Modelo Log-Normal - Latitud
Grupo 1
0.- Carga de librerías
library(openxlsx)1.- Carga de datos
datos <- read.xlsx("DerramesEEUU.xlsx", sheet = 1)
datos$LatitudAccidente <- as.numeric(datos$LatitudAccidente)
variable_original <- na.omit(datos$LatitudAccidente)2.- Selección de la variable aleatoria
variable_original## [1] 38.63064 39.91934 32.61100 42.45589 30.19071 29.70647 42.20753 32.53091
## [9] 32.52582 30.25989 28.85030 30.16801 29.63023 47.37210 29.62478 29.71831
## [17] 37.08414 29.84703 30.23955 41.62340 39.38235 42.02244 30.01240 30.12428
## [25] 30.11356 34.94418 28.05529 32.71141 31.87685 42.56794 41.57770 41.51718
## [33] 30.14790 31.15910 29.76713 35.93019 29.25640 30.22981 33.54657 39.50693
## [41] 29.84904 29.84853 38.59970 29.85415 38.50182 32.60750 38.81386 44.77328
## [49] 30.43420 30.38923 38.72582 41.94352 29.98722 31.13244 46.41379 41.60865
## [57] 38.34136 39.19306 30.32637 42.46833 31.50653 35.53424 34.05821 35.86572
## [65] 31.55556 29.34900 27.55292 32.56184 29.54619 29.92084 30.78251 35.85326
## [73] 40.36468 36.22193 38.36098 43.28654 29.78152 32.77757 34.27734 32.54090
## [81] 32.54060 29.23886 40.61428 29.85325 29.37530 30.11472 27.72222 27.95952
## [89] 40.55080 39.08049 38.93903 28.80417 34.76231 29.72703 30.03403 29.70989
## [97] 33.81170 38.98742 34.83433 33.75640 43.47546 41.64510 41.41450 30.55720
## [105] 35.02529 33.58266 29.86809 30.16485 29.85635 36.89254 41.93805 36.38298
## [113] 36.41306 40.62252 37.94441 41.63902 37.79518 37.96330 38.28588 33.78114
## [121] 48.81835 39.61412 29.87886 29.43880 42.07471 35.96788 34.05223 41.60721
## [129] 39.71134 33.53866 33.41670 30.01612 39.27126 31.78341 41.04755 29.75901
## [137] 37.78947 40.59631 34.13313 46.86168 40.09176 47.67386 43.42656 29.95115
## [145] 34.16078 27.97348 31.82144 34.97289 30.79696 32.25117 41.30700 34.94212
## [153] 40.73625 29.78700 31.36222 33.86429 41.14888 30.35452 30.35533 35.94085
## [161] 39.46308 33.17535 34.18972 46.71783 46.24913 30.08890 42.73839 30.08890
## [169] 29.27467 32.77933 35.04474 34.00551 43.72835 45.05919 34.32044 40.31277
## [177] 30.14570 29.37860 33.83799 32.65500 33.33278 29.06023 29.34855 41.49806
## [185] 35.46720 40.13682 30.16414 32.23587 38.08131 40.89480 31.47285 32.47042
## [193] 40.62460 37.81700 35.35994 33.69380 38.98759 30.79796 30.80147 40.40966
## [201] 37.79580 44.02195 48.99555 44.00022 30.47904 30.06611 40.76664 32.70298
## [209] 30.06611 31.53179 41.18497 38.91689 42.51862 33.81583 30.03188 40.58548
## [217] 38.85160 44.81592 42.13131 47.37855 41.68411 42.06139 29.71895 35.95885
## [225] 48.96572 30.06066 33.20242 41.68411 32.86057 42.15140 41.17840 42.95776
## [233] 42.95950 29.34578 41.21235 41.56550 41.56563 34.52110 36.17115 38.67070
## [241] 35.23317 30.45372 35.55435 31.58929 36.77451 38.37239 38.36930 46.85126
## [249] 41.41093 41.77310 35.87218 35.63760 33.17972 36.33746 36.20138 35.55441
## [257] 27.91036 38.78052 43.94028 38.56947 39.36359 42.85480 44.75965 31.49797
## [265] 32.86279 32.87425 32.81300 32.84745 29.70862 37.04441 44.37956 37.80326
## [273] 29.95687 42.22275 42.90150 29.40090 27.68402 40.55097 30.05600 29.37360
## [281] 29.98070 35.94607 45.72241 29.71831 34.63366 32.06456 36.13261 35.94109
## [289] 35.94595 35.56572 29.79428 36.12128 29.79449 29.82533 29.79201 37.78977
## [297] 37.81841 37.80218 35.46720 35.11917 29.99480 40.40100 36.13158 35.94607
## [305] 41.36417 43.29183 31.42717 38.88188 39.13805 29.47450 30.43779 36.13252
## [313] 46.87722 39.75888 39.13844 39.13776 44.26055 39.00810 39.08605 41.68148
## [321] 45.89417 41.68429 29.99763 29.99766 43.54571 41.93805 39.12851 39.13622
## [329] 44.87601 29.89640 29.74777 29.96887 28.48092 43.29194 33.30708 34.24437
## [337] 38.86661 31.43275 33.79555 34.24507 32.65200 29.34750 35.94670 29.14520
## [345] 31.76885 34.24278 29.19462 33.57389 32.48130 33.97000 31.43427 28.93510
## [353] 30.00899 