Variable Cuantitativa Continua: Latitud del Accidente
Variable Original: Accident.Latitude
Brandon
Justificación de la variable
La latitud se parametriza como una variable cuantitativa continua esencial para cartografiar la varianza Norte-Sur de los siniestros. Su modelado permite validar si los incidentes se ajustan a una distribución probabilística focalizada, dictada por la densidad de la infraestructura industrial a lo largo de este eje.
1 Cargar Librerias
La estructuración del entorno de programación es el requisito
esencial para el análisis. La activación de la librería
dplyr permite una manipulación fluida de las coordenadas,
mientras que knitr y kableExtra aseguran que
las tablas de frecuencias se presenten con la formalidad y el rigor
técnico requeridos en el ámbito académico.
library(htmltools)
library(gt)
library(dplyr)##
## Adjuntando el paquete: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(e1071)## Warning: package 'e1071' was built under R version 4.5.3library(knitr)
library(ggplot2)##
## Adjuntando el paquete: 'ggplot2'## The following object is masked from 'package:e1071':
##
## elementlibrary(scales)2 Cargar datos
Importamos el archivo “database-1.csv” desde una ruta local y lo almacena en el objeto datos, usando comas como separador.
datos <- read.csv("database-_1_.csv", header = TRUE, sep = ",", dec = ".", check.names = FALSE)
names(datos)## [1] "Report Number"
## [2] "Supplemental Number"
## [3] "Accident Year"
## [4] "Accident Date/Time"
## [5] "Operator ID"
## [6] "Operator Name"
## [7] "Pipeline/Facility Name"
## [8] "Pipeline Location"
## [9] "Pipeline Type"
## [10] "Liquid Type"
## [11] "Liquid Subtype"
## [12] "Liquid Name"
## [13] "Accident City"
## [14] "Accident County"
## [15] "Accident State"
## [16] "Accident Latitude"
## [17] "Accident Longitude"
## [18] "Cause Category"
## [19] "Cause Subcategory"
## [20] "Unintentional Release (Barrels)"
## [21] "Intentional Release (Barrels)"
## [22] "Liquid Recovery (Barrels)"
## [23] "Net Loss (Barrels)"
## [24] "Liquid Ignition"
## [25] "Liquid Explosion"
## [26] "Pipeline Shutdown"
## [27] "Shutdown Date/Time"
## [28] "Restart Date/Time"
## [29] "Public Evacuations"
## [30] "Property Damage Costs"
## [31] "Lost Commodity Costs"
## [32] "Public/Private Property Damage Costs"
## [33] "Emergency Response Costs"
## [34] "Environmental Remediation Costs"
## [35] "Other Costs"
## [36] "All Costs"3 Extrae la variable
Para este apartado, se aísla la variable referente a la latitud de los incidentes (Accident Latitude). Este parámetro es fundamental para el análisis geoespacial de la red de tuberías. Se procede a una depuración técnica, eliminando valores nulos para asegurar que la muestra sea representativa y esté lista para su posterior agrupación mediante marcas de clase.
zona<-datos$`Accident Latitude`4 Conteo
Debido a que trabajamos con coordenadas precisas, la tabulación de frecuencias absolutas requiere un enfoque de agrupación. Este conteo inicial permite identificar la dispersión de los registros. (Nota técnica: Para efectos del presente análisis, los resultados obtenidos servirán de base para establecer los rangos de Marca de Clase, permitiendo una representación espacial más adecuada que el uso de grados brutos).
conteo_zona <- table(zona)
print(conteo_zona)## zona
## 18.44801 21.30438 21.31668 21.31774 23.336784 25.964238
## 1 1 1 1 1 1
## 26.650465 27.5529182 27.68402 27.72222 27.770422 27.783128
## 1 1 1 1 1 1
## 27.79952 27.80113016 27.80859 27.8125 27.8144306 27.815402
## 1 1 1 1 1 1
## 27.8189044 27.8215 27.826919 27.829677 27.829994 27.831131
## 1 1 1 1 1 1
## 27.83125 27.83146 27.832444 27.83668 27.839803 27.86028
## 1 1 1 1 1 1
## 27.8608333 27.87527711 27.91036 27.943 27.9469444 27.959521
## 1 1 1 1 1 1
## 27.97348 28.00917 28.05529 28.059821 28.059862 28.0684416
## 1 1 1 1 1 1
## 28.10406 28.16015 28.260372 28.279502 28.29088 28.33034
## 2 1 1 1 1 1
## 28.3445 28.3448 28.3563889 28.37 28.40632 28.408293
## 1 1 1 1 1 1
## 28.41922 28.422635 28.422698 28.43916 28.4601 28.4622222
## 1 1 2 1 1 1
## 28.46343 28.480925 28.488488 28.5088889 28.510104 28.524255
## 1 1 1 1 2 1
## 28.525786 28.526987 28.54022 28.558649 28.560826 28.57446
## 1 1 1 1 1 1
## 28.58189 28.605919 28.60758 28.61171 28.617778 28.618056
## 1 1 1 1 1 1
## 28.63112 28.68555 28.69666 28.711239 28.7692347 28.804167
## 1 1 1 1 1 2
## 28.809202 28.8239 28.84642 28.84754 28.85030001 28.8559
## 1 1 1 1 1 1
## 28.885881 28.894955 28.91382 28.920722 28.928655 28.9351
## 1 1 1 1 1 1
## 28.93564 28.948749 28.949113 28.94921 28.949425 28.949448
## 1 1 1 1 1 3
## 28.949612 28.949672 28.949889 28.950662 28.95081 28.950953
## 1 1 1 1 1 1
## 28.951037 28.951204 28.9598 29.013562 29.04464 29.04718
## 1 1 1 1 1 1
## 29.06023333 29.066379 29.066613 29.069927 29.074975 29.084431
## 1 1 1 1 1 1
## 29.08966 29.089664 29.1049 29.105684 29.10788 29.11242
## 1 1 1 1 1 1
## 29.119939 29.1425929 29.145153 29.1452 29.145494 29.146389
## 1 1 1 1 1 1
## 29.1514 29.193322 29.193445 29.19462 29.206868 29.21194
## 1 1 1 1 1 1
## 29.214284 29.22007944 29.238862 29.245664 29.253809 29.2564
## 1 1 1 1 1 1
## 29.25694 29.26536 29.274667 29.286841 29.30541 29.310878
## 1 1 1 1 1 1
## 29.31589 29.317764 29.3191 29.337541 29.345095 29.34525
## 1 1 1 1 1 4
## 29.345358 29.345464 29.34551 29.34578 29.3475 29.348547
## 1 1 1 1 1 1
## 29.348769 29.349 29.34921 29.358902 29.36555 29.36557
## 1 1 1 1 1 1
## 29.36586 29.366003 29.368056 29.3736 29.374592 29.3753
## 1 1 1 1 1 1
## 29.3786 29.37889 29.38357 29.39972 29.4009 29.419652
## 1 1 1 1 1 1
## 29.419868 29.422222 29.422303 29.4305 29.4313 29.43573
## 1 1 1 3 1 6
## 29.4388 29.441693 29.44778 29.461595 29.466936 29.46867
## 1 1 1 1 1 1
## 29.47 29.470028 29.47097 29.473497 29.4745 29.485
## 1 1 1 1 1 1
## 29.51419 29.52032 29.52107 29.52225 29.526883 29.54619
## 1 1 1 1 1 1
## 29.56687 29.57863 29.579031 29.605714 29.610094 29.614125
## 1 1 1 1 1 1
## 29.614404 29.615889 