[R-sig-Geo] How to calculate the integral of the sum of two kernel density functions in R?
Ferra Xu
ferra.xu at yahoo.com
Mon Apr 6 21:21:36 CEST 2015
I want to calculate the non-deterministic integral (0 to t) of the sum of two kernel density functions in R. Here is the code that I wrote:
library(ks) library(rgl)
zz <- " longitude latitude depth time magnitude 363.218744 52.38412991 3.04532258 9.241866766 0.838097648363.685488 53.85946071 0.25531946 0.578126952 0.854703175319.732091 32.23166292 4.2952681 1.06539397 0.781598317315.812817 36.98421462 3.27938697 2.295483245 0.769473951119.498255 75.1280934 0.83253364 8.783517513 0.969860223138.588107 169.629965 1.89874255 9.745653758 0.972609198139.158872 169.6452912 3.67211991 15.03850063 0.881092856139.247168 169.3478202 2.85800531 15.26106239 0.80957094565.1234 147.3603323 2.84478705 16.82280753 0.8795771565.55518 147.0377814 2.69845292 20.23640417 0.90054614467.954278 148.6017748 3.41456545 21.21715903 0.96836922766.968587 146.3484298 2.33379707 22.02860946 0.726200657359.087074 42.8644051 2.85850316 23.70757068 0.861703105357.875617 40.08052697 2.90391604 23.84198256 0.828534981358.483231 41.26875168 1.98773836 26.06830006 0.885146048358.218523 40.27344373 0.61176635 28.24887694 0.86766276356.391874 87.82219658 1.18588976 31.82632342 0.76775520656.355593 87.68729915 1.37666954 33.07983844 0.73135585956.274533 88.16157107 1.8140712 33.21245517 0.70299329758.264625 90.59810498 0.71927382 36.35112295 0.717745991296.051213 47.32622119 3.55526758 37.01360264 0.796795711296.428135 47.14235728 0.37586386 40.99409991 0.933842952296.483974 47.11833773 1.63577079 42.59987436 0.800643576149.978704 40.21568522 0.86039359 43.88742522 0.885870584152.913486 41.02065553 1.60530239 44.22730093 0.997865715148.90665 41.08012738 3.93188008 45.45667836 0.894401708346.076543 139.8808064 1.85955423 46.43473917 0.861932746346.414328 139.4533544 1.11412982 47.08968108 0.769676426345.144434 138.4076443 1.90880173 47.41656879 0.921949668347.214491 139.3465751 2.37729226 48.71147851 0.966697704332.753563 192.22991 2.28814891 50.57969649 0.957942288334.317276 189.9511419 3.86455092 50.68494991 0.879118237333.754131 189.9786093 2.97285931 51.75537529 0.896425643369.001883 49.03757175 3.850737 53.25133012 0.974504198373.451478 47.04323055 2.68174275 53.26729487 0.829954924371.270915 48.75191315 1.48038601 53.65752507 0.786928227100.980042 229.3257773 0.34910759 53.95915957 0.88956469185.373887 191.1246659 0.77164573 55.59813846 0.788626552186.209454 190.9779546 1.56667836 57.767241 0.886608637185.124518 191.2527261 0.29458722 60.01364617 0.714260258185.914337 190.2745825 2.52740599 60.61554743 0.99838296967.896372 155.4809072 0.28886827 61.31286449 0.762029245142.43641 227.5860602 4.14452355 62.29628681 0.882209187141.364062 228.3322702 4.1635609 63.89678201 0.804289098347.840723 114.6970218 0.56248091 63.95948138 0.91532112253.564593 174.113376 1.2621932 64.24838467 0.708397989253.984435 174.5656449 1.51828163 65.07176672 0.720052528253.0236 173.9265349 1.23375198 65.94064053 0.978119242231.629097 211.4394495 1.30405063 66.38331454 0.726331528232.328374 210.8879029 2.03407748 66.68961587 0.799719569232.644377 211.2277656 0.97238417 68.10333701 0.857854269232.56663 211.1678557 0.13184224 68.29747246 0.773992637112.295704 228.7487399 2.55766852 70.99561628 0.862869837113.023663 228.1650996 3.59402383 