29.89160 29.72680 30.01190 33.79630 29.71820 35.32750 30.15710
## [361] 29.10490 30.11504 30.17240 34.24278 34.36098 32.00480 33.86357 29.19345
## [369] 35.95219 33.97004 29.34546 33.86345 33.68092 28.93564 33.79555 29.14515
## [377] 28.95095 29.95222 29.14549 41.55690 41.55690 30.04946 37.05250 38.04121
## [385] 33.85571 38.84853 42.27847 40.58823 40.58888 40.58823 35.59243 38.38052
## [393] 42.38229 33.86379 32.87476 39.82292 32.48325 32.87476 40.70825 39.03543
## [401] 40.33750 32.87718 32.87476 32.94910 32.53275 32.49783 31.77650 32.53270
## [409] 32.48190 32.46539 32.75732 29.75079 29.41965 29.95503 32.11386 32.77698
## [417] 32.15320 32.53242 31.77654 32.53270 29.25381 37.64416 29.76750 29.91150
## [425] 30.01667 29.91168 37.07036 29.91149 29.95199 31.15279 39.48263 33.25417
## [433] 32.47850 37.93455 39.89550 39.89783 30.66880 31.77393 32.63239 32.07290
## [441] 32.48130 32.07290 32.26812 30.14080 47.68857 48.72036 48.24063 30.28649
## [449] 30.85680 40.52243 30.26631 40.64794 40.58548 32.77594 32.77597 36.90060
## [457] 32.53750 31.42962 30.08749 32.00836 32.00836 32.53048 32.01705 32.01426
## [465] 35.93820 32.08823 31.79049 32.53200 31.13284 31.79133 31.13193 32.01798
## [473] 31.96060 31.89631 40.62199 32.08087 31.79180 31.13575 32.08014 31.01183
## [481] 32.01435 37.05253 34.89185 32.51846 30.28670 32.06704 33.22053 32.26812
## [489] 31.12252 30.14105 39.86222 32.11470 32.06704 31.16110 33.86329 32.34464
## [497] 34.37332 32.48300 31.16110 35.48550 36.41936 32.47831 33.80197 33.90593
## [505] 33.76400 29.98219 29.98219 37.80072 32.74780 32.06839 32.06839 32.47831
## [513] 29.98779 36.00943 30.94037 31.65608 32.48191 29.74697 32.06839 35.42148
## [521] 32.48248 32.06839 32.07267 27.86028 38.38166 30.00667 36.13137 33.84112
## [529] 38.02539 30.49616 29.84931 33.68090 30.51870 30.18240 29.87895 29.72034
## [537] 35.93749 35.93750 35.93611 33.76702 32.55991 37.80389 38.09496 30.05006
## [545] 37.35591 29.97497 29.97714 38.09347 33.40700 35.76698 38.09072 34.92544
## [553] 34.75114 33.45542 63.93074 70.25666 65.31111 39.60887 42.63521 43.96535
## [561] 44.62351 45.95307 39.86822 39.71864 35.76889 35.05932 35.15444 35.01937
## [569] 31.63251 29.91232 36.57460 38.32113 38.32113 30.54741 30.54741 30.54710
## [577] 37.44967 33.69845 38.73302 34.20969 41.43585 32.53213 33.86206 29.70862
## [585] 40.16833 32.11581 39.72708 33.38649 33.03138 33.03138 31.06576 35.93198
## [593] 42.57833 38.66916 35.27901 33.80933 41.68722 43.85167 43.85167 35.92536
## [601] 35.56033 47.92555 40.60827 40.60828 40.60684 39.80035 33.91269 30.02609
## [609] 40.60647 31.82049 42.88895 42.92890 42.26259 41.65801 39.81060 40.60540
## [617] 43.29306 30.79320 30.79392 30.00160 33.00709 35.94466 33.07358 39.12851
## [625] 35.94595 33.93623 33.93651 37.76123 35.73756 35.94373 39.12889 30.24100
## [633] 30.15957 29.71717 30.23927 30.15869 30.23932 30.16020 47.71696 42.85544
## [641] 46.49535 47.63487 35.68463 45.79417 35.68491 35.09731 35.01937 40.60840
## [649] 32.77207 31.78490 37.04520 38.33861 45.47989 38.13370 38.13370 39.84580
## [657] 41.49188 41.25581 35.22377 32.08908 31.52570 31.13665 29.34921 35.95156
## [665] 40.60545 41.39565 37.64411 40.11109 41.80708 43.86069 40.70642 40.70622
## [673] 39.68524 44.81723 38.79206 44.81564 30.70863 42.27202 38.82805 38.79106
## [681] 44.81602 38.82855 39.32368 39.06007 46.81970 45.67299 40.55660 39.45627
## [689] 46.81974 28.27950 32.29488 27.83146 36.03403 31.95870 32.07110 33.87367
## [697] 48.39475 33.73638 41.28850 30.54741 42.87907 47.68889 41.41355 45.89341
## [705] 32.22471 41.17974 33.45494 40.71147 30.07950 30.18348 29.74772 29.43050
## [713] 29.43050 29.43050 29.72694 40.52243 41.76780 40.58925 29.43573 40.59348
## [721] 29.43573 40.59441 40.59327 40.52243 29.72694 29.43573 40.59042 40.59166
## [729] 29.43573 29.43573 40.52243 40.52243 40.59076 40.52333 40.52243 40.52243
## [737] 