29.617889 29.6218722 29.62333683 29.623347
## 1 1 1 1 1 1
## 29.62478 29.630232 29.630833 29.631459 29.633617 29.646875
## 1 1 1 1 1 1
## 29.66904 29.68112 29.69373658 29.69438 29.69581 29.701113
## 1 1 1 1 1 1
## 29.70158 29.705369 29.705972 29.70639 29.706473 29.706587
## 1 1 2 1 1 1
## 29.706862 29.70687777 29.708617 29.70989 29.712258 29.71478
## 1 1 3 1 1 1
## 29.715674 29.716111 29.716471 29.7169 29.717115 29.717169
## 1 1 1 1 1 1
## 29.717371 29.7177027 29.717845 29.71816 29.7182 29.71831
## 1 1 1 1 1 1
## 29.718312 29.71871 29.718767 29.718947 29.71897 29.71927
## 1 1 1 1 3 1
## 29.720014 29.72034 29.72056 29.724843 29.72536 29.726669
## 1 1 1 1 6 1
## 29.7268 29.726944 29.72703 29.72941 29.72979 29.73069
## 1 2 1 1 7 1
## 29.73525 29.73667 29.74462 29.745503 29.74697 29.74734
## 1 1 1 1 1 1
## 29.747375 29.7474 29.747453 29.747625 29.74772 29.747769
## 1 1 1 1 1 1
## 29.74787 29.74789 29.747986 29.74799 29.74804 29.748058
## 1 1 1 1 1 1
## 29.748169 29.748201 29.74863 29.75023 29.750786 29.75079
## 1 1 1 2 1 1
## 29.750895 29.752401 29.7525 29.758902 29.759006 29.760156
## 1 1 1 1 1 2
## 29.7632 29.763813 29.763824 29.764311 29.765054 29.765783
## 1 1 1 1 1 1
## 29.76621 29.76673 29.766845 29.76713 29.7675 29.781516
## 1 1 1 1 1 1
## 29.787 29.78732 29.787397 29.79064 29.79114 29.79181
## 1 1 2 1 1 1
## 29.792012 29.79428 29.79449 29.79477 29.79489 29.79545
## 1 1 1 1 1 1
## 29.79556 29.7961139 29.79637 29.79733 29.79734 29.80955
## 1 1 1 1 1 1
## 29.816369 29.819151 29.81987246 29.821878 29.825329 29.8261
## 1 1 3 1 1 1
## 29.8279 29.82961 29.841234 29.84136111 29.8441496 29.845934
## 1 1 1 1 1 2
## 29.84671 29.84692774 29.847028 29.84722 29.847222 29.848528
## 1 1 1 1 1 1
## 29.84893 29.84904 29.84931 29.85325 29.8538 29.854022
## 1 1 1 1 1 1
## 29.854148 29.85635 29.856513 29.8567 29.85731 29.857514
## 1 1 1 1 1 1
## 29.857787 29.85836 29.858881 29.859222 29.86 29.862472
## 1 1 1 1 1 1
## 29.86809 29.87283 29.87727 29.878747 29.878864 29.878953
## 1 1 1 1 1 1
## 29.885833 29.88604163 29.887222 29.88794 29.88878 29.8916
## 1 1 1 1 1 1
## 29.893363 29.8964 29.89936 29.9006722 29.90083 29.90087416
## 1 1 1 1 1 2
## 29.906433 29.90801 29.90848 29.90949 29.91122222 29.91125
## 1 1 2 1 1 1
## 29.911449 29.911491 29.9115 29.91156 29.911676 29.912017
## 1 1 1 1 1 1
## 29.9121 29.91232 29.916355 29.920836 29.92317489 29.926686
## 1 1 1 1 1 1
## 29.926983 29.935 29.93538 29.94075 29.950028 29.95115
## 1 1 1 1 1 1
## 29.951987 29.952028 29.952065 29.952222 29.955034 29.95687
## 1 1 1 1 1 1
## 29.96887 29.970953 29.97101 29.974782 29.97496932 29.974993
## 1 1 1 1 1 1
## 29.975 29.97501 29.97504 29.97507 29.97523 29.97583
## 1 1 1 1 1 1
## 29.976335 29.9771376 29.9774 29.977871 29.978557 29.9807
## 1 1 1 1 1 1
## 29.98219 29.98266 29.98722 29.9877906 29.99103 29.991106
## 2 1 1 1 1 1
## 29.9912 29.991266 29.991413 29.994064 29.9944083 29.99447
## 1 1 1 1 1 1
## 29.9948 29.99604 29.99763 29.997663 30.0016 30.0038889
## 1 1 1 1 1 1
## 30.0039 30.00458 30.004722 30.0058083 30.006233 30.0064
## 1 1 1 1 1 1
## 30.0065888 30.006667 30.008867 30.008992 30.0095 30.010536
## 1 1 2 1 1 1
## 30.010784 30.010811 30.011111 30.0113 30.01172 30.01173
## 1 1 1 1 1 1
## 30.01177 30.0119001 30.0124001 30.013719 30.01372 30.0142962
## 3 1 1 1 1 1
## 30.015334 30.01612 30.0166509 30.016667 30.016724 30.02448
## 1 1 1 1 1 1
## 30.0250818 30.02609 30.02767 30.030029 30.03188 30.034033
## 1 1 1 1 1 1
## 30.042343 30.04236 30.042394 30.049461 30.05006 30.05012
## 1 1 1 1 1 1
## 30.0503 30.055571 30.056 30.056628 30.05777 30.060572
## 1 1 1 1 1 1
## 30.06066 30.066112 30.07313 30.07415 30.0751806 30.0795
## 1 2 1 1 1 1
## 30.08493 30.08533 30.08566 30.087494 30.0889 30.10556
## 1 1 1 1 2 1
## 30.11356 30.11472 30.1150416 30.124278 30.1291 30.13945
## 1 1 1 1 1 1
## 30.14044 30.1408 30.14105 30.145154 30.1457 30.145766
## 1 1 1 2 1 2
## 30.1458 30.1479 30.155076 30.15683 30.1571 30.15735228
## 1 1 1 1 1 1
## 30.158686 30.15957 30.16 30.160197 30.16414 30.16485
## 1 1 1 1 1 1
## 30.164856 30.16801 30.16954 30.16968 30.170532 30.1724
## 1 1 1 1 1 1
## 30.17253 30.17319 30.18148 30.18156 30.1824 30.18348
## 1 1 1 1 1 1
## 30.19071 30.19156 30.20382 30.2298122 30.2304266 30.239269
## 1 1 1 1 1 1
## 30.239319 30.239547 30.241 30.25989 30.26630836 30.26632292
## 1 1 1 1 1 1
## 30.26667 30.28649 30.2867 30.294432 30.30467 30.30867
## 1 1 1 1 1 1
## 30.314425 30.315859 30.318509 30.32637 30.332597 30.354517
## 1 1 1 1 1 1
## 30.355333 30.383529 30.386817 30.3892333 30.390281 30.4342
## 1 1 1 1 1 1
## 30.43779 30.4446 30.44471 30.452391 30.45372 30.47386943
## 1 1 1 1 1 1
## 30.47832 30.479042 30.483056 30.484345 30.492551 30.496161
## 1 1 1 1 1 1
## 30.50214 30.5187 30.528648 30.528877 30.542863 30.54601111
## 1 1 1 1 1 1
## 30.5471 30.54741 30.54774 30.54775 30.548063 30.549182
## 1 4 1 1 1 1
## 30.554483 30.5572 30.566736 30.592658 30.61829 30.61843
## 1 1 1 1 1 1
## 30.6337 30.6688 30.671323 30.684 30.70863 30.71051
## 1 1 1 1 1 1
## 30.71105 30.71116 30.71121 30.711259 30.71133 30.71263
## 1 1 1 1 3 1
## 30.713929 30.718259 30.72194 30.737681 30.75774 30.77929
## 5 1 1 1 1 1
## 30.78251 30.7932 30.793919 30.796962 30.79796 30.80147
## 1 1 1 1 1 1
## 30.81167 30.83705 30.83709 30.84377614 30.8568 30.878502
## 1 1 1 4 1 1
## 30.909265 30.90931 30.90944 30.92696 30.92773 30.92979
## 1 1 1 1 1 1
## 30.93182 30.94037 30.94062 30.942414 30.958681 31.01183
## 1 1 1 1 1 1
## 31.06576 31.1158 31.12252 31.13193 31.13244 31.13284
## 1 2 1 1 1 1
## 31.13488 31.13575 31.136282 31.13665 31.136868 31.136905
## 1 1 1 1 1 1
## 31.137224 31.13735 31.15279 31.155589 31.15885 31.15903
## 1 1 1 1 1 1
## 31.1591 31.15918 31.1611 31.166 31.169097 31.19309
## 1 1 2 1 1 1
## 31.1931 31.215 31.219899 31.36115 31.362222 31.41808
## 1 1 1 1 1 1
## 31.42565 31.427166 31.42962 31.43275 31.432815 31.43284
## 1 1 1 1 1 1
## 31.434268 31.434858 31.436508 31.4396 31.47285 31.49797
## 1 1 1 1 1 1
## 