 coeff[8]<- 3724.8210442210797737 coeff[9]<- -575.3010240825640267 coeff[10]<- -1132.8470957343699865 coeff[11]<- -3185.8491853514701688 coeff[12]<- -12114.0604245739996259 coeff[13]<- -37188.4461185576001299 coeff[14]<- -46728.4902772303976235 coeff[15]<- 1091033.8830570799764246 coeff[16]<- 2283.4134354658599477 coeff[17]<- 5439.2671741114299948 coeff[18]<- 24353.6573658400011482 coeff[19]<- 111115.4488745029957499 coeff[20]<- 628930.4190170180518180 coeff[21]<- 1223553.7335877700243145 coeff[22]<- -110927165.0631210058927536 coeff[23]<- -3537.1481676574398989 coeff[24]<- -10720.7538563246998820 coeff[25]<- -68625.6275327045004815 coeff[26]<- -434411.7892833459773101 coeff[27]<- -649224.5160784049658105 coeff[28]<- -6337931.3223554901778698 coeff[29]<- 6004627948.2364101409912109 } } qmvsr3<- sqrt(sum(1/vary*coeff)) qmvsr3 }