40.35290 40.52243 40.59063 40.59063 40.52243 42.00461 37.84552 31.78341
## [745] 31.52811 33.82679 31.96551 30.81167 40.51973 36.18977 46.41428 32.00836
## [753] 33.42163 30.90927 33.86348 29.71816 38.83505 40.57704 29.97583 33.85596
## [761] 32.78111 38.83492 29.97504 30.90944 33.99271 29.71871 32.02821 29.97499
## [769] 40.57729 29.97501 32.02879 33.85729 34.55306 36.07076 38.34519 39.19103
## [777] 37.41750 37.41750 37.61590 37.41438 38.09973 36.80530 39.10878 29.66904
## [785] 47.90556 40.00230 38.34024 40.31491 43.08091 30.01111 42.53250 42.27480
## [793] 41.32251 46.21990 39.64343 29.11242 33.58903 41.67288 37.18835 41.51016
## [801] 25.96424 30.00389 30.94062 29.73069 40.52243 35.96143 35.28500 31.98743
## [809] 33.80272 29.47350 29.92669 43.99262 39.03543 32.02064 32.49781 32.53214
## [817] 27.82692 33.85602 32.84800 30.15683 40.78155 30.14580 36.63216 30.02767
## [825] 28.92072 38.58556 31.93856 40.52243 40.52243 36.54755 36.01167 32.38719
## [833] 35.84613 30.10556 40.51348 41.28664 40.71169 37.05446 30.49255 47.09889
## [841] 45.65805 47.09880 45.79290 36.18992 33.79660 35.43959 35.27696 35.27696
## [849] 36.25334 33.84494 39.12024 33.80000 36.01663 36.01526 30.00640 29.89336
## [857] 29.88583 29.88722 27.83125 30.01054 29.81987 29.81637 35.97916 38.82204
## [865] 38.82204 38.35257 35.29605 29.90083 36.64235 37.75878 32.47413 32.28594
## [873] 45.01056 41.55455 38.78564 33.73500 35.22560 40.51617 41.27461 40.51608
## [881] 42.11445 35.32395 40.35290 40.52243 37.97020 29.36555 34.23884 29.71478
## [889] 39.22226 38.20502 40.31960 36.06889 33.59872 34.55261 32.02821 32.02879
## [897] 39.36101 35.28580 37.66168 30.16954 39.81694 39.36139 37.51111 39.36139
## [905] 35.48354 30.71121 37.15778 33.85651 40.57083 29.71877 34.91801 33.59667
## [913] 29.97500 29.90801 29.85836 32.97722 34.55261 40.57083 28.35639 41.55804
## [921] 37.46699 45.89504 42.22592 30.00950 28.54022 28.95081 29.46159 35.95778
## [929] 28.63112 34.55346 29.97523 32.61009 47.32444 35.94473 33.31354 35.95348
## [937] 39.67354 34.42154 29.82961 29.90087 35.97916 38.82204 37.22648 34.09367
## [945] 41.12338 35.38336 30.23043 30.15508 32.72611 40.52243 31.68154 42.10430
## [953] 34.07083 29.34551 39.85162 41.67284 40.60522 30.17319 47.68889 37.57966
## [961] 30.84378 40.64794 34.09229 40.52243 31.19309 37.05255 41.50667 35.95885
## [969] 38.78778 46.68889 46.68889 46.68889 47.68889 35.95885 35.95885 35.94016
## [977] 33.05365 33.41305 30.14577 30.14515 41.62672 47.32444 43.26707 46.93944
## [985] 47.32444 46.68889 46.68930 37.91083 35.93985 29.84722 35.95885 28.80417
## [993] 28.34450 28.00917 29.63083 29.84722 30.08533 41.84583 36.39836 42.88420
## [1001] 47.38361 40.52243 29.76381 29.69374 29.62334 37.05239 29.71690 29.70639
## [1009] 38.37799 46.68889 39.02559 29.90949 32.53198 36.94722 29.76431 44.67167
## [1017] 40.20361 37.80556 34.87456 44.05727 40.60828 33.83299 36.77414 37.80249
## [1025] 37.80480 38.34021 29.72979 47.78260 39.54400 42.05314 37.84074 41.75298
## [1033] 30.71263 36.02959 40.50560 39.91596 32.06374 40.35194 29.82790 37.49519
## [1041] 33.86306 47.68950 32.93920 32.54948 28.82390 33.95600 30.15735 36.77390
## [1049] 37.06111 31.77670 32.78206 32.70141 32.56273 37.79167 29.71611 28.61171
## [1057] 29.89936 28.50889 32.39482 30.02448 32.02343 28.89495 39.70737 32.61094
## [1065] 38.33620 34.37306 31.97435 30.13945 37.66279 40.57741 30.92773 35.06351
## [1073] 38.00366 42.91798 32.07110 36.43020 36.67346 35.31795 39.39548 33.26013
## [1081] 41.60760 29.88878 38.58563 41.60995 39.99230 41.76430 41.66710 41.64240
## [1089] 29.31589 29.14639 31.15903 35.94336 32.06432 35.69559 29.04464 30.92696
## [1097] 29.44778 35.26528 39.81660 38.82204 48.21111 39.84110 35.95885 28.41922
## [1105] 40.59146 40.52243 40.59213 40.59014 41.61955 33.13868 35.93962 42.28292
## [1113] 40.51355 40.51438 40.60851 40.69604 40.29213 40.69450 39.89600 