QQ-Plot
Tania Nayeli Chávez Mañón
2 de octubre de 2018
Cargamos la función que grafica los qqplots de la estimación K-M comparándola con las distribuciones Gompertz, Gamma, Gamma Generalizada, Log-Logistic y F Generalizada.
comparacion<-function(ajuste){
require(flexsurv)
require(EnvStats)
set.seed(1234)
##qqplot vs Gamma
sim_gamma<-rgamma(10000,1, 1)
plot_gamma<-qqPlot(ajuste$time, sim_gamma, add.line=TRUE, line.col = "red", main="QQ-Plot Gammma")
##qqplot vs genf
sim_genf<-rgenf(10000,0, 1, 1,1)
plot_genf<-qqPlot(ajuste$time, sim_genf, add.line = TRUE, line.col = "red", main="QQ-Plot F Generalizada")
##qqplot vs log logística
sim_llogist<-rllogis(10000, 1,1 )
plot_llogist<-qqPlot(ajuste$time, sim_llogist, add.line = TRUE, line.col = "red", main="QQ-Plot Log logística")
##qqplot vs gompertz
sim_gompertz<-rgompertz(10000)
plot_gompertz<-qqPlot(ajuste$time, sim_gompertz, add.line = TRUE, line.col = "red", main = "QQ-Plot Gompertz")
##qqplot vs gamma generalizada
sim_gengamma<-rgengamma(10000, 0,1,1)
plot_gengamma<-qqPlot(ajuste$time, sim_gengamma, add.line = TRUE, line.col = "red", main="QQ-Plot Gamma Generalizada")
return(list(Gamma=plot_gamma, F_Gen=plot_genf, Gamma_Gen=plot_gengamma, Gompertz=plot_gompertz, Log_logist=plot_llogist))
}Cargamos los datos y ajustamos un modelo de supervivencia con la estimacion K-M.
require(survival)## Loading required package: survivalrequire(survminer)## Loading required package: survminer## Loading required package: ggplot2## Loading required package: ggpubr## Loading required package: magrittrdatos<-read.csv("churn.csv", header = TRUE)
datos$churn <- ifelse(datos$churn == "Yes", 1, 0)
ajuste1 <- surv_fit(Surv(accountlength, churn) ~ 1, data = datos)Aplicamos la función al ajuste K-M que hicimos
comparacion(ajuste1)## Loading required package: flexsurv## Loading required package: EnvStats##
## Attaching package: 'EnvStats'## The following objects are masked from 'package:stats':
##
## predict, predict.lm## The following object is masked from 'package:base':
##
## print.default
## $Gamma
## $Gamma$x
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
## [18] 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
## [35] 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
## [52] 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
## [69] 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
## [86] 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
## [103] 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119
## [120] 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136
## [137] 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153
## [154] 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
## [171] 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187
## [188] 188 189 190 191 192 193 194 195 196 197 199 200 201 202 204 205 208
## [205] 209 210 212 215 216 217 221 222 224 225 232 233 238 243
##
## $Gamma$y
## [1] 0.003413107 0.008025701 0.013146868 0.018724481 0.023265238
## [6] 0.028492896 0.032469414 0.037198807 0.041784074 0.045708138
## [11] 0.050063955 0.054282007 0.059327841 0.064046950 0.069611903
## [16] 0.073296791 0.077351146 0.082572395 0.088997339 0.095094956
## [21] 0.101406885 0.107334569 0.112447239 0.117891829 0.123563577
## [26] 0.130286212 0.135698248 0.142162593 0.147225535 0.154169665
## [31] 0.159352053 0.165202419 0.171112521 0.175703117 0.181205197
## [36] 0.186660826 0.192959979 0.197510398 0.203721313 0.210688617
## [41] 0.216724675 0.221325825 0.226823798 0.231924498 0.237063546
## [46] 0.244044832 0.250278945 0.256340702 0.262685260 0.268029710
## [51] 0.273918738 0.280949158 0.288379119 0.294964050 0.299944779
## [56] 0.307052204 0.313751192 0.319541993 