31.504092 31.50653 31.50897 31.525701 31.52811 31.531786
## 1 1 1 1 1 1
## 31.54706 31.54937 31.553051 31.55556 31.58929 31.6256
## 2 1 1 1 1 1
## 31.62733 31.63251 31.63511 31.635562 31.636831 31.647774
## 1 1 1 1 1 1
## 31.648653 31.64875 31.651352 31.651389 31.655975 31.65608
## 2 1 1 1 1 1
## 31.656494 31.66159 31.6777 31.68154 31.70798 31.718902
## 1 1 1 1 1 2
## 31.7316 31.76285 31.76762 31.76885 31.769437 31.76976
## 1 1 1 1 1 1
## 31.771673 31.77339 31.77393 31.7765 31.77654 31.776632
## 1 1 1 1 1 1
## 31.7767 31.7768 31.77691 31.78341 31.784903 31.78542
## 1 1 2 2 1 1
## 31.788398 31.790487 31.79133 31.7918 31.79747 31.79952
## 1 1 1 1 1 1
## 31.80071 31.80148 31.8015 31.8029 31.8063 31.81685
## 1 1 1 2 1 1
## 31.81845 31.819742 31.8198 31.820486 31.821045 31.821442
## 1 1 1 1 1 1
## 31.83244 31.84825 31.852417 31.8526 31.85330114 31.85557
## 1 1 1 1 1 1
## 31.870006 31.8768505 31.88918 31.89631 31.899645 31.899768
## 1 1 1 1 2 1
## 31.91401 31.925091 31.93103 31.931914 31.93856 31.944422
## 1 1 1 1 1 1
## 31.948696 31.95023 31.950527 31.9525 31.9587 31.960602
## 1 1 1 1 1 1
## 31.96551 31.968284 31.97435 31.9810444 31.98743 32.000452
## 1 1 1 1 1 1
## 32.004805 32.0079 32.00836 32.008424 32.010188 32.011423
## 1 1 3 1 1 1
## 32.01202 32.0126 32.01425 32.01426 32.01435 32.01493
## 1 1 1 1 1 1
## 32.016023 32.017047 32.017924 32.01798 32.018203 32.01921
## 1 1 1 1 1 1
## 32.019332 32.019351 32.02031 32.020434 32.02064 32.021211
## 1 1 1 1 1 1
## 32.021534 32.021937 32.023108 32.02343 32.02363 32.023877
## 1 1 1 1 3 1
## 32.02424 32.02821 32.02879 32.04704 32.062707 32.063649
## 3 2 2 1 1 1
## 32.06374 32.06417 32.06432 32.06456 32.06704 32.06784
## 1 1 1 1 2 1
## 32.06839 32.06854 32.06899 32.07056 32.07073 32.0711
## 4 1 1 1 1 7
## 32.07175 32.07254 32.07267 32.0729 32.072932 32.0757
## 2 1 1 2 1 1
## 32.079424 32.08014 32.080668 32.08076 32.080874 32.08145
## 1 1 1 1 1 1
## 32.081519 32.08164 32.081667 32.08342 32.088227 32.088721
## 1 1 1 1 1 1
## 32.089083 32.090307 32.10503 32.1057904 32.108042 32.113857
## 1 1 1 1 1 1
## 32.11457 32.1147 32.11581 32.15284 32.1532 32.15603
## 1 1 1 1 1 1
## 32.16315 32.18726 32.209977 32.210556 32.21265 32.22471
## 1 1 1 1 1 1
## 32.23587 32.251168 32.26812 32.285819 32.28594 32.28877
## 1 1 2 1 1 1
## 32.28981 32.29488 32.3006 32.303575 32.3288 32.34464
## 1 1 1 1 1 1
## 32.359487 32.36876 32.368825 32.38719 32.39482 32.40169
## 1 1 1 1 1 1
## 32.407275 32.412292 32.429722 32.43048 32.431944 32.44166
## 1 1 1 1 1 1
## 32.45279 32.46539 32.465709 32.47042 32.473589 32.47413
## 1 1 1 1 1 1
## 32.475 32.47599 32.47696 32.47831 32.4785 32.48128
## 1 1 1 2 1 1
## 32.4813 32.481377 32.4819 32.48191 32.48248 32.48252
## 2 1 1 1 1 1
## 32.483 32.483217 32.48325 32.4836 32.49781 32.49783
## 1 1 1 1 1 1
## 32.49804 32.4982 32.49829 32.50059 32.5007778 32.511567
## 3 1 1 1 1 1
## 32.51846 32.519797 32.524731 32.52582 32.52944 32.529914
## 1 1 1 1 2 1
## 32.53021 32.53024 32.53048 32.53091 32.53151 32.53193
## 1 1 1 1 1 1
## 32.53198 32.531983 32.532 32.532127 32.532145 32.53242
## 1 1 1 1 1 1
## 32.5327 32.53275 32.533014 32.533257 32.53403 32.5343
## 2 1 1 1 1 1
## 32.53707 32.5374 32.5375 32.540604 32.5409 32.54213
## 1 1 1 1 1 1
## 32.54426 32.54948 32.55991 32.56184 32.56273 32.56757
## 1 1 1 1 1 1
## 32.577172 32.599125 32.603333 32.6075 32.61009 32.61094
## 1 1 1 1 1 1
## 32.611 32.61263 32.63239 32.650231 32.650336 32.650552
## 1 1 1 1 1 1
## 32.650565 32.650659 32.65151 32.652 32.652052 32.652787
## 1 1 1 1 1 1
## 32.655 32.665279 32.70141 32.70276 32.70298 32.70464
## 1 1 1 1 1 1
## 32.71141 32.71949 32.7261111 32.7478 32.75619 32.756261
## 1 1 1 1 1 1
## 32.75732 32.757835 32.75828 32.76118 32.772073 32.775858
## 1 1 1 1 1 1
## 32.775943 32.77597 32.77698 32.777568 32.779328 32.78111
## 1 1 1 1 1 1
## 32.782062 32.782428 32.78448 32.794161 32.8076 32.813
## 1 1 1 1 1 1
## 32.81384 32.83256 32.833 32.842833 32.847106 32.84745
## 1 1 1 1 2 1
## 32.848 32.86057 32.8618 32.862785 32.86467 32.874236
## 1 1 1 1 1 1
## 32.874247 32.87476 32.87718 32.89621 32.907579 32.933
## 1 3 1 1 1 1
## 32.9392 32.9491 32.960694 32.9689722 32.97035 32.97722
## 1 1 1 1 1 1
## 32.989666 32.99344 32.99376 32.9942 33.007092 33.007445
## 1 1 1 1 1 1
## 33.03138 33.034328 33.03568558 33.05193 33.05365 33.057483
## 2 1 2 1 1 1
## 33.07358 33.098846 33.138683 33.139575 33.139747 33.155227
## 1 1 1 1 1 1
## 33.17535 33.179721 33.20242 33.204379 33.22053 33.22973
## 1 1 1 1 1 1
## 33.236374 33.24043 33.24455 33.247889 33.251978 33.25417
## 1 1 1 1 1 1
## 33.26013184 33.28139 33.28207 33.28411 33.286639 33.287449
## 1 1 1 1 1 1
## 33.289744 33.29701 33.307077 33.31354 33.31601 33.33278
## 1 2 1 1 1 1
## 33.34157 33.34219 33.347755 33.38649 33.404778 33.407
## 1 1 1 1 1 1
## 33.40752 33.41305 33.4166975 33.4188 33.42163 33.424148
## 1 1 1 1 1 1
## 33.45494 33.45542 33.4604 33.4614 33.5124 33.5352
## 1 1 1 1 1 1
## 33.53866 33.538716 33.54657 33.56399 33.569382 33.573889
## 1 1 1 1 1 1
## 33.58266 33.5890316 33.59202 33.59667 33.59872 33.598881
## 1 1 1 1 1 1
## 33.616375 33.619833 33.655692 33.6594 33.6809 33.68092
## 1 1 1 1 1 1
## 33.6938 33.698451 33.7161833 33.719236 33.734846 33.735001
## 1 1 1 1 2 1
## 33.736385 33.756403 33.758661 33.76233 33.764 33.764961
## 1 1 1 1 1 1
## 33.767016 33.769722 33.7697415 33.771038 33.77596 33.77754
## 1 1 1 1 1 1
## 33.78114 33.787393 33.787864 33.795549 33.7963 33.7966
## 1 1 1 2 1 1
## 33.8000022 33.800211 33.80197 33.802717 33.80313 33.803335
## 1 1 1 1 1 1
## 33.804707 33.805501 33.806106 33.806255 33.806372 33.806917
## 1 1 1 1 1 1
## 33.80808 33.80933 33.811699 33.81583 33.826786 33.828281
## 1 1 1 1 1 1
## 33.83017 33.83299 33.83799 33.841119 33.84494 33.846624
## 1 1 1 1 1 1
## 33.84735 33.85545 33.855711 33.85596 33.85602 33.85623
## 1 1 1 1 1 1
## 33.85651 33.856638 33.857292 33.86206 33.863 33.8630556
## 1 1 1 1 2 1
## 33.863186 33.86329 33.863326 33.863333 33.86343 33.86345