45.78611
## [1121] 40.41010 42.99167 41.61360 30.93182 32.48128 37.12022 30.45239 39.58940
## [1129] 29.78740 40.61145 40.52243 30.83705 47.93493 44.66545 45.25032 35.34960
## [1137] 44.06900 43.60670 35.09721 35.72694 31.93191 40.29173 28.60592 33.86319
## [1145] 30.54601 33.86333 29.39972 38.38154 40.52000 37.79193 48.45564 48.45564
## [1153] 33.84735 29.78740 40.52243 40.60901 28.48849 29.85731 39.36863 36.07076
## [1161] 38.33954 38.34434 32.84283 41.32251 33.84662 29.75089 37.35789 43.78507
## [1169] 47.68512 30.54774 42.18381 46.61780 38.34434 33.91766 40.52243 33.91495
## [1177] 43.04560 41.55849 41.60973 37.35595 32.89621 32.40169 35.34866 45.88371
## [1185] 40.60932 33.03569 45.14306 45.69804 27.83980 34.31371 40.51925 31.77680
## [1193] 39.03517 30.90931 41.56520 28.94967 41.68778 35.93619 41.62685 29.75023
## [1201] 35.94072 33.24455 35.95778 32.99420 41.61292 35.43186 40.60860 38.19639
## [1209] 36.77556 33.80626 36.60930 41.61669 40.58858 27.83113 43.89561 35.98630
## [1217] 30.71051 31.62733 38.50143 36.18085 47.96935 41.27468 30.06057 40.52243
## [1225] 29.37459 30.12910 29.42222 36.57243 32.36876 31.78840 29.85402 33.28411
## [1233] 30.71126 29.22008 35.94066 39.74636 35.52919 47.55403 32.70276 44.46084
## [1241] 30.38353 40.67650 40.16005 29.70659 47.30177 39.27793 21.31668 70.15120
## [1249] 43.14017 67.79870 42.72143 40.97604 42.80667 43.58698 42.94222 43.05284
## [1257] 42.85475 42.79375 42.81144 43.93146 38.47623 41.50711 33.31601 33.97676
## [1265] 41.12688 31.41808 35.69050 35.69179 28.46222 27.86083 32.83300 41.62646
## [1273] 38.83618 37.86810 39.36293 33.93657 36.66590 30.05557 29.87727 28.80920
## [1281] 33.61637 30.54741 35.93964 32.10503 34.43528 32.59913 38.33928 35.96576
## [1289] 33.59202 37.89533 34.21654 29.76382 38.58193 29.71647 31.21500 32.07110
## [1297] 37.32108 33.80021 32.53430 31.63683 32.28877 33.86300 37.97255 31.81845
## [1305] 46.69000 28.91382 41.61566 38.10190 40.94267 45.15209 37.66399 37.20534
## [1313] 30.14515 41.51616 48.32572 34.82512 29.75023 28.95980 33.24789 32.35949
## [1321] 41.41579 37.61590 39.78913 29.85380 43.14070 33.94963 30.71133 32.07254
## [1329] 39.17837 35.93785 29.63362 33.78786 36.13518 36.03385 41.83116 32.28981
## [1337] 32.50059 47.32556 29.97095 28.37000 29.68112 44.64213 38.68098 41.12740
## [1345] 29.81987 41.12740 30.07518 31.80630 36.48798 36.43090 40.52243 29.81987
## [1353] 36.07123 36.07123 29.81915 36.34627 33.82828 32.96069 38.06698 34.87656
## [1361] 35.96984 32.75619 28.94989 33.83017 31.50897 34.47886 27.83668 35.83778
## [1369] 34.55773 34.55747 32.47599 48.30405 31.81974 29.52225 30.75774 29.90067
## [1377] 40.03985 41.68700 39.85361 36.78890 32.01792 29.71711 30.00659 30.00581
## [1385] 35.44499 33.91457 32.53024 29.76673 37.64384 29.91156 29.93500 32.83256
## [1393] 35.93785 41.80661 40.80216 35.55167 32.76118 29.91210 36.00758 30.02508
## [1401] 30.83709 41.55694 32.07293 48.32342 47.88222 48.33114 48.36535 48.32569
## [1409] 48.28449 47.78822 47.58239 47.52413 33.90203 48.27904 41.41942 40.47829
## [1417] 34.48197 38.82925 32.48360 32.49820 41.51487 42.53934 38.04575 35.52919
## [1425] 67.79870 31.65598 32.65057 31.96828 34.20661 34.31435 35.94805 35.95325
## [1433] 42.05679 36.01910 33.80692 29.97101 32.44166 29.73525 38.95973 31.66159
## [1441] 29.52032 43.11444 36.38322 43.29709 39.81880 40.58547 40.58548 35.23167
## [1449] 36.03385 37.77662 40.39553 35.73910 36.64924 32.07110 41.12688 39.04758
## [1457] 41.42186 33.91486 40.51994 44.85338 32.51980 40.52243 32.53740 40.83135
## [1465] 42.87036 36.47280 31.64875 35.26528 40.52243 48.24275 31.81685 39.36939
## [1473] 32.04704 29.37889 38.50252 35.94603 38.06144 47.68889 34.23910 32.07175
## [1481] 31.62560 30.71133 29.99447 27.80859 35.59748 41.68141 29.79114 28.69666
## [1489] 41.65929 40.58061 35.94745 32.08152 45.15209 40.52243 42.22554 31.43960
## [1497] 42.30863 