71.87466297 0.934260355112.538871 228.4575775 1.45766956 77.57275212 0.856564714113.814248 228.2794604 3.42350373 78.59894388 0.97958498183.44226 9.61564954 3.18554848 79.43332479 0.744133594183.54304 9.19009803 3.26511022 80.64811426 0.825029711183.268762 9.301064 2.44033259 85.7161253 0.784087865.369079 116.1726895 1.63053766 86.89113268 0.8794300954.970461 116.4974335 2.93526191 87.42088984 0.7109424576.345342 116.6858803 0.89072222 87.63073063 0.7191059515.492747 115.8670653 1.61844848 89.67642448 0.796864752343.385969 193.322461 2.62979605 89.94483446 0.729513559344.352781 193.5268701 4.29402892 90.4154695 0.751013388345.668421 193.0400517 3.1033618 91.93169629 0.81134914344.640169 194.248506 1.57956728 92.33756179 0.711928487167.038399 5.96957805 3.55962707 94.67162694 0.912772286166.987777 6.09536737 3.45933516 96.09079729 0.892402408168.510068 6.14462771 3.46656886 96.53093276 0.752218258167.103837 6.28745699 3.55633497 97.11208455 0.718645583183.30843 45.57593198 0.24446465 98.29165891 0.821997826183.036565 51.9529565 0.52456176 98.81054412 0.838918878183.144323 45.93514679 0.47791706 99.81095514 0.76080229338.977521 169.6576259 2.49761535 100.8103695 0.960864967338.821559 170.0718334 2.66390501 101.5614461 0.879382111337.682972 172.5078824 2.44075925 102.5406185 0.706904061339.414764 168.484822 3.07636237 102.5455371 0.969827931336.702388 194.6364837 3.67393227 103.0440893 0.835883835360.026772 184.3444998 3.62982366 103.3028211 0.717407853361.460234 184.3184775 0.96558388 103.369371 0.731880813247.557142 184.8726881 4.39064255 103.4793669 0.999527587249.630948 186.9021382 3.2051117 104.2020101 0.959898221246.647174 185.7989473 1.89101073 104.2744971 0.884561739248.079025 184.8060252 3.64218348 106.7323829 0.708083345343.213475 214.4993165 0.45176581 107.1307404 0.796756791345.720762 213.6341763 1.63235709 108.0652973 0.83913287345.016305 212.8656785 1.28675708 108.2516714 0.72970517345.462936 213.150121 2.88754323 110.0171049 0.871296443186.053395 7.62715418 2.02691573 112.650555 0.797762528182.455458 4.26944797 2.45740267 114.2678386 0.835147701182.235994 4.39627706 0.26503411 114.7318806 0.873353139409.403475 82.39618618 0.06216757 115.4464072 0.722453292409.052314 82.35559269 0.16314584 115.5665069 0.717202801215.780351 0.08912318 1.39563448 116.2344263 0.790286931214.837434 1.45883443 0.97705113 117.218643 0.856516375461.589113 9.86224616 0.9972708 117.971268 0.868564071459.202929 11.42966468 1.15177071 118.8073097 0.772466431459.088894 15.47868051 2.3559397 121.4164909 0.973816049256.903777 87.43673381 2.04200349 121.5194263 0.947720281257.382498 86.97386698 3.79079014 121.6251341 0.833363765256.697794 87.54199636 2.55432997 121.6996209 0.994618769222.945818 200.9308941 2.84077044 121.7241906 0.873480268222.819858 201.6746837 2.29641155 122.7084014 0.770327049222.130409 201.4562846 1.27840311 123.3858524 0.943177133384.260699 147.0320964 2.79131573 123.5775361 0.835382249381.993241 146.3060028 1.35450405 124.1866165 0.774990751382.080971 147.3370846 3.71228941 125.0491715 0.98663126381.648904 146.8234101 1.83454687 125.0912787 0.742795104474.324216 21.06180692 0.11079926 125.1323202 0.853769015475.098888 18.72632807 0.7689708 125.1400455 0.991577541472.708781 21.18145004 1.53044597 126.206574 0.894496186261.054388 196.4845601 2.85653651 126.4870562 0.884401301261.104845 196.6365273 2.96048717 126.8060731 