## 1 1 1 1 1 1
## 33.863481 33.86357 33.86379 33.864289 33.86657 33.87367
## 1 1 1 1 1 1
## 33.885958 33.902032 33.90593 33.91269 33.91446 33.914572
## 1 1 1 1 2 1
## 33.91486 33.914949 33.91765556 33.923171 33.923263 33.93594
## 1 1 1 1 1 1
## 33.936233 33.936514 33.936574 33.947489 33.949629 33.956
## 1 1 1 1 1 1
## 33.96455 33.97 33.970039 33.975062 33.97676 33.99271
## 1 1 1 1 1 1
## 34.001474 34.00551 34.044058 34.0522342 34.0577675 34.058206
## 1 1 1 1 1 1
## 34.0599 34.059928 34.07083 34.091 34.092292 34.093675
## 1 2 1 1 1 1
## 34.105033 34.12899 34.133131 34.146191 34.16078 34.183191
## 1 1 1 1 1 1
## 34.1897222 34.2021 34.206615 34.20969 34.216537 34.217554
## 1 1 1 1 1 1
## 34.23884 34.238914 34.2391 34.24278 34.244372 34.245072
## 1 1 1 2 1 1
## 34.263642 34.27734 34.283001 34.31371 34.314349 34.32044
## 1 1 1 1 1 1
## 34.32184 34.333794 34.36098 34.37306 34.37332 34.394601
## 1 1 1 1 1 1
## 34.421537 34.43528 34.462434 34.462837 34.472502 34.478859
## 1 1 1 1 1 1
## 34.481971 34.48407 34.521102 34.5401306 34.544428 34.545017
## 1 1 1 1 1 1
## 34.55261 34.55306 34.5530703 34.553462 34.55747 34.55773
## 2 1 1 1 1 1
## 34.63366 34.6428 34.70203 34.723949 34.751139 34.753426
## 1 1 1 1 1 1
## 34.76231 34.816479 34.81979 34.82512 34.83433167 34.84251
## 1 1 1 1 1 1
## 34.84676 34.874565 34.87656 34.882052 34.89185 34.89285
## 1 1 2 1 1 1
## 34.9175 34.91801 34.92544 34.94194 34.94212 34.94418
## 1 1 1 1 1 1
## 34.96406 34.972892 34.99659 34.998458 35.01673757 35.01937
## 1 1 1 1 1 2
## 35.019374 35.019746 35.02529 35.04474 35.05097 35.054
## 1 1 1 1 1 1
## 35.059321 35.0614452 35.063508 35.097214 35.097314 35.10335
## 1 1 1 1 1 1
## 35.119174 35.13221 35.134147 35.139732 35.1544444 35.203837
## 1 1 1 1 1 1
## 35.22377 35.225037 35.2256 35.231666 35.23317 35.2482
## 1 1 1 1 1 1
## 35.26177777 35.265278 35.276957 35.27901 35.28036 35.285
## 1 3 4 1 1 1
## 35.2858 35.296047 35.298901 35.31111 35.317952 35.32395
## 1 1 1 1 1 1
## 35.3275 35.347873 35.34866 35.3496 35.3599366 35.383359
## 1 1 1 1 1 1
## 35.42148 35.431862 35.435057 35.435228 35.43959 35.439682
## 1 1 1 1 1 1
## 35.444988 35.449592 35.46577 35.466951 35.4672 35.467203
## 1 1 1 1 1 1
## 35.47321 35.48354 35.48374 35.483852 35.4855 35.500176
## 1 1 1 1 1 1
## 35.529177 35.5291888 35.5314135 35.534236 35.535471 35.539578
## 1 2 1 1 1 1
## 35.55167 35.551979 35.55435 35.55441 35.56033 35.565292
## 1 1 1 1 1 1
## 35.56572 35.59243 35.597478 35.6376 35.646475 35.68463
## 1 1 1 1 1 1
## 35.684911 35.6905 35.69179 35.69559 35.7042 35.719298
## 1 1 1 1 1 2
## 35.726944 35.73235 35.737564 35.7391 35.74395 35.76698
## 1 1 1 1 1 1
## 35.768817 35.7688889 35.8377778 35.84613 35.849254 35.85326
## 1 1 1 1 1 1
## 35.86561 35.86572 35.87218 35.92536 35.92612 35.93019
## 1 1 1 1 1 1
## 35.9303 35.93198 35.93444 35.9361111 35.936195 35.936355
## 1 1 1 1 1 1
## 35.936666 35.936677 35.93749 35.9375 35.93784934 35.9382
## 1 1 1 1 3 1
## 35.938355 35.938719 35.939625 35.93964 35.93985 35.940151
## 1 1 1 1 1 1
## 35.940158 35.940183 35.940253 35.940287 35.94066 35.94072
## 1 1 1 1 1 1
## 35.94085 35.94109 35.94155 35.94336 35.943703 35.94373
## 1 1 1 1 1 1
## 35.943731 35.94466 35.944728 35.94498 35.945098 35.945288
## 1 1 1 1 1 1
## 35.94595 35.94596 35.94603 35.94607 35.946697 35.94745
## 2 1 1 2 1 1
## 35.94754 35.947714 35.94805 35.948453 35.950352 35.951482
## 1 1 1 1 1 1
## 35.951559 35.95201 35.952194 35.953247 35.953482 35.95778
## 1 1 1 1 1 2
## 35.95837 35.9585 35.95885 35.95886 35.95902 35.96143
## 1 1 6 1 1 1
## 35.964394 35.96576 35.96788 35.96953 35.96984 35.97916323
## 1 1 1 1 1 4
## 35.97974 35.982628 35.983 35.986205 35.9863 35.989585
## 1 1 1 1 1 1
## 36.00758 36.00943 36.01167 36.011954 36.0146585 36.01526
## 1 1 1 1 1 1
## 36.01663 36.0191 36.029589 36.03385 36.03403 36.04031
## 1 1 1 2 1 1
## 36.06382 36.06684 36.06889 36.07076 36.07101 36.07123064
## 2 1 1 3 1 2
## 36.07129 36.0724 36.086068 36.12128 36.13064 36.13137
## 1 1 1 1 1 1
## 36.13158 36.13218 36.13252 36.1326083 36.135178 36.13715
## 1 1 1 1 1 1
## 36.13824 36.162774 36.17115 36.18085 36.18977222 36.18992091
## 1 1 1 1 1 1
## 36.20138 36.202923 36.221931 36.232606 36.253344 36.274497
## 1 1 1 1 1 1
## 36.29392 36.33746 36.346272 36.38298 36.38322 36.39836
## 1 1 1 1 1 1
## 36.413056 36.41801 36.41936 36.4302 36.4309 36.472798
## 1 1 1 1 1 2
## 36.4740589 36.487768 36.48794 36.48798 36.49701 36.54755
## 1 1 1 1 1 1
## 36.54928 36.55711482 36.56083 36.57243 36.5746 36.58261
## 1 1 1 1 1 1
## 36.605085 36.6093 36.632156 36.64234919 36.649239 36.6659
## 1 1 1 4 1 1
## 36.67346274 36.715463 36.735435 36.765308 36.773611 36.773902
## 1 1 1 1 1 1
## 36.77414 36.774166 36.774347 36.77451 36.775556 36.77616
## 1 1 1 1 1 1
## 36.7889 36.79693 36.800991 36.8053 36.81045 36.810495
## 1 1 1 1 1 1
## 36.827669 36.8480438 36.892543 36.9006 36.905274 36.927591
## 1 1 1 1 1 1
## 36.93117 36.947219 37.027049 37.04441 37.045196 37.052386
## 1 1 1 1 1 1
## 37.0525 37.05253 37.052548 37.05446 37.057847 37.058121
## 1 1 1 1 1 1
## 37.061114 37.070361 37.08136 37.08414 37.08543 37.10847
## 1 1 1 1 1 1
## 37.12022 37.12897 37.139844 37.14269 37.15778 37.1647
## 1 1 1 1 1 1
## 37.188347 37.202167 37.205338 37.21353203 37.226483 37.321081
## 1 2 1 1 1 1
## 37.355914 37.35595 37.357891 37.3612 37.414383 37.4175
## 1 1 1 1 1 2
## 37.44967 37.462217 37.46699 37.471 37.495186 37.50301661
## 1 1 1 1 1 1
## 37.51111 37.579665 37.586723 37.6159 37.64292 37.643839
## 1 1 1 2 1 1
## 37.644112 37.64416 37.66168 37.66279 37.6633 37.66330708
## 1 1 1 1 1 1
## 37.66399 37.67502 37.6754 37.679044 37.680384 37.68779
## 1 1 1 1 2 1
## 37.69212 37.721661 37.721901 37.72575 37.72926 37.742029
## 1 1 1 1 1 1
## 37.745816 37.75134722 37.75877757 37.761233 37.761305 37.7766173
## 1 1 1 1 1 2
## 37.78947 37.78977 37.79167 37.79193 37.795178 37.7958
## 1 1 1 1 1 1
## 37.800717 37.80218 37.80225 37.80249 37.803255 37.80348
## 1 1 1 1 1 1
## 37.80389 37.8041 