29.69581 30.71133 31.55305 29.08966 29.71737 33.22973 35.13221
## [1505] 28.92865 33.13975 32.65055 35.95035 32.48252 32.02363 35.94771 37.97665
## [1513] 29.75240 35.94754 32.77586 39.96675 32.87424 29.56687 29.34525 34.55307
## [1521] 35.98300 37.10847 32.32880 48.39696 40.69710 30.04236 30.20382 29.87283
## [1529] 33.56399 29.72941 41.78260 30.04234 36.93117 29.72979 29.43573 40.52243
## [1537] 30.52888 35.46577 30.01177 33.25198 43.94972 38.81491 30.30467 29.36586
## [1545] 37.02705 37.14269 41.41037 41.73889 42.53889 36.47280 30.18148 34.14619
## [1553] 32.53193 42.24329 37.67502 40.55081 41.84402 38.61770 29.71927 30.19156
## [1561] 41.51556 48.52425 35.26178 35.34787 33.28664 31.71890 36.55711 35.98263
## [1569] 41.63611 28.33034 38.00366 38.00366 41.64267 29.71226 30.77929 29.08443
## [1577] 41.90877 36.64235 29.34525 47.52353 29.72484 37.80225 29.06638 28.42270
## [1585] 37.08543 30.73768 42.23326 48.72036 33.76972 35.43506 29.43130 35.86561
## [1593] 46.38995 39.70808 26.65047 32.02424 31.71890 39.84635 32.01935 29.34525
## [1601] 46.69354 33.24043 32.97035 30.55448 37.88750 40.69753 29.76621 45.97528
## [1609] 38.78939 31.80150 40.70825 38.88162 41.60760 30.16968 32.78243 28.52699
## [1617] 42.85115 39.78594 29.04718 28.94945 35.92612 29.95003 29.72667 40.52243
## [1625] 41.62263 41.55556 43.01628 44.77084 32.02363 35.94025 27.79952 33.80611
## [1633] 40.52243 38.88144 28.52579 32.56757 41.52983 29.06661 37.12897 47.12312
## [1641] 37.94013 46.68850 40.16254 32.61263 39.25279 31.78542 29.95207 29.47003
## [1649] 39.84900 32.11457 30.56674 31.13628 35.93668 28.42270 35.05097 36.07076
## [1657] 46.39053 34.70203 29.97507 45.14306 37.86364 38.79294 33.86343 32.53403
## [1665] 32.08167 31.11580 35.71930 31.94870 39.84541 30.01672 32.52944 34.87656
## [1673] 40.52243 35.27696 31.89964 28.42263 32.65279 37.69212 39.76357 38.12745
## [1681] 42.55741 40.36474 29.76578 39.15386 42.51414 32.16315 36.48777 30.05012
## [1689] 32.99344 35.94845 35.01937 38.86332 29.10568 35.93635 28.94921 38.84564
## [1697] 29.99141 41.60767 33.03569 35.97916 34.54502 46.68389 29.76320 44.80341
## [1705] 37.81654 29.97633 33.92317 44.94151 30.01177 32.40727 34.00147 32.01820
## [1713] 32.01142 30.31586 30.18156 41.01816 46.35992 30.71116 38.34044 42.53632
## [1721] 35.28036 29.91145 38.62284 33.80333 41.82868 36.48794 37.77662 36.04031
## [1729] 47.68946 40.69754 37.74203 40.70115 42.95170 40.16254 40.94486 30.00623
## [1737] 38.92355 48.11215 31.43651 28.60758 39.13839 29.41987 40.74573 39.84515
## [1745] 34.96406 31.85557 35.44959 35.50018 40.60916 30.01177 35.55198 41.51114
## [1753] 35.31111 34.81648 31.76976 36.92759 70.25715 40.60919 41.09048 32.01493
## [1761] 35.13415 35.20384 40.70825 48.01496 40.29832 39.37571 29.70862 36.77435
## [1769] 40.13682 36.58261 36.77361 29.71770 34.33379 31.95053 32.65205 32.65023
## [1777] 31.43284 32.00790 38.77659 29.79064 29.86247 29.61009 29.71897 39.23043
## [1785] 29.57863 29.74799 35.70420 32.53151 38.77706 36.64235 31.64865 29.74820
## [1793] 29.19332 29.74806 35.01975 30.71826 41.69767 29.25694 35.98620 35.94510
## [1801] 47.32556 29.71785 40.31860 35.95886 35.94370 33.13958 42.86444 36.07240
## [1809] 29.88604 38.78015 37.46222 44.66547 29.74799 31.43282 29.74817 36.71546
## [1817] 39.02601 38.79190 34.94194 33.71924 33.92326 35.94529 32.02363 32.65034
## [1825] 29.76016 28.94945 32.02388 29.34877 33.91446 37.76131 40.53583 29.90643
## [1833] 41.60767 30.87850 29.90087 29.72979 70.26126 32.01019 37.72190 30.17053
## [1841] 34.88205 35.64648 41.55556 47.92184 36.41801 32.07942 33.59888 28.40632
## [1849] 40.52243 31.73160 35.97916 38.26485 34.48407 46.68867 36.64235 31.85260
## [1857] 29.84671 29.21428 32.08872 29.70537 34.12899 34.46284 32.81384 35.93667
## [1865] 44.73486 40.58900 29.35890 47.45833 40.94329 29.70686 41.65526 41.14364
## [1873] 41.14364 38.21578 29.70688 29.34525 45.23801 