0.840895112260.23671 197.1606291 2.73990119 128.0764361 0.873334209261.085155 196.6737482 2.69219319 128.5328058 0.97339396812.009559 160.8273903 0.89371542 129.4377345 0.81286608511.849503 160.841293 1.14120928 129.6794689 0.76862943212.345148 160.5244702 1.28818423 129.8214878 0.82705746111.135317 160.7668114 1.65208029 130.7028618 0.78207886631.623888 130.3067685 2.1127655 132.5014859 0.83336975327.170348 129.6318075 1.40646722 132.5051924 0.88825451431.403392 130.7047954 2.29731991 132.8479736 0.86039237629.923974 131.9784448 1.92817547 133.6366443 0.81563264890.074671 59.07610607 1.23271524 134.6497729 0.9620350387.906549 54.82957282 0.65955499 135.3859154 0.7901046289.899048 57.83154064 0.30141145 135.5092119 0.820008915276.323019 6.86787982 1.7776151 135.5215818 0.855317054275.970301 7.91419119 3.21748128 135.6636361 0.718547414275.727285 8.3243395 1.94806409 136.057032 0.769410166276.514291 7.01085361 1.43467439 137.343003 0.735545797330.040302 144.5877302 0.66277381 137.4281315 0.729634011324.893213 146.4365159 0.88234134 137.6037721 0.967082637291.11468 49.33367767 2.47072766 138.7895341 0.710016723293.43458 48.62581312 1.98062144 139.3682232 0.951710498250.764567 198.5016519 0.85846877 140.0507716 0.852180017253.539089 201.132831 1.49089404 140.9996563 0.734114932253.512945 201.0537249 2.4727616 141.0409587 0.847133697253.542791 201.2490377 1.98635162 142.6391569 0.879832516257.795509 216.9359492 0.78064425 145.1118214 0.72706484257.764285 216.4872431 2.80925094 145.1624047 0.99346721257.818943 216.6897931 2.33814072 145.9038514 0.895905632257.774863 216.6051295 2.44114347 145.9367341 0.838339638367.514438 31.4793139 0.78736947 146.1964166 0.959127433367.588968 31.4867048 0.96941256 146.2887533 0.778848722369.492049 30.48020726 2.4794555 150.0217156 0.947188883143.865075 233.3690032 1.67318663 150.4491923 0.798692592144.098544 234.3763707 0.23773927 150.5166887 0.982390159218.32888 216.7083106 2.74041746 151.0604421 0.773232421325.353164 143.7297267 2.96706415 151.763207 0.98713305326.419993 143.5201895 3.63452168 152.3832321 0.853247489325.936613 144.5316032 2.32157168 153.3589663 0.869373958325.810082 144.356522 4.39008693 153.4582455 0.99811483931.910325 124.5598197 2.33494244 153.6579228 0.93129518231.351707 125.4332729 2.30507449 154.0737073 0.79414057631.574903 124.0463483 0.75565309 154.0886993 0.71736178732.54375 122.7135364 2.18675079 154.2861579 0.71322213890.008543 124.8990934 1.97911207 154.3444858 0.94388319190.28441 126.6897782 1.01474716 154.9277926 0.82362198387.735243 125.8623578 3.00304403 155.2644112 0.815248951260.385862 96.59499166 3.96772436 156.995524 0.85693796259.739291 97.04823338 2.61008235 157.5583662 0.96764469260.311284 96.68968926 4.22429753 157.6724828 0.821776192260.229276 95.34657991 2.54473831 157.7533106 0.881316669260.212422 187.7862368 4.31051589 157.9162288 0.728441067260.231256 188.2226327 3.3502332 158.0074879 0.800794383261.545309 191.0387749 3.93897914 158.0767802 0.743452552272.998243 214.0871297 0.58707332 158.0785985 0.773464159272.69374 214.5296828 1.42084384 159.6240869 0.813691498274.126863 212.7891744 0.26609394 159.9565838 0.781095884367.90561 15.41286762 2.95145208 160.5243755 0.76467979367.864872 15.25877454 2.64007335 161.3173639 0.890119333367.649781 19.91579374 3.97005021 161.9414598 0.939914671148.118458 177.8767452 0.7438971 162.0120391 0.762554208147.655051 