37.8048 37.80556 37.81654 37.817
## 1 1 1 1 1 1
## 37.817162 37.81841 37.84074 37.84552 37.86364 37.8681
## 1 1 1 1 1 1
## 37.8875 37.89533 37.91083 37.93455 37.940135 37.94181
## 1 1 1 1 1 1
## 37.94261 37.944408 37.963297 37.9702 37.972548 37.976654
## 1 1 1 1 1 1
## 38.003663 38.004227 38.008562 38.0251564 38.025394 38.04121
## 4 1 1 1 1 1
## 38.045747 38.061436 38.066978 38.08131 38.090565 38.09072
## 1 1 1 1 1 1
## 38.09347 38.093693 38.09496 38.09973 38.1019 38.1021533
## 1 1 1 1 1 1
## 38.12745 38.13059 38.1337 38.17264002 38.19639 38.205021
## 1 1 2 1 1 1
## 38.215783 38.264304 38.264829 38.26485 38.27373 38.274267
## 1 1 1 1 1 1
## 38.28366 38.28588 38.32113 38.332983 38.3362 38.338614
## 1 1 2 1 1 1
## 38.339275 38.339543 38.340005 38.34021 38.34024 38.34044
## 1 1 1 1 1 1
## 38.341141 38.34136 38.344339 38.34519 38.352573 38.35257318
## 1 1 2 1 1 1
## 38.36098 38.36818 38.3693 38.37239 38.37783053 38.377992
## 1 1 1 1 1 1
## 38.38052 38.38154 38.38166 38.47623 38.501433 38.501817
## 1 1 1 1 1 1
## 38.50252 38.55560816 38.569474 38.581933 38.58556 38.585632
## 1 1 1 1 1 1
## 38.5997 38.6092 38.617704 38.622839 38.62313 38.623253
## 1 1 1 1 1 1
## 38.63064 38.66916 38.6707 38.680985 38.72582 38.73302
## 1 1 1 1 1 1
## 38.776587 38.77706 38.780153 38.780525 38.78564 38.78777
## 1 1 1 1 1 1
## 38.78778 38.789242 38.7893921 38.79106 38.7919 38.792059
## 1 1 1 1 1 1
## 38.792939 38.793803 38.81386 38.814911 38.82204 38.82204498
## 2 1 1 1 2 2
## 38.82684 38.827249 38.828047 38.82855 38.829252 38.832199
## 1 1 1 1 1 1
## 38.834923 38.835046 38.83618 38.845635 38.848525 38.851604
## 1 1 1 1 1 1
## 38.852094 38.863322 38.866606 38.869483 38.88144 38.88162
## 1 1 1 1 1 1
## 38.88188 38.91689 38.923554 38.938778 38.939028 38.94905
## 1 1 1 1 1 1
## 38.95973 38.98742 38.98759 39.0081 39.025364 39.025586
## 1 1 1 1 1 1
## 39.02601 39.02942 39.03517 39.03543 39.0355 39.04705
## 1 1 1 2 1 1
## 39.04758 39.060075 39.06405 39.080486 39.08605 39.10878
## 1 1 1 1 1 1
## 39.120239 39.12071 39.12851 39.12889 39.136219 39.13776
## 1 1 2 1 1 1
## 39.13805 39.13839 39.13844 39.1393 39.1402 39.15386
## 1 1 1 1 1 1
## 39.173564 39.17837 39.191028 39.193056 39.22226 39.230426
## 1 1 1 1 1 1
## 39.252793 39.27126 39.277928 39.305031 39.323679 39.32604
## 1 1 1 1 1 1
## 39.3271159 39.328029 39.36101 39.36139 39.36293 39.363277
## 1 1 1 2 1 1
## 39.36359 39.36863 39.369394 39.37571 39.38235 39.395483
## 1 1 1 1 1 1
## 39.40797563 39.411914 39.414038 39.45627 39.46308 39.482631
## 1 1 1 1 1 1
## 39.484724 39.506925 39.517036 39.544 39.587875 39.5894
## 2 1 1 1 1 1
## 39.59606 39.60887 39.61412 39.632574 39.64343 39.67171
## 1 1 1 1 1 1
## 39.673538 39.67439 39.68524 39.6854 39.70736769 39.70808
## 1 1 1 1 1 1
## 39.711344 39.71864 39.72708 39.74636 39.75888 39.763568
## 1 1 1 1 1 1
## 39.772846 39.784839 39.7859444 39.786953 39.789126 39.800348
## 1 1 1 1 1 1
## 39.8106 39.816597 39.81694 39.8188 39.822925 39.8411
## 1 1 1 1 1 1
## 39.844773 39.84512 39.84515 39.84541 39.8458 39.846349
## 1 1 1 1 1 2
## 39.846715 39.846972 39.849005 39.85162 39.853611 39.86216
## 1 2 1 1 1 1
## 39.862222 39.8653 39.86822 39.89486 39.8955 39.896
## 1 1 1 1 1 1
## 39.897834 39.915961 39.91934 39.94024 39.96675 39.9923
## 1 1 1 1 1 1
## 39.995669 40.002304 40.010475 40.039849 40.041721 40.069353
## 1 1 1 1 1 1
## 40.091758 40.111093 40.136819 40.16005 40.162536 40.16833
## 1 1 2 1 2 1
## 40.20069 40.203611 40.203877 40.21421 40.262706 40.262939
## 1 1 1 1 2 1
## 40.265185 40.279346 40.291648 40.291729 40.29213 40.29832
## 1 1 1 1 1 1
## 40.31277 40.31491 40.318604 40.3196 40.3375 40.34117
## 2 1 1 1 1 1
## 40.351944 40.352903 40.36468 40.36474 40.366817 40.395534
## 1 2 1 1 1 1
## 40.401 40.40966 40.4101 40.4329 40.456096 40.45772
## 1 1 1 1 1 1
## 40.47829444 40.480804 40.4840972 40.505602 40.513477 40.513554
## 1 1 1 1 1 1
## 40.514382 40.51608 40.5161701 40.519254 40.519728 40.519942
## 1 1 1 1 1 1
## 40.519999 40.52243 40.52275 40.523327 40.535033 40.535833
## 1 32 1 4 1 1
## 40.536111 40.547339 40.548003 40.550801 40.55081 40.550972
## 1 1 1 1 1 1
## 40.5566 40.563565 40.57083 40.574722 40.57667 40.57704
## 1 1 2 1 1 1
## 40.57729 40.57741 40.58061 40.58513 40.58547 40.585479
## 1 1 1 1 1 3
## 40.588225 40.588583 40.58888 40.589 40.58925 40.590142
## 2 1 1 1 1 1
## 40.590422 40.59063 40.59064 40.590763 40.591463 40.591656
## 1 2 2 1 1 1
## 40.59213 40.593267 40.59348 40.59441 40.596305 40.6017
## 1 1 1 1 1 1
## 40.605222 40.6054 40.60545 40.60614 40.606466 40.606837
## 1 1 1 1 1 1
## 40.608154 40.608272 40.608277 40.6082833 40.608328 40.6084
## 1 1 1 1 1 1
## 40.608511 40.6086 40.609013 40.609164 40.609186 40.609319
## 1 1 1 1 1 1
## 40.61145 40.61154 40.612444 40.61428 40.620667 40.621988
## 1 1 1 1 1 1
## 40.62252 40.6246 40.630937 40.631074 40.647936 40.64995921
## 1 1 1 1 2 1
## 40.650639 40.650953 40.654111 40.65728842 40.657443 40.657792
## 1 1 1 1 1 1
## 40.6581344 40.661111 40.66506 40.676504 40.689287 40.69436
## 1 1 1 1 1 1
## 40.6945 40.695592 40.696043 40.697102 40.697155 40.6972222
## 1 1 1 1 1 1
## 40.697527 40.697537 40.701149 40.70498 40.706216 40.706418
## 1 2 1 1 1 1
## 40.7076 40.70825 40.708665 40.70942 40.70945 40.711466
## 1 3 1 1 1 1
## 40.711686 40.73625 40.74573 40.759869 40.76505 40.766643
## 1 1 1 1 1 1
## 40.770458 40.78155 40.80216 40.803479 40.804771 40.831354
## 1 1 1 1 1 1
## 40.858546 40.894805 40.94267 40.943291 40.944856 40.97604
## 1 1 1 1 1 1
## 41.01816 41.04755 41.056079 41.090482 41.10621 41.11988
## 1 1 1 1 1 1
## 41.123379 41.126883 41.1274 41.14364 41.148878 41.1784
## 1 2 2 2 1 1
## 41.17974 41.184974 41.187143 41.21235 41.2289 41.255797
## 1 1 1 1 1 1
## 41.255807 41.258087 41.27461 41.274678 41.286642 41.2885
## 1 1 1 1 1 1
## 41.299079 41.307 41.311708 41.31825 41.322508 41.34767937
## 1 1 1 1 2 1
## 41.35429 41.36417 41.38284113 41.39281106 41.395652 41.40817
## 1 1 1 1 1 1
## 41.410372 41.410931 41.41355 41.414332 41.4145 