38.26430 32.30358 34.04406
## [1881] 31.11580 37.72166 39.14020 28.94945 32.02424 32.00045 31.65649 40.76505
## [1889] 40.69716 40.69754 28.88588 30.01130 41.25580 41.80042 37.50302 33.29701
## [1897] 32.10579 34.84676 32.49804 30.01081 40.52243 35.46695 30.71105 39.41191
## [1905] 29.99441 34.81979 32.71949 42.86444 32.50078 27.80113 29.92317 41.53268
## [1913] 31.88918 41.67284 32.60333 31.19310 41.50506 46.68972 36.01466 32.30060
## [1921] 35.47321 29.97740 40.52243 29.70597 47.13750 29.79181 41.51769 29.84415
## [1929] 43.86179 33.28745 42.13333 30.47387 32.75784 27.81443 40.26271 40.26271
## [1937] 35.48374 33.85623 29.42230 31.85330 39.32803 35.48385 46.68690 28.58189
## [1945] 32.90758 42.84905 41.40817 35.93785 41.93695 45.20609 45.56545 38.33298
## [1953] 28.94911 29.74789 32.10804 28.06844 29.47000 29.92698 42.91798 38.79294
## [1961] 38.78924 40.31277 34.54013 29.72979 38.17264 29.79733 32.46571 39.58787
## [1969] 32.79416 32.75828 32.07110 46.37078 29.95203 39.32712 32.52944 27.77042
## [1977] 45.52605 41.86305 38.86948 29.72536 29.72979 36.13715 32.01260 31.80290
## [1985] 47.58254 35.01674 41.50890 29.74863 47.30380 29.72536 29.97478 31.89964
## [1993] 32.49804 40.45772 40.34117 32.43048 32.52473 35.10335 34.05990 36.73544
## [2001] 37.13984 47.32528 32.07110 32.07175 31.13735 38.34114 35.53547 39.78695
## [2009] 31.84825 29.70597 29.99103 47.09855 40.26294 38.93878 35.27696 32.02424
## [2017] 29.72536 41.05608 31.81980 28.05986 31.77339 48.45564 40.06935 31.15885
## [2025] 31.80148 45.69801 29.75250 28.94961 29.71897 31.13690 28.95120 40.69722
## [2033] 35.95902 29.73667 30.08493 30.01172 32.51157 30.05030 34.75343 29.34536
## [2041] 29.52688 29.93538 31.95250 30.29443 29.87875 40.57472 33.29701 39.13930
## [2049] 36.27450 40.70945 44.73368 30.03003 47.26120 39.84512 44.77085 48.23510
## [2057] 36.81045 32.41229 29.91202 33.80471 29.75079 35.97974 45.65549 32.02121
## [2065] 37.66330 29.74762 31.89977 29.71897 28.34480 29.79477 32.65151 36.49701
## [2073] 40.70867 29.46867 32.47500 36.77616 37.75135 32.21056 36.82767 36.80099
## [2081] 47.90761 34.99659 32.06271 39.89486 29.06993 30.01533 31.64865 32.48322
## [2089] 46.68904 31.54937 39.32604 29.85922 29.76505 35.53141 29.97856 38.79380
## [2097] 32.42972 35.13973 32.02194 29.74745 32.02311 29.34510 36.54928 31.76285
## [2105] 31.15918 29.85888 29.98266 29.76016 32.53707 39.84635 42.95773 31.93103
## [2113] 28.16015 28.43916 32.84711 29.84693 41.56348 35.84925 41.62247 33.09885
## [2121] 42.02405 33.34157 36.13064 32.53326 39.03550 36.07101 36.07129 38.82684
## [2129] 46.90292 33.42415 41.63156 41.51458 33.91446 31.50409 29.91125 30.71393
## [2137] 29.94075 39.78484 40.04172 41.52278 30.00887 39.17356 33.28207 35.22504
## [2145] 35.53958 34.21755 37.68779 28.94875 40.52333 40.52333 39.86530 70.10762
## [2153] 30.16486 30.01078 30.00887 38.28366 30.54775 36.06684 33.71618 40.70498
## [2161] 35.71930 32.08076 32.99376 32.54213 31.42565 32.53021 32.36883 30.00458
## [2169] 39.86216 39.12071 40.27935 42.12294 36.23261 42.22637 34.54443 46.68329
## [2177] 32.47696 39.48472 36.16277 29.99127 45.56923 32.08164 40.60170 29.36600
## [2185] 35.73235 31.13687 40.80477 30.07313 32.28582 38.55561 40.53503 40.53611
## [2193] 39.99567 40.60833 40.61244 38.13059 40.56356 30.94241 41.11988 33.40752
## [2201] 44.79377 39.30503 44.78881 30.01372 32.07073 30.07415 38.10215 29.79611
## [2209] 35.06145 38.02516 35.93836 33.94749 29.62187 41.64323 40.59064 40.61154
## [2217] 37.66331 30.95868 34.23891 34.26364 38.62325 37.47100 32.01202 31.63556
## [2225] 31.77691 29.38357 43.72077 43.94201 43.67298 43.78913 43.83264 43.87591
## [2233] 32.18726 34.47250 36.60509 27.78313 31.79747 34.99846 43.95679 43.84203
## [2241] 31.92509 63.42546 29.70111 37.05785 31.80290 40.65744 41.29908 41.64071
## [2249] 40.01047 38.60920 31.16600 39.68540 30.52865 33.77104 30.61843 42.20813