0.326025492 0.332704005
## [61] 0.339689013 0.344991348 0.350955574 0.357312106 0.364354827
## [66] 0.370097810 0.376554620 0.383232220 0.389054250 0.394954089
## [71] 0.401897523 0.409517319 0.415973463 0.422906276 0.429389618
## [76] 0.436263846 0.443536128 0.450787217 0.457187953 0.464231147
## [81] 0.471133613 0.477511710 0.485641093 0.492018771 0.500167797
## [86] 0.506902723 0.515720303 0.523577215 0.530554915 0.536538480
## [91] 0.543098440 0.553046209 0.559355688 0.566577019 0.575232172
## [96] 0.583865089 0.591801517 0.599736701 0.607181315 0.615632303
## [101] 0.624814839 0.634218631 0.641337169 0.648795944 0.655088420
## [106] 0.663851012 0.674004146 0.683234159 0.690803425 0.699884057
## [111] 0.707450413 0.716750639 0.729125779 0.736935468 0.747399829
## [116] 0.758076197 0.768701440 0.779115587 0.790486266 0.803419285
## [121] 0.813986181 0.823231922 0.832726723 0.842941431 0.850457453
## [126] 0.860346941 0.869780300 0.878294082 0.887448873 0.897471263
## [131] 0.909279429 0.920568763 0.931195088 0.942656116 0.953076247
## [136] 0.964757187 0.978043892 0.991784506 1.004498279 1.016541121
## [141] 1.028793858 1.044090671 1.052861824 1.064113049 1.075926774
## [146] 1.089561852 1.102558172 1.116773696 1.132008941 1.146075727
## [151] 1.155955396 1.169574995 1.185898115 1.203835110 1.215545965
## [156] 1.227098130 1.239706519 1.258310307 1.276130697 1.294645717
## [161] 1.311597338 1.330866476 1.352863111 1.371848196 1.391302506
## [166] 1.410672959 1.435663143 1.453363372 1.482426925 1.499407577
## [171] 1.517873704 1.536423377 1.562559753 1.579547833 1.600782520
## [176] 1.626156784 1.647162265 1.668775865 1.689261385 1.716701193
## [181] 1.742088656 1.764434019 1.799221559 1.825391071 1.847046021
## [186] 1.882514647 1.920614494 1.958032162 1.994697898 2.032041422
## [191] 2.065459304 2.100526085 2.140046898 2.174983223 2.231226393
## [196] 2.269926889 2.310737230 2.352427538 2.413413309 2.470335183
## [201] 2.516571195 2.578498067 2.646550544 2.721605794 2.795760749
## [206] 2.855909246 2.939527188 3.024206792 3.135693340 3.235172036
## [211] 3.358874433 3.485824821 3.643782272 3.813875978 4.094250422
## [216] 4.420550686 5.193332250 6.210318050
##
##
## $F_Gen
## $F_Gen$x
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
## [18] 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
## [35] 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
## [52] 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
## [69] 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
## [86] 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
## [103] 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119
## [120] 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136
## [137] 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153
## [154] 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
## [171] 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187
## [188] 188 189 190 191 192 193 194 195 196 197 199 200 201 202 204 205 208
## [205] 209 210 212 215 216 217 221 222 224 225 232 233 238 243
##
## $F_Gen$y
## [1] 0.000581338 0.002002060 0.003664022 0.005440476 0.007444728
## [6] 0.010375010 0.012861556 0.015801761 0.018934259 0.022273747
## [11] 0.025086448 0.028368495 0.032061395 0.035532125 0.038589415
## [16] 0.042104798 0.045508734 0.049596863 0.053528274 0.056833428
## [21] 0.061807682 0.065962958 0.069068750 0.074453082 0.079793623
## [26] 0.084378090 0.088808659 0.092069212 0.097188258 0.102298810
## [31] 0.107381424 0.111766613 0.116708195 0.122101324 0.127342016
## [36] 0.132416442 0.137213445 0.142702615 0.148314898 0.151912579
## [41] 0.157064125 0.162691009 0.168117360 0.173461105 0.178386331
## [46] 0.184426253 0.188707984 