176.9144773 1.3703557 162.030937 0.968876858148.050091 176.9031162 1.30790609 162.3061767 0.923712841147.649022 175.9846377 0.01212553 162.6304654 0.860915742356.818492 67.21939123 1.76786772 164.2579604 0.990989558355.622664 68.75829882 3.19659511 164.3880109 0.869464951355.844738 68.88550929 4.36517304 164.7900766 0.76530697108.71847 215.0266242 1.98752526 166.393087 0.957328986109.014859 214.6488939 3.20229933 167.6177713 0.958599795109.164433 215.2627269 1.93777216 167.8951075 0.793990658108.131203 215.0862499 2.35653921 168.2758637 0.798095263196.231361 70.49924437 1.97858279 168.4511479 0.952004021197.737244 72.88240664 0.65482871 169.5036831 0.847759836339.257305 120.888616 1.34736322 169.6356306 0.715570745340.781081 117.0187847 2.51971051 169.6790878 0.933405511338.606336 121.5834442 1.80270464 170.3047686 0.828001716338.041063 120.7029464 1.73078138 170.3913998 0.783988564338.99619 35.10033383 2.97337925 170.4444717 0.800052404337.200856 33.51899806 1.09814538 170.613345 0.810081986336.985755 34.21892728 0.24128014 170.8469088 0.938437723220.803763 53.14430613 1.29837937 170.8645578 0.711607236221.630219 52.1940613 1.79796509 171.6146056 0.91800080198.635642 121.5862813 2.9432507 171.8511343 0.96180533898.382482 121.1350972 1.85599348 171.9082703 0.78574443595.692992 121.8135249 2.76335185 172.186239 0.89705477895.455554 121.1536975 3.06349446 172.3154888 0.76956598829.902259 220.4663988 0.032004 172.6212011 0.88658618228.41221 220.079011 0.64563437 172.71164 0.7225371328.608348 219.9848542 0.81174981 173.474008 0.99002676328.837549 219.7118007 0.88414209 176.6881568 0.882990987417.469016 60.71793319 3.13009015 178.4274218 0.815114554420.412299 59.95963986 3.77420788 178.5608842 0.709170932417.835488 61.34888422 3.412701 179.0698474 0.957269676266.303184 148.8628134 4.14332284 179.975606 0.881062956266.264066 149.8292293 4.17012164 180.080254 0.954352122290.584215 94.18249675 2.09946968 180.3264641 0.851384874211.043848 164.8354141 0.38617853 180.4780309 0.702373251394.665914 165.8533229 2.94896243 180.6401804 0.975721953396.948844 164.3185096 2.95721695 181.189757 0.823211439394.152446 166.1863908 2.85283338 181.4459117 0.919709724355.861861 151.482828 1.79907458 181.5735067 0.745331584355.604564 151.2328554 1.42786694 182.0786425 0.944569983355.977914 151.7258945 2.60632787 182.2734472 0.9728807655.193224 70.13457335 1.95421619 182.4681836 0.93338273855.121245 70.26190069 1.7134954 182.7419885 0.927136941466.029024 43.60374817 3.02745392 183.048289 0.821559257466.713681 43.04071215 3.34442703 183.0495735 0.910570324361.343579 38.84946077 4.09011265 183.1337707 0.869638281107.494724 224.061154 0.64225969 184.3347164 0.875420906109.403587 222.7703059 1.02129489 184.5405119 0.80347438108.536435 221.8397702 1.32737534 185.2302114 0.911269972108.966261 223.5009692 0.64308213 185.599194 0.748259104319.258848 64.01371204 4.34421863 185.7281496 0.70045418321.53673 62.05801435 4.02840039 185.9683567 0.868600256320.136879 62.7561261 2.02796518 186.1012058 0.863945237426.321536 79.57156783 1.80279196 186.1655452 0.865248329425.254692 80.84699203 0.53246863 186.351376 0.908361028424.301716 81.17660654 0.05602379 186.4132518 0.978248228424.827296 81.04033515 1.33209986 186.4734765 0.983263093119.807247 187.958236 3.33382966 186.7652667 0.970978999120.210092 189.4849366 2.84489764 187.4376306 0.881231886120.205569 