41.41579
## 1 1 1 1 1 1
## 41.419421 41.421858 41.435852 41.437931 41.49188 41.49806
## 1 1 1 1 1 1
## 41.50506 41.50667 41.507105 41.508897 41.510158 41.511142
## 1 1 1 1 1 1
## 41.51458 41.51487 41.51556 41.51616 41.51718 41.51769
## 1 1 1 1 1 1
## 41.52278 41.529826 41.532684 41.5543361 41.55455 41.55556
## 1 1 1 1 1 2
## 41.5569 41.55694 41.55804 41.55849 41.56244 41.56348
## 2 1 1 1 1 1
## 41.5652 41.565497 41.56563 41.577697 41.606561 41.60720541
## 1 1 1 1 1 1
## 41.6076 41.60766736 41.60865 41.609732 41.609953 41.612919
## 2 2 1 1 1 1
## 41.6136 41.61566 41.616693 41.61955 41.619586 41.621205
## 1 1 1 1 1 1
## 41.62247 41.62263 41.6234 41.626461 41.62672 41.626855
## 1 1 1 1 1 1
## 41.63156 41.63611 41.639016 41.640712 41.6424 41.642669
## 1 1 1 1 1 1
## 41.643229 41.644119 41.644934 41.645101 41.6514111 41.655265
## 1 1 1 1 1 1
## 41.658008 41.659288 41.6671 41.67284 41.67288 41.675883
## 1 1 1 2 1 1
## 41.68140797 41.68148 41.684108 41.68411 41.684292 41.686997
## 1 1 1 1 1 1
## 41.6872222 41.6877778 41.69229 41.697667 41.73889472 41.752979
## 1 1 1 1 1 2
## 41.7643 41.7678 41.7731 41.782605 41.78788 41.800416
## 1 1 1 1 1 1
## 41.801632 41.805792 41.806608 41.80708 41.828677 41.831164
## 1 1 1 1 1 1
## 41.844019 41.8458333 41.86305 41.890476 41.90199 41.90877
## 1 1 1 1 1 1
## 41.93695 41.93805 41.94352 41.95138 42.00461 42.02244
## 1 2 1 1 1 1
## 42.024045 42.024238 42.053138 42.05679 42.06139 42.07471
## 1 1 1 1 1 1
## 42.1043 42.11445 42.115822 42.116313 42.12294 42.131311
## 1 1 1 1 1 1
## 42.133334 42.1514 42.183809 42.20753 42.20813 42.222753
## 1 1 1 1 2 1
## 42.225543 42.22588 42.225925 42.226368 42.23326 42.24329
## 1 1 1 1 1 1
## 42.26259 42.272024 42.2748 42.278472 42.282925 42.308506
## 1 1 1 1 1 1
## 42.308627 42.352666 42.38229 42.45589 42.46833 42.514136
## 1 1 1 1 1 1
## 42.51862 42.5325 42.53632 42.53743 42.53889 42.53934
## 1 1 1 1 1 1
## 42.557406 42.56794 42.5783333 42.63521 42.72143 42.73839
## 1 1 1 1 1 1
## 42.79375 42.80667 42.81144 42.849051 42.851147 42.854755
## 1 1 1 1 1 1
## 42.854803 42.855444 42.864441 42.870358 42.87907 42.8842
## 1 1 2 1 1 1
## 42.887382 42.88895 42.9015 42.917984 42.9289 42.94222
## 1 1 1 2 1 1
## 42.9517 42.957732 42.957763 42.959503 42.9916667 43.016283
## 1 1 1 1 1 1
## 43.0456 43.05284 43.080915 43.114444 43.14017 43.1407
## 1 1 1 1 1 1
## 43.189245 43.2180944 43.240356 43.26707 43.286542 43.29183
## 1 1 1 1 1 1
## 43.29194 43.2930556 43.297089 43.31996 43.37233 43.38106666
## 1 1 1 1 1 1
## 43.3831 43.42656 43.4625 43.475465 43.50343 43.51946392
## 1 1 1 1 1 1
## 43.54566 43.54571 43.58698 43.6067 43.635 43.6666
## 1 1 1 1 1 1
## 43.666603 43.66693333 43.67297971 43.72077 43.72835 43.78306944
## 1 1 1 1 1 1
## 43.78507 43.78774166 43.787925 43.787975 43.788025 43.78813056
## 1 1 1 1 1 1
## 43.78846666 43.788561 43.788581 43.78913 43.791797 43.832639
## 1 1 1 1 3 1
## 43.842033 43.8516667 43.860695 43.861789 43.87591331 43.895611
## 1 2 1 1 1 1
## 43.93146 43.94028 43.94200833 43.94972 43.9567944 43.965346
## 1 1 1 1 1 1
## 43.992624 44.000221 44.021949 44.05727 44.069 44.15348
## 1 1 1 1 1 1
## 44.26055 44.378889 44.37956 44.460839 44.5311 44.62351
## 1 1 1 1 1 1
## 44.642128 44.665449 44.66547 44.67167 44.73368 44.73486
## 1 1 1 1 1 1
## 44.759651 44.77084 44.77085 44.77328 44.788806 44.7937698
## 1 1 1 1 1 1
## 44.803407 44.815639 44.815919 44.81602 44.817233 44.85338
## 1 1 1 1 1 1
## 44.87601 44.94151 45.010556 45.05919 45.143056 45.152093
## 1 1 1 1 2 1
## 45.15209388 45.206089 45.238011 45.250322 45.479889 45.526048
## 1 1 1 1 1 1
## 45.565381 45.56545 45.569231 45.655486 45.65804642 45.672992
## 1 1 1 1 1 1
## 45.698007 45.698036 45.722409 45.77906 45.78611 45.792899
## 1 1 1 1 1 1
## 45.79417 45.794368 45.883706 45.89341 45.894167 45.89504
## 1 1 1 1 1 1
## 45.95307 45.97528 46.2199 46.24913 46.359919 46.370782
## 1 1 1 1 1 2
## 46.38995 46.39053 46.41379 46.41428 46.49535 46.6178
## 1 1 1 1 1 1
## 46.68329 46.683889 46.6869 46.6885 46.688674 46.68889
## 1 1 1 1 1 5
## 46.68904 46.6893 46.689722 46.69 46.69354 46.71782754
## 1 1 1 1 1 1
## 46.8197 46.81973992 46.851256 46.861678 46.877218 46.902916
## 1 1 1 1 1 1
## 46.93944 46.9803 47.03163 47.089551 47.0966335 47.09855
## 1 1 1 1 1 1
## 47.0988 47.098889 47.104525 47.12312 47.1375 47.261205
## 1 1 1 1 1 1
## 47.30177 47.303798 47.31006 47.324386 47.32444 47.325278
## 1 1 1 1 3 1
## 47.32556 47.372103 47.378551 47.38361 47.458331 47.4593167
## 2 1 1 1 1 1
## 47.52353 47.524128 47.55403 47.582395 47.582544 47.634874
## 1 1 1 1 1 1
## 47.673856 47.68412 47.685115 47.68857 47.68889 47.689461
## 1 1 1 1 4 1
## 47.6895 47.68973 47.6899 47.71696 47.732308 47.7606333
## 1 1 1 1 1 1
## 47.7826 47.78822 47.80327 47.805537 47.86055 47.882222
## 1 1 1 1 1 1
## 47.90556 47.907607 47.91906322 47.921839 47.92555 47.934931
## 1 1 1 1 1 1
## 47.96935 47.97958 48.014962 48.112149 48.21111 48.2351
## 1 1 1 1 1 1
## 48.24063 48.24275 48.27904 48.284494 48.304045 48.323422
## 1 1 1 1 1 1
## 48.325686 48.325724 48.331143 48.365352 48.39475 48.39696
## 1 1 1 1 1 1
## 48.455641 48.524251 48.7134237 48.720364 48.81835 48.85108984
## 3 1 1 2 1 1
## 48.888796 48.96572 48.99555 50.839319 63.42546 63.93074
## 1 1 1 1 1 1
## 65.31111 66.812823 67.7987 70.10762 70.15120454 70.25666
## 1 1 2 1 1 1
## 70.257147 70.261265
## 1 15 Tabla de frecuencia
5.1 Regla de sturges
Extraemos la variable latitud, omitimos las celdas en blanco o valores iguales a cero y verificamos el tamaño muestral. En la tabla de distribución de frecuencias de la variable Latitud del Accidente, el número de clases se determinó mediante la regla de Sturges y el ancho de clase se calculó a partir del rango geoespacial total de los datos, asegurando una cobertura completa desde la coordenada más al Sur hasta la más al Norte.
# Cargar librería necesaria para la tabla
library(knitr)
# Cargar y limpiar datos
df <- read.csv("database-_1_.csv", header = TRUE, sep = ",", dec = ".")