0.193797563 0.198910318 0.204775457
## [51] 0.210352574 0.215604311 0.220521167 0.226950470 0.234176715
## [56] 0.240990834 0.247464781 0.252500774 0.259048801 0.265222049
## [61] 0.272004591 0.279942702 0.287535834 0.294331106 0.301501819
## [66] 0.308464529 0.315061824 0.320911687 0.325785602 0.331613620
## [71] 0.336480327 0.341513612 0.348696101 0.353966654 0.359675001
## [76] 0.366379540 0.373441803 0.379157522 0.386920707 0.395781698
## [81] 0.404079529 0.412173903 0.418931332 0.425371814 0.433411329
## [86] 0.440677570 0.449177369 0.455992907 0.462723536 0.470870184
## [91] 0.478034251 0.485194684 0.493570211 0.500963072 0.509349147
## [96] 0.517833442 0.526181794 0.536832176 0.549851586 0.558259745
## [101] 0.566213102 0.576383718 0.585576872 0.598120941 0.607062690
## [106] 0.614923363 0.622099488 0.630444661 0.640445042 0.651018107
## [111] 0.661297532 0.670499492 0.679458830 0.689071171 0.702622749
## [116] 0.712392900 0.723276868 0.734022535 0.745205117 0.758803331
## [121] 0.768749943 0.779709084 0.791202525 0.802096283 0.811473541
## [126] 0.823573496 0.833623367 0.847839445 0.860411558 0.873490203
## [131] 0.885702083 0.898243680 0.910963823 0.921834224 0.931806969
## [136] 0.947036064 0.958255936 0.971763920 0.984889265 0.997459077
## [141] 1.014757929 1.030518298 1.044736499 1.056863359 1.072400407
## [146] 1.086742700 1.099745108 1.116304189 1.131005683 1.152707548
## [151] 1.168141344 1.184990019 1.199473818 1.217037435 1.235829070
## [156] 1.254199552 1.270335310 1.289379342 1.309579498 1.332934272
## [161] 1.351190711 1.370910042 1.390357069 1.414298126 1.435169889
## [166] 1.460982298 1.486254693 1.511506057 1.536475634 1.558303733
## [171] 1.578747160 1.605152636 1.630234950 1.656679887 1.689432296
## [176] 1.718386406 1.747456095 1.776631242 1.803635269 1.834506661
## [181] 1.864459285 1.889695285 1.920617573 1.955886587 1.990755832
## [186] 2.022707700 2.069782755 2.112008829 2.152823720 2.196058255
## [191] 2.257997798 2.309944153 2.359308075 2.403840987 2.451953644
## [196] 2.523691354 2.587527324 2.651455912 2.727763717 2.830180857
## [201] 2.903677895 3.006420194 3.110638148 3.269035098 3.398433529
## [206] 3.531212793 3.684986582 3.901292201 4.096153690 4.272693511
## [211] 4.513336718 4.828179542 5.175456035 5.462009413 5.976506397
## [216] 6.812227818 8.141261933 12.120287087
##
##
## $Gamma_Gen
## $Gamma_Gen$x
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
## [18] 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
## [35] 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
## [52] 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
## [69] 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
## [86] 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
## [103] 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119
## [120] 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136
## [137] 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153
## [154] 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
## [171] 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187
## [188] 188 189 190 191 192 193 194 195 196 197 199 200 201 202 204 205 208
## [205] 209 210 212 215 216 217 221 222 224 225 232 233 238 243
##
## $Gamma_Gen$y
## [1] 0.002796942 0.009879308 0.015425857 0.019410088 0.023515137
## [6] 0.028134840 0.032079451 0.035186393 0.039881119 0.044093788
## [11] 0.048673283 0.053738618 0.058316237 0.063299967 0.069006740
## [16] 0.074332845 0.078573432 0.084863230 0.090676537 0.095554316
## [21] 0.100811770 0.106419379 0.111139102 0.116875037 0.121840722
## [26] 0.126795076 0.133212669 0.137911590 0.144458862 0.151374877
## [31] 0.158013628 0.163556996 0.167869409 0.172780850 0.177960282