189.1727403 4.18836325 187.4622579 0.977862927247.808605 146.4244449 0.83110586 188.5004803 0.735083878249.294833 144.1907226 1.22128356 188.962155 0.802240452250.204516 146.4749518 1.7944476 189.3051254 0.711019133334.654137 11.15448488 3.46662664 189.8126837 0.861510955333.659862 11.64954098 2.1332473 190.1436423 0.92116864333.427405 10.95652538 2.75561873 191.3076606 0.7543667519.482643 85.46858555 1.15438219 191.3293578 0.8278739989.378643 85.45893223 2.23185957 191.4270999 0.7294503879.333447 84.55839727 1.36554428 192.1174705 0.79096647439.424485 237.4993259 0.59464444 192.4302016 0.934036784438.638525 238.1309002 0.47642958 192.835047 0.861088125439.977322 237.950318 1.51017279 193.0183715 0.93072143438.636146 237.9862702 1.3178479 193.2070887 0.891683094330.410302 62.51368701 2.99926551 193.8201965 0.967944474329.790522 62.17494892 2.86913557 194.8657309 0.718207116329.460954 62.13150555 3.26717085 195.1562923 0.752731464474.563651 69.88329745 4.03771076 195.1657446 0.824899558285.627382 72.98472026 1.95847784 196.1019459 0.921937552286.820235 72.90395374 1.26502975 196.2494223 0.967886438236.897161 134.567653 1.15564329 196.4295919 0.707755992234.806852 133.6690276 0.210115 196.5220457 0.741268909233.53859 132.9487054 2.28750244 196.5612547 0.82722623277.005222 47.68301903 4.36155011 196.6331458 0.929370035277.336998 44.11638043 3.06712344 197.5726448 0.857331156277.800836 43.03107739 3.70528439 197.5837294 0.926344408276.793356 44.16753185 3.20462984 197.9290181 0.750939533165.177531 248.6222625 0.3374573 197.9766126 0.901818102164.463612 249.5902955 1.32364566 198.1684532 0.885595823161.499292 251.3536746 1.75217305 198.2615641 0.702053827440.799878 176.1199082 3.19808685 198.3114499 0.922067657441.798136 176.5611422 2.98843581 198.9449421 0.997520643441.027104 176.7791779 3.08648705 199.572324 0.738454407"
y1 <- read.table(text=zz, header = TRUE)
zzz <- " longitude latitude depth time magnitude277.728371 139.925845 0.75103658 26.40786514 0.943718276426.087586 168.903095 0.2957441 0.241456485 0.759137864331.549444 74.168092 0.55140397 66.51363095 0.77617643393.078983 78.588053 0.15328453 104.9418546 0.834896464492.359229 11.082291 0.08173915 111.3391451 0.87479811986.85704 42.34973 0.23081904 152.8098572 0.878111793128.038949 73.935782 0.66160123 157.8933315 0.990100773295.300125 1.935765 0.49789785 159.9134319 0.842815655294.688309 1.024583 0.44789667 165.7092358 0.886545275221.246937 151.217171 0.6337224 167.6213491 0.885163617111.240376 156.04214 0.55752237 171.2039395 0.88527352625.929383 136.975153 0.0271747 172.6574772 0.812214826415.726989 158.482975 0.37340509 184.3767148 0.9083717473.921877 60.031908 0.15224511 189.6429637 0.7914032288.811256 124.676545 0.26806101 193.7498013 0.813638308"y2 <- read.table(text=zzz, header = TRUE)
evpts1 <-do.call(expand.grid, lapply(y1,quantile, prob=c(.1,.15,.2,.25,.3,.35,.4,.45,.5,.55,.6,.65,.7,.75,.8, .85,.9,.95)))hat1 <- kde(y1, eval.points= evpts1)
evpts2 <-do.call(expand.grid, lapply(y2,quantile, prob=c(.1,.15,.2,.25,.3,.35,.4,.45,.5,.55,.6,.65,.7,.75,.8, .85,.9,.95)))hat2 <- kde(y2, eval.points= evpts2)
str(hat1)str(hat2)
integrand1 <- function(p){hat1(p,y1)+hat2(p,y2)}
Vintegrand <- Vectorize(integrand1)
integrate( Vintegrand, lower = 0, upper = t)
But it gives me error. I appreciate any help in advance.
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