Accident_Latitude <- df$Accident.Latitude
Accident_Latitude <- na.omit(Accident_Latitude)
# 1. Regla de Sturges (Rango, K, Amplitud)
xmin <- min(Accident_Latitude)
xmax <- max(Accident_Latitude)
R <- xmax - xmin
# Usamos round y 3.322 para mayor precisión estadística
K <- round(1 + 3.322 * log10(length(Accident_Latitude)))
A <- R / K
# 2. Límites y Marca de Clase
Li <- round(seq(from = xmin, by = A, length.out = K), 2)
Ls <- round(seq(from = xmin + A, by = A, length.out = K), 2)
MC <- round((Li + Ls) / 2, 2)
# 3. Frecuencias Absolutas (ni)
ni <- numeric(K)
# Bucle corregido
for (i in 1:(K-1)) {
ni[i] <- sum(Accident_Latitude >= Li[i] & Accident_Latitude < Ls[i])
}
# Asegurar que el último dato se incluya en el último intervalo
ni[K] <- sum(Accident_Latitude >= Li[K] & Accident_Latitude <= xmax)
# 4. Frecuencias Relativas y Acumuladas
hi <- ni / sum(ni) * 100
Ni_asc <- cumsum(ni)
Ni_desc <- rev(cumsum(rev(ni)))
Hi_asc <- cumsum(hi)
Hi_desc <- rev(cumsum(rev(hi)))
# 5. Construcción del Dataframe
TDF <- data.frame(
Li, Ls, MC, ni,
hi_porc = round(hi, 2),
Ni_asc, Ni_desc,
Hi_asc_porc = round(Hi_asc, 2),
Hi_desc_porc = round(Hi_desc, 2)
)
TDF_a <- subset(TDF, ni > 0)
kable(TDF_a,
row.names = FALSE,
caption = "Tabla No. 1: Distribución de Frecuencias de latitud del accidente",
col.names = c("Lím. Inf.", "Lím. Sup.", "Marca Clase", "ni", "hi (%)", "Ni Asc.", "Ni Desc.", "Hi Asc. (%)", "Hi Desc. (%)"),
digits = 2)| Lím. Inf. | Lím. Sup. | Marca Clase | ni | hi (%) | Ni Asc. | Ni Desc. | Hi Asc. (%) | Hi Desc. (%) |
|---|---|---|---|---|---|---|---|---|
| 18.45 | 22.77 | 20.61 | 3 | 0.11 | 3 | 2794 | 0.11 | 100.00 |
| 22.77 | 27.08 | 24.92 | 3 | 0.11 | 6 | 2791 | 0.21 | 99.89 |
| 27.08 | 31.40 | 29.24 | 733 | 26.23 | 739 | 2788 | 26.45 | 99.79 |
| 31.40 | 35.72 | 33.56 | 759 | 27.17 | 1498 | 2055 | 53.61 | 73.55 |
| 35.72 | 40.04 | 37.88 | 580 | 20.76 | 2078 | 1296 | 74.37 | 46.39 |
| 40.04 | 44.35 | 42.20 | 525 | 18.79 | 2603 | 716 | 93.16 | 25.63 |
| 44.35 | 48.67 | 46.51 | 171 | 6.12 | 2774 | 191 | 99.28 | 6.84 |
| 48.67 | 52.99 | 50.83 | 9 | 0.32 | 2783 | 20 | 99.61 | 0.72 |
| 61.63 | 65.94 | 63.78 | 3 | 0.11 | 2786 | 11 | 99.71 | 0.39 |
| 65.94 | 70.26 | 68.10 | 8 | 0.29 | 2794 | 8 | 100.00 | 0.29 |
5.2 Tabla simplificada
Se seleccionó el rango central de la variable Latitud del Accidente para el análisis, omitiendo las coordenadas atípicas (outliers), debido a que en esta zona se concentra la mayor densidad de los datos. Esta elección permite construir la tabla de frecuencia y gráficas más claras y legibles, facilitando la interpretación de la distribución espacial de los siniestros y evitando distorsiones visuales provocadas por ubicaciones extremas (por ejemplo, en latitudes muy altas) con baja frecuencia.
# Cargar librería necesaria
library(knitr)
# 1. Cálculos de Sturges
xmin <- min(Accident_Latitude)
xmax <- max(Accident_Latitude)
R <- xmax - xmin
K <- round(1 + 3.322 * log10(length(Accident_Latitude)))
A <- R / K
# 2. Límites y Marca de Clase
Li <- round(seq(from = xmin, by = A, length.out = K), 2)
Ls <- round(seq(from = xmin + A, by = A, length.out = K), 2)
MC <- round((Li + Ls) / 2, 2)
# 3. Formato del Intervalo
Intervalo <- paste0("[", Li, " - ", Ls, ")")
Intervalo[K] <- paste0("[", Li[K], " - ", Ls[K], "]")
# 4. Frecuencias Absolutas (ni)
ni <- numeric(K)
for (i in 1:(K-1)) {
ni[i] <- sum(Accident_Latitude >= Li[i] & Accident_Latitude < Ls[i])
}
ni[K] <- sum(Accident_Latitude >= Li[K] & Accident_Latitude <= xmax)
# 5. Frecuencia Relativa
hi_porc <- round((ni / sum(ni)) * 100, 2)
# 6. Construcción del Dataframe
TDF_simple <- data.frame(
Intervalo,
MC,
ni,
hi_porc
)
# NUEVO: Filtrar las filas omitiendo los ceros
TDF_sin_ceros <- subset(TDF_simple, ni > 0)
# 7. Renderizado de la Tabla (con row.names = FALSE)
kable(TDF_sin_ceros,
row.names = FALSE,
caption = "Tabla No. 2: Distribución de Frecuencias de latitud (Simplificada)",
col.names = c("Intervalo", "Marca Clase", "Frec. Absoluta (ni)", "Frec. Relativa (%)"),
align = "c")| Intervalo | Marca Clase | Frec. Absoluta (ni) | Frec. Relativa (%) |
|---|---|---|---|
| [18.45 - 22.77) | 20.61 | 3 | 0.11 |
| [22.77 - 27.08) | 24.92 | 3 | 0.11 |
| [27.08 - 31.4) | 29.24 | 733 | 26.23 |
| [31.4 - 35.72) | 33.56 | 759 | 27.17 |
| [35.72 - 40.04) | 37.88 | 580 | 20.76 |
| [40.04 - 44.35) | 42.20 | 525 | 18.79 |
| [44.35 - 48.67) | 46.51 | 171 | 6.12 |
| [48.67 - 52.99) | 50.83 | 9 | 0.32 |
| [61.63 - 65.94) | 63.78 | 3 | 0.11 |
| [65.94 - 70.26] | 68.10 | 8 | 0.29 |
6 Gráficas
6.1 Cantidad de latitud del accidente
Esta visualización macroscópica modela la función de masa espacial en su dominio latitudinal absoluto. El histograma global permite identificar la dispersión total de los eventos y la posible presencia de asimetrías generadas por ubicaciones muy al norte o al sur del clúster principal.
library(ggplot2)
library(dplyr)
library(scales)
datos <- read.csv("database-_1_.csv")
variable_interes <- na.omit(datos$Accident.Latitude)
volumen <- variable_interes
k <- 1 + (3.322 * log10(length(volumen)))
bins_calc <- floor(k)
p_global <- ggplot(data.frame(val=volumen), aes(x = val)) +
geom_histogram(bins = 30, fill = "steelblue", color = "white", alpha = 0.8) +
scale_x_continuous(labels = number_format(suffix = "°")) +
scale_y_continuous(expand = expansion(mult = c(0, 0.05))) +
labs(
title = "Gráfica 1: Distribución Global de Latitud del Accidentes",
x = "Latitud Geográfica (°)",
y = "Cantidad de Accidentes"
) +
theme_classic() +
theme(
plot.title = element_text(hjust = 0.5, face = "bold"),
axis.text.x = element_text(angle = 45, hjust = 1)
)
print(p_global)
6.2 Cantidad de latitud del accidente
Al aislar estadísticamente las colas de la distribución, este apartado evalúa de forma exclusiva el núcleo operativo. Esta amplificación visual revela el comportamiento empírico de la densidad de incidentes en la franja latitudinal de mayor criticidad.
library(ggplot2)
library(dplyr)
library(scales)
limit_min_zoom <- quantile(variable_interes, 0.10) # Cortamos el 10% inferior
limit_max_zoom <- quantile(variable_interes, 0.90) # Cortamos el 10% superior
datos_zoom <- datos %>%
filter(!is.na(Accident.Latitude)) %>%
filter(Accident.Latitude >= limit_min_zoom & Accident.Latitude <= limit_max_zoom)
p_zoom_5barras <- ggplot(datos_zoom, aes(x = Accident.Latitude)) +
geom_histogram(bins = 10, fill = "steelblue", color = "white", alpha = 0.8) +
scale_x_continuous(labels = number_format(accuracy = 0.1, suffix = "°")) +
scale_y_continuous(expand = expansion(mult = c(0, 0.05))) +
labs(
title = paste("Gráfica No 2: Distribución detallada en rango principal\n(", round(limit_min_zoom,1), "° a", round(limit_max_zoom,1), "°)"),
x = "Latitud Geográfica (°)",
y = "Cantidad"
) +
theme_classic() +
theme(
plot.title = element_text(hjust = 0.5, face = "bold"),
axis.text.x = element_text(hjust = 0.5)
)
print(p_zoom_5barras)
6.3 Cantidad relativa de latitud del accidente
La transformación estocástica de frecuencias absolutas a proporciones relativas internas permite evaluar la probabilidad de ocurrencia de un evento dentro de los sub-intervalos del núcleo principal, estandarizando la escala de análisis latitudinal.
p_zoom_5barras_pct <- ggplot(datos_zoom, aes(x = Accident.Latitude)) +
geom_histogram(
aes(y = after_stat(count / sum(count))),
bins = 10,
fill = "steelblue",
color = "white",
alpha = 0.8
) +
scale_x_continuous(labels = number_format(accuracy = 0.1, suffix = "°")) +
scale_y_continuous(
labels = scales::percent_format(accuracy = 1),
expand = expansion(mult = c(0, 0.05))
) +
labs(
title = "Gráfica No 3: Distribución porcentual local del rango principal",
x = "Latitud Geográfica (°)",
y = "Porcentaje (%)"
) +
theme_classic() +
theme(
plot.title = element_text(hjust = 0.5, face = "bold"),
axis.text.x = element_text(hjust = 0.5)
)
print(p_zoom_5barras_pct)
6.4 Cantidad relativa de latitud del accidente
Para dimensionar el peso real de la zona de aglomeración, se contrastan las frecuencias del rango principal contra el universo total de los datos. Esto cuantifica la probabilidad empírica de que un accidente aleatorio pertenezca a este corredor Norte-Sur específico.