## [36] 0.183326215 0.188984883 0.193975912 0.199697248 0.205561813
## [41] 0.211581984 0.216956813 0.222629583 0.227582894 0.234010627
## [46] 0.240704830 0.245635429 0.252080084 0.256844240 0.262509344
## [51] 0.267814687 0.273537534 0.280057856 0.284928358 0.291880428
## [56] 0.297239042 0.303938653 0.310844159 0.317608902 0.324807821
## [61] 0.331372399 0.336585455 0.343576320 0.351543732 0.358825655
## [66] 0.364212150 0.370643901 0.376722716 0.382198543 0.387689550
## [71] 0.392563208 0.399885794 0.406282186 0.412402318 0.419890736
## [76] 0.426034207 0.432863976 0.439801480 0.447419601 0.453846020
## [81] 0.462911693 0.471602127 0.478392445 0.485104159 0.489937341
## [86] 0.498270659 0.505450250 0.513710938 0.522670806 0.530488849
## [91] 0.538894738 0.547122206 0.553514241 0.558612578 0.567164813
## [96] 0.575648581 0.583295838 0.593574019 0.602280232 0.611929004
## [101] 0.620473401 0.629204358 0.637676802 0.647538987 0.657773801
## [106] 0.666909018 0.675588925 0.682824230 0.689737931 0.698915725
## [111] 0.708339279 0.718337518 0.727472546 0.737620626 0.744422043
## [116] 0.755857475 0.764508363 0.773677595 0.783630822 0.792992902
## [121] 0.805143101 0.818235317 0.826328628 0.837724367 0.848691797
## [126] 0.858164762 0.868017760 0.878955045 0.890109989 0.899509330
## [131] 0.911568260 0.920758918 0.933176626 0.943265381 0.955027282
## [136] 0.966802310 0.976021780 0.986079182 0.998206786 1.011292879
## [141] 1.024968651 1.040204981 1.053708285 1.068421614 1.081406995
## [146] 1.095957633 1.109557787 1.123100983 1.135351974 1.150778031
## [151] 1.164715977 1.177783803 1.190902699 1.205949317 1.220691231
## [156] 1.234556296 1.254544779 1.272342697 1.288007985 1.302339744
## [161] 1.320283815 1.340868560 1.353958908 1.370899465 1.392071265
## [166] 1.405029898 1.428141912 1.449562809 1.469389171 1.492601491
## [171] 1.513710591 1.532568992 1.555922412 1.579180676 1.604233685
## [176] 1.625130533 1.647951261 1.675819757 1.696784443 1.715235314
## [181] 1.744144485 1.769453822 1.799115226 1.830016938 1.855908175
## [186] 1.886929548 1.919110289 1.958102020 1.987525421 2.030837019
## [191] 2.071627158 2.111015783 2.151733306 2.194625136 2.236433855
## [196] 2.294581898 2.343637357 2.385634162 2.468496152 2.526898810
## [201] 2.579420369 2.623856157 2.680857008 2.750915024 2.813859852
## [206] 2.883662403 2.975012426 3.057098833 3.149981688 3.275043637
## [211] 3.385491094 3.495408015 3.638099463 3.831909907 4.034486276
## [216] 4.413915491 4.888568036 6.332587034
##
##
## $Gompertz
## $Gompertz$x
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
## [18] 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
## [35] 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
## [52] 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
## [69] 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
## [86] 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
## [103] 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119
## [120] 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136
## [137] 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153
## [154] 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
## [171] 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187
## [188] 188 189 190 191 192 193 194 195 196 197 199 200 201 202 204 205 208
## [205] 209 210 212 215 216 217 221 222 224 225 232 233 238 243
##
## $Gompertz$y
## [1] 0.004257861 0.009105692 0.014125149 0.018586996 0.022914761
## [6] 0.026782685 0.031746388 0.035200772 0.039574155 0.044240905
## [11] 0.049144072 0.053778738 0.059074365 0.062143013 0.065920980
## [16] 0.069925872 0.074456598 0.078137363 0.083140110 0.087401314
## [21] 0.093750034 0.099781234 0.104443577 