## [2257] 32.49804 34.39460 30.00472 40.52333 40.36682 29.99120 37.20217 40.57667
## [2265] 31.87001 42.20813 29.85670 35.52918 42.22588 35.93444 30.44471 39.02536
## [2273] 33.65940 30.08566 28.95104 30.31851 31.77663 28.57446 32.75626 32.49829
## [2281] 32.02043 30.00390 32.07570 33.40478 43.66660 43.21809 43.66660 43.50343
## [2289] 30.05663 38.09369 41.69229 30.68400 30.26632 32.70464 31.16910 28.51010
## [2297] 41.31171 35.94018 41.80579 38.00856 47.31006 33.05748 35.95201 41.56244
## [2305] 31.77691 47.80327 38.26483 29.74738 29.14259 37.20217 29.36557 32.01933
## [2313] 29.74740 29.31776 34.32184 28.94943 40.60614 47.68412 29.91635 35.95148
## [2321] 29.61440 30.31442 30.30867 31.77167 33.41880 34.10503 43.63500 29.86000
## [2329] 32.43194 29.99604 29.72979 40.65411 29.79734 40.58513 41.22890 31.65135
## [2337] 35.95850 31.85242 29.72056 32.07110 36.79693 32.06365 41.95138 30.26667
## [2345] 66.81282 30.72194 32.08145 39.06405 31.76762 33.97506 33.28139 43.51946
## [2353] 30.14577 29.97787 35.24820 29.72001 48.71342 34.89285 34.84251 32.15603
## [2361] 32.96897 40.48410 39.63257 33.77596 33.73485 32.21265 34.20210 31.94442
## [2369] 32.65066 30.67132 37.05812 30.16000 41.65141 30.04239 32.07056 41.78788
## [2377] 35.93872 35.76882 34.28300 39.48472 29.85651 40.77046 29.88794 39.77285
## [2385] 30.54286 31.76944 36.47406 36.76531 47.03163 36.81050 33.80808 37.80348
## [2393] 30.01173 37.67904 38.85209 30.01665 30.59266 37.72926 34.18319 28.76923
## [2401] 40.20069 33.96455 33.85664 37.16470 33.03433 39.67439 32.00842 41.62121
## [2409] 31.83244 37.08136 28.29088 28.51010 33.28974 29.76684 32.98967 37.80410
## [2417] 32.86467 41.61959 48.85109 40.62067 41.75298 41.60656 38.00423 36.13218
## [2425] 35.95837 41.41433 28.95066 40.54800 39.84697 42.53743 32.01921 29.71567
## [2433] 40.65813 35.96439 40.65095 40.65779 40.66111 21.30438 28.52426 36.13824
## [2441] 39.84672 33.76233 37.67540 29.75890 29.62335 29.84136 32.06854 29.69438
## [2449] 37.68038 37.68038 35.94596 29.70158 35.05400 30.54806 30.47832 30.48306
## [2457] 31.43486 31.15559 29.63146 32.52991 42.11631 42.11582 41.64493 39.59606
## [2465] 32.53301 40.70760 33.34775 40.66506 29.33754 35.43968 45.56538 30.17253
## [2473] 37.58672 33.77754 27.82968 33.93594 32.84711 30.71393 29.90848 29.90848
## [2481] 41.25809 40.65064 29.85751 28.46343 42.35267 34.05993 33.86333 33.34219
## [2489] 29.31088 33.86300 34.91750 33.53872 41.43793 41.39281 41.38284 41.34768
## [2497] 48.88880 47.76063 47.86055 35.26528 29.79637 45.79437 32.01602 40.48080
## [2505] 32.48138 21.31774 30.01372 35.94373 29.80955 36.77417 29.08966 47.68973
## [2513] 31.82105 31.54706 31.54706 30.14044 29.72979 35.94498 33.56938 32.02153
## [2521] 38.37783 32.45279 27.81250 41.31825 47.73231 33.05193 41.64412 36.29392
## [2529] 46.37078 41.67588 33.85545 29.01356 35.98958 40.80348 30.61829 47.45932
## [2537] 39.84477 30.84378 30.84378 30.84378 37.72575 35.96953 31.13488 47.09663
## [2545] 41.18714 41.10621 43.46250 43.78802 43.78856 43.79180 43.78858 43.78813
## [2553] 43.79180 43.79180 44.53110 40.60815 43.54566 29.74804 28.84754 30.38682
## [2561] 27.83244 31.21990 37.21353 29.82610 31.79952 31.65139 28.05982 40.85855
## [2569] 42.02424 47.80554 29.84893 42.30851 40.21421 29.74734 38.09056 37.81716
## [2577] 30.71393 29.84593 36.01195 41.80163 32.08342 43.38310 43.37233 31.98104
## [2585] 38.00366 30.05777 32.08067 35.29890 30.44460 40.45610 29.72536 38.36818
## [2593] 47.97958 40.69436 41.90199 27.82150 29.74787 29.57903 29.61589 29.61789
## [2601] 43.18924 35.94029 46.98030 32.06784 27.81540 43.78798 40.70942 34.05777
## [2609] 43.78307 47.32439 43.66693 43.78793 43.78774 36.08607 39.02942 33.75866
## [2617] 33.76496 39.36328 43.31996 38.83220 30.92979 30.63370 41.55434 33.20438
## [2625] 29.74462 39.04705 32.09031 40.75987 36.20292 41.35429 47.08955 29.79545
## [2633] 32.15284 29.99406 