0.108956637 0.114002975
## [26] 0.117725949 0.122745723 0.127041148 0.131527647 0.135828153
## [31] 0.140656409 0.145133825 0.150500869 0.155043015 0.159382560
## [36] 0.163378452 0.168794052 0.173491151 0.178131090 0.181372128
## [41] 0.185664777 0.190441366 0.195375352 0.199901956 0.204756599
## [46] 0.209415100 0.214449408 0.219522024 0.223894581 0.229678608
## [51] 0.233546981 0.237909701 0.242025704 0.248122294 0.255129612
## [56] 0.259410758 0.262627916 0.267698999 0.272160085 0.276723195
## [61] 0.281161277 0.286471244 0.291551539 0.296930143 0.300991613
## [66] 0.306064655 0.310458820 0.315087644 0.320439907 0.325485657
## [71] 0.329977574 0.335049388 0.340753602 0.345687337 0.349909603
## [76] 0.353812821 0.358831469 0.363541350 0.370778504 0.375934725
## [81] 0.380557671 0.385903627 0.391081131 0.395108349 0.399819567
## [86] 0.405380152 0.411847526 0.417243664 0.421275445 0.426108731
## [91] 0.430522382 0.434316296 0.438242586 0.443113701 0.447199543
## [96] 0.452216286 0.457267700 0.462289248 0.467622287 0.473011786
## [101] 0.477733333 0.482006478 0.487973316 0.492213508 0.496594779
## [106] 0.502948604 0.507572974 0.512442045 0.517608618 0.523495852
## [111] 0.527864422 0.532656435 0.537784034 0.542791170 0.549038581
## [116] 0.555292150 0.560707602 0.565907650 0.571735139 0.579864525
## [121] 0.584631026 0.590128511 0.595760908 0.601658686 0.607391669
## [126] 0.612755109 0.618038148 0.624123707 0.630386854 0.637281971
## [131] 0.641412049 0.649158293 0.655095835 0.660807990 0.665630248
## [136] 0.671084334 0.677109182 0.683956454 0.689457005 0.698466357
## [141] 0.705530366 0.711384446 0.718601429 0.724652781 0.730402564
## [146] 0.735620537 0.742722009 0.747953116 0.754564662 0.761792094
## [151] 0.770413848 0.777097416 0.783510825 0.789403265 0.796228592
## [156] 0.804027152 0.812334076 0.821016400 0.829551438 0.836425587
## [161] 0.843153167 0.850029553 0.858259828 0.867143985 0.874337665
## [166] 0.882894903 0.892304631 0.900559765 0.907301281 0.913541315
## [171] 0.922136821 0.932333283 0.938681987 0.948874200 0.958680488
## [176] 0.967573972 0.975068192 0.984961838 0.995026482 1.003107934
## [181] 1.013289529 1.022785816 1.032317894 1.042448838 1.052094703
## [186] 1.063170192 1.073442260 1.084513210 1.095699726 1.104735462
## [191] 1.117023306 1.130097997 1.141531597 1.151846734 1.164176217
## [196] 1.181728588 1.193497116 1.207802459 1.226610003 1.245692456
## [201] 1.260322302 1.276461643 1.294462227 1.310382639 1.329804497
## [206] 1.349536902 1.372976438 1.398644042 1.423543172 1.457026433
## [211] 1.490971023 1.518165853 1.552466767 1.588938973 1.628567042
## [216] 1.714409949 1.804182543 1.971501837
##
##
## $Log_logist
## $Log_logist$x
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
## [18] 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
## [35] 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
## [52] 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
## [69] 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
## [86] 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
## [103] 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119
## [120] 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136
## [137] 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153
## [154] 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
## [171] 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187
## [188] 188 189 190 191 192 193 194 195 196 197 199 200 201 202 204 205 208
## [205] 209 210 212 215 216 217 221 222 224 225 232 233 238 243
##
## $Log_logist$y
## [1] 2.656276e-03 7.059501e-03 1.267009e-02 1.761968e-02 2.289124e-02
## [6] 2.898697e-02 3.344914e-02 3.719672e-02 4.244539e-02 4.711130e-02
## [11] 5.220805e-02 5.782133e-02 6.310062e-02 6.732294e-02 7.092106e-02
## [16] 7.537158e-02 8.005957e-02 8.515560e-02 8.962666e-02 9.622967e-02
## [21] 1.013000e-01 1.077638e-01 1.149338e-01 1.209362e-01 1.259303e-01
## [26] 1.312963e-01 1.367173e-01 1.417191e-01 1.479510e-01 1.537203e-01
## [31] 1.592722e-01 1.657834e-01 1.713476e-01 1.782297e-01 1.868344e-01
## [36] 1.934631e-01 1.991478e-01 2.046411e-01 2.099133e-01 2.163479e-01
## [41] 2.229204e-01 2.291072e-01 2.350903e-01 2.400900e-01 2.469021e-01
## [46] 2.532309e-01 2.588902e-01 2.679358e-01 2.742337e-01 2.825711e-01
## [51] 2.906710e-01 2.992973e-01 3.067486e-01 3.154871e-01 3.241078e-01
## [56] 3.313008e-01 3.394698e-01 3.456388e-01 3.556115e-01 3.647875e-01
## [61] 3.735420e-01 3.832353e-01 3.899006e-01 3.979780e-01 4.044194e-01
## [66] 4.140418e-01 4.235245e-01 4.329193e-01 4.415869e-01 4.523102e-01
## [71] 4.615576e-01 4.753832e-01 4.825428e-01 4.919849e-01 5.027541e-01
## [76] 5.124954e-01 5.225027e-01 5.327577e-01 5.452288e-01 5.564271e-01
## [81] 5.664759e-01 5.771751e-01 5.870316e-01 6.014637e-01 6.151009e-01
## [86] 6.254860e-01 6.384742e-01 6.538857e-01 6.681830e-01 6.793954e-01
## [91] 6.897245e-01 7.029528e-01 7.157032e-01 7.317791e-01 7.456764e-01
## [96] 7.612014e-01 7.801510e-01 7.992005e-01 8.105711e-01 8.261602e-01
## [101] 8.404410e-01 8.579087e-01 8.699692e-01 8.899314e-01 9.082633e-01
## [106] 9.247654e-01 9.398332e-01 9.567479e-01 9.743816e-01 9.951772e-01
## [111] 1.013309e+00 1.030612e+00 1.049413e+00 1.066534e+00 1.086192e+00
## [116] 1.108472e+00 1.128543e+00 1.151804e+00 1.176515e+00 1.203209e+00
## [121] 1.228573e+00 1.252070e+00 1.271948e+00 1.289166e+00 1.315145e+00
## [126] 1.339249e+00 1.360743e+00 1.387806e+00 1.412464e+00 1.440216e+00
## [131] 1.466889e+00 1.494591e+00 1.519852e+00 1.551202e+00 1.580341e+00
## [136] 1.615356e+00 1.651793e+00 1.691542e+00 1.723947e+00 1.757259e+00
## [141] 1.800472e+00 1.836296e+00 1.873290e+00 1.903849e+00 1.940220e+00
## [146] 1.980529e+00 2.012753e+00 2.051411e+00 2.096106e+00 2.152126e+00
## [151] 2.189298e+00 2.226420e+00 2.268567e+00 2.315450e+00 2.375404e+00
## [156] 2.424100e+00 2.479526e+00 2.541597e+00 2.595881e+00 2.672832e+00
## [161] 2.738198e+00 2.799827e+00 2.867074e+00 2.951975e+00 3.026691e+00
## [166] 3.082084e+00 3.143768e+00 3.206716e+00 3.295251e+00 3.377596e+00
## [171] 3.462147e+00 3.532828e+00 3.646162e+00 3.727542e+00 3.839985e+00
## [176] 3.937815e+00 4.050184e+00 4.204521e+00 4.333698e+00 4.453458e+00
## [181] 4.586924e+00 4.720100e+00 4.908333e+00 5.067832e+00 5.226730e+00
## [186] 5.430317e+00 5.609764e+00 5.792779e+00 6.082462e+00 6.332084e+00
## [191] 6.593984e+00 6.867201e+00 7.217805e+00 7.500806e+00 7.837602e+00
## [196] 8.231610e+00 8.659521e+00 9.200283e+00 9.751243e+00 1.034773e+01
## [201] 1.104110e+01 1.186682e+01 1.285454e+01 1.407593e+01 1.508074e+01
## [206] 1.626619e+01 1.785412e+01 1.979952e+01 2.234385e+01 2.468325e+01
## [211] 2.878952e+01 3.432522e+01 4.017232e+01 4.826416e+01 6.462523e+01
## [216] 9.056794e+01 1.426175e+02 6.072131e+02Buscamos en el qqplot una relación lineal. Preferentemente que fuera la identidad, sin embargo esto sólo para cuando los datos están en la misma escala y los parámetros de la distribución con la que comparamos son los reales, por lo que sólo nos fijaremos qué tanto se asemeja el qqplot a una recta.
En este ejemplo claramente el modelo paramétrico que mejor ajusta es el de la distribución Gompertz. Recordando que los qq-plots son sensibles en las colas, podríamos asumir que sigue esta distribución o quizás también la distribución log-logística, pues en la mayoría de los puntos se comporta linealmente a excepción de la cola que varía mucho.