33.78739 29.64688 39.94024 42.88738 29.74550 34.72395
## [2641] 40.54734 31.67770 38.78777 38.62313 30.01430 40.65729 29.72536 29.72536
## [2649] 40.52275 31.64777 32.20998 33.80637 33.80550 27.81890 43.38107 39.84697
## [2657] 31.13722 29.79556 47.68990 30.50214 31.80071 40.43290 35.94015 34.05993
## [2665] 29.28684 29.21194 40.64996 32.57717 34.09100 38.35257 36.84804 29.84593
## [2673] 44.15348 32.01425 30.71393 32.66528 44.37889 37.94261 37.94181 37.74582
## [2681] 29.99111 35.74395 38.34000 40.26519 47.91906 35.93030 37.36120 31.70798
## [2689] 40.20388 45.77906 32.78448 27.82999 29.44169 40.63094 32.47359 40.69559
## [2697] 33.88596 32.02031 34.64280 29.91122 32.53198 38.27373 36.90527 33.61983
## [2705] 39.67171 30.71393 33.00744 38.82725 35.43523 29.85779 33.73485 33.76974
## [2713] 33.86657 29.47097 28.55865 28.46010 28.84642 47.10453 31.63511 31.91401
## [2721] 28.40829 29.78732 29.82188 29.79489 32.80760 38.94905 29.07497 31.95023
## [2729] 29.84123 33.15523 35.94155 38.27427 40.59064 39.51704 36.06382 36.06382
## [2737] 32.93300 43.78847 31.36115 40.29165 29.61413 30.54918 39.41404 33.65569
## [2745] 37.64292 40.63107 29.31910 40.68929 32.54426 30.48435 39.40798 29.30541
## [2753] 32.06899 33.23637 43.24036 32.86180 35.56529 30.33260 33.80313 29.368063.- Transformación logarítmica
log_var1 <- log(variable_original)
ulog1 <- mean(log_var1)
sigmalog1 <- sd(log_var1)4.- Gráfica de distribución de frecuencia
Histograma con ajuste Log-Normal
hist(variable_original,
freq = FALSE,
ylim = c(0,0.08),
col = "lightgreen",
main = "Histograma de Latitud de los accidentes",
xlab = "Latitud del accidente",
ylab = "Frecuencia relativa (Probabilidad)")
curve(dlnorm(x, meanlog = ulog1, sdlog = sigmalog1),
col = "skyblue4",
lwd = 3,
add = TRUE)
5.- Conjetura
Eliminación de valores atípicos
caja <- boxplot(variable_original, plot = FALSE)
variable_modelo <- variable_original[variable_original < min(caja$out)]6.- Parámetros
Parámetros del modelo Log-Normal
log_var <- log(variable_modelo)
ulog <- mean(log_var)
sigmalog <- sd(log_var)7.- Sobreposición de la realidad con el modelo
Cálculo de intervalos
xmin <- 20
xmax <- 50
HistZoom <- hist(variable_modelo,
freq = FALSE,
breaks = 7,
plot = FALSE)## Warning in hist.default(variable_modelo, freq = FALSE, breaks = 7, plot =
## FALSE): argument 'freq' is not made use ofFrecuencias observadas y esperadas
Fo <- HistZoom$counts
h <- length(Fo)
P <- numeric(h)
for(i in 1:h){
P[i] <- plnorm(HistZoom$breaks[i+1], ulog, sigmalog) -
plnorm(HistZoom$breaks[i], ulog, sigmalog)
}
Fe <- P * length(variable_modelo)8.- Test de bondad
Test de Pearson
Correlacion_log <- cor(Fo, Fe) * 100Prueba Chi-Cuadrado
n <- length(variable_modelo)
Fo_pct <- (Fo/n) * 100
Fe_pct <- P * 100
x2 <- sum((Fe_pct - Fo_pct)^2 / Fe_pct)
gl <- (h - 1) - 2
critico <- qchisq(0.95, gl)
decision <- ifelse(x2 < critico, "Aprobado", "Rechazado")9.- Cálculo de probabilidades
Probabilidades esperadas del modelo
P## [1] 0.008301937 0.120179123 0.344380335 0.330805284 0.148734235 0.03929764510.- Intervalo de confianza
Resultados del modelo Log-Normal
tabla <- data.frame(
Variable = "Latitud",
Modelo = "Log-Normal",
Pearson = round(Correlacion_log,2),
Chi_Cuadrado = round(x2,2),
Umbral = round(critico,2),
Resultado = decision
)
print(tabla)## Variable Modelo Pearson Chi_Cuadrado Umbral Resultado
## 1 Latitud Log-Normal 93.81 7.42 7.81 Aprobado11.- Conclusión
El comportamiento de la variable Latitud de los accidentes en oleoductos de EE.UU. (2010–2017) se ajusta adecuadamente a un modelo Log-Normal. El test de bondad de ajuste fue aprobado, ya que el estadístico Chi-cuadrado calculado (7.42) es menor que el valor crítico (7.81), con un nivel de confianza del 95 %. Además, el coeficiente de correlación de Pearson fue de 93.81 %, lo que indica un buen ajuste entre las frecuencias observadas y las esperadas del modelo Log-Normal.