p_zoom_5barras_100 <- ggplot(datos_zoom, aes(x = Accident.Latitude)) +
geom_histogram(
aes(y = after_stat(count / sum(count))),
bins = 10,
fill = "steelblue",
color = "white",
alpha = 0.8
) +
scale_x_continuous(labels = number_format(accuracy = 0.1, suffix = "°")) +
scale_y_continuous(
labels = scales::percent_format(accuracy = 1),
limits = c(0, 1), # Escala de 0 a 100%
expand = expansion(mult = c(0, 0.05))
) +
labs(
title = "Gráfica No 4: Distribución porcentual global del rango principal",
x = "Latitud Geográfica (°)",
y = "Porcentaje (%)"
) +
theme_classic() +
theme(
plot.title = element_text(hjust = 0.5, face = "bold"),
axis.text.x = element_text(hjust = 0.5)
)
print(p_zoom_5barras_100)
6.5 Ojivas combinadas
El modelado de la función de distribución acumulada (FDA) bidireccional cartografía la progresión espacial de los incidentes. La intersección de las trayectorias Sur-Norte (ascendente) y Norte-Sur (descendente) señala gráficamente la mediana espacial de la siniestralidad.
library(ggplot2)
library(dplyr)
library(scales)
# Datos locales (del rango principal definido antes)
datos_local <- variable_interes[variable_interes >= limit_min_zoom & variable_interes <= limit_max_zoom]
k_local <- 10 # Número de cortes para la ojiva
min_val <- min(datos_local)
max_val <- max(datos_local)
R_local <- max_val - min_val
A_local <- R_local / k_local
Li_num <- seq(min_val, max_val - A_local, length.out = k_local)
Ls_num <- Li_num + A_local
ni_local <- numeric(k_local)
for(i in 1:k_local){
if(i == k_local){
ni_local[i] <- sum(datos_local >= Li_num[i] & datos_local <= max_val)
} else {
ni_local[i] <- sum(datos_local >= Li_num[i] & datos_local < Ls_num[i])
}
}
Niasc <- cumsum(ni_local)
Nidsc <- rev(cumsum(rev(ni_local)))
datos_asc <- data.frame(
x = c(min_val, Ls_num),
y = c(0, Niasc),
Tipo = "Ascendente"
)
datos_dsc <- data.frame(
x = c(Li_num, max_val),
y = c(Nidsc, 0),
Tipo = "Descendente"
)
datos_ojivas_plot <- rbind(datos_asc, datos_dsc)
p_ojiva_cruzada_solida <- ggplot(datos_ojivas_plot, aes(x = x, y = y, color = Tipo, linetype = Tipo)) +
geom_line(linewidth = 0.8) +
geom_point(size = 2) +
scale_x_continuous(
labels = scales::number_format(accuracy = 0.1, suffix = "°"),
breaks = scales::pretty_breaks(n = 6)
) +
scale_color_manual(values = c("Ascendente" = "black", "Descendente" = "blue")) +
scale_linetype_manual(values = c("Ascendente" = "solid", "Descendente" = "solid")) +
labs(
title = "Gráfica 5: Ojivas Geoespaciales de latitud",
x = "Latitud Geográfica (°)",
y = "Cantidad Acumulada",
color = NULL,
linetype = NULL
) +
theme_bw() +
theme(
plot.title = element_text(hjust = 0.5, face = "bold", size = 14),
legend.position = c(0.85, 0.5),
legend.background = element_rect(color = "black", fill = "white"),
axis.text = element_text(color = "black")
)
print(p_ojiva_cruzada_solida)
6.6 Diagrama de cajas
Mediante un enfoque no paramétrico, este diagrama evalúa la dispersión central y el rango intercuartílico (RIC) de las coordenadas latitudinales. Es la herramienta visual óptima para comprobar el grado de apuntamiento y el sesgo direccional de la mediana respecto a la media espacial.
variable_box <- datos_local # Usamos el filtro local
par(mar = c(5, 2, 4, 2))
b <- boxplot(variable_box,
horizontal = TRUE,
col = "skyblue",
border = "gray30",
medcol = "red",
boxwex = 0.6,
outline = FALSE,
main = "Gráfica 6: Distribución de Latitud",
xlab = "Latitud (°)",
xaxt = "n",
yaxt = "n",
frame = FALSE
)
limite_visible_inf <- min(variable_box)
limite_visible_sup <- max(variable_box)
puntos_eje <- pretty(c(limite_visible_inf, limite_visible_sup))
axis(1, at = puntos_eje, labels = format(puntos_eje, nsmall = 2), col = "gray30", col.axis = "gray30")
grid(nx = NULL, ny = NA, col = "lightgray", lty = "dotted", lwd = 1)
7 Tabla estadísticos
Como marco de referencia absoluto, se calculan los estimadores univariantes para la totalidad del vector espacial Norte-Sur. La comparación paramétrica con la tabla local permite medir la distorsión matemática introducida por las latitudes extremas.
library(e1071)
library(knitr)
variable_analisis <- variable_interes # Global
n <- length(variable_analisis)
k_global <- floor(1 + 3.322 * log10(n))
R <- max(variable_analisis) - min(variable_analisis)
A_global <- R / k_global
Li <- seq(min(variable_analisis), max(variable_analisis) - A_global, length.out = k_global)
if(max(Li) + A_global < max(variable_analisis)) {
Li <- c(Li, tail(Li, 1) + A_global)
k_global <- k_global + 1
}
Ls <- Li + A_global
MC <- (Li + Ls) / 2
ni <- numeric(length(MC))
for(i in 1:length(MC)){
if(i == length(MC)) ni[i] <- sum(variable_analisis >= Li[i] & variable_analisis <= (max(variable_analisis) + 0.001))
else ni[i] <- sum(variable_analisis >= Li[i] & variable_analisis < Ls[i])
}
media_agrupada <- sum(MC * ni) / sum(ni)
desviacion_estandar <- sd(variable_analisis)
error_estandar <- desviacion_estandar / sqrt(n)
margen_error <- 1.96 * error_estandar
ic_inferior <- media_agrupada - margen_error
ic_superior <- media_agrupada + margen_error
texto_media_intervalo <- paste0("[", format(round(ic_inferior, 2), big.mark=","), " ; ", format(round(ic_superior, 2), big.mark=","), "]")
ri <- min(variable_analisis)
rs <- max(variable_analisis)
mediana <- median(variable_analisis)
t <- table(round(variable_analisis, 1))
Mo <- as.numeric(names(t)[which.max(t)])
cv <- (desviacion_estandar / abs(media_agrupada)) * 100
As <- skewness(variable_analisis)
K <- kurtosis(variable_analisis)
Tabla_global <- data.frame(
"Latitud del accidente",
paste(format(ri, nsmall=2), "°"),
paste(format(rs, nsmall=2), "°"),
texto_media_intervalo,
paste(format(round(mediana, 2), big.mark=","), "°"),
paste(format(round(Mo, 2), big.mark=","), "°"),
paste(format(round(desviacion_estandar, 2), big.mark=","), "°"),
paste(round(cv, 2), "%"),
round(As, 2),
round(K, 2)
)
colnames(Tabla_global) <- c("Variable","Min","Max","Media (IC 95%)","Mediana","Moda","Desv. S","CV","As","K")
kable(Tabla_global, format = "markdown", caption = "Tabla 2: Indicadores Globales de Latitud.")| Variable | Min | Max | Media (IC 95%) | Mediana | Moda | Desv. S | CV | As | K |
|---|---|---|---|---|---|---|---|---|---|
| Latitud del accidente | 18.44801 ° | 70.26126 ° | [35.69 ; 36.11] | 34.93 ° | 30 ° | 5.65 ° | 15.74 % | 1.06 | 2.97 |
7.1 Valores Atípicos
Aplicando el criterio analítico de Tukey sobre los cuartiles globales, esta sección identifica las coordenadas espaciales extremas. Estos puntos representan anomalías geográficas severas, es decir, siniestros ubicados a distancias marginales hacia el extremo Norte o Sur.
# --- ANÁLISIS GLOBAL ---
variable_global <- variable_interes
stats_outliers_global <- boxplot.stats(variable_global)$out
num_outliers_global <- length(stats_outliers_global)
minimooutliers_global <- if(num_outliers_global > 0) min(stats_outliers_global) else NA
maximooutliers_global <- if(num_outliers_global > 0) max(stats_outliers_global) else NA
cat("\n--- Análisis de Outliers---\n")##
## --- Análisis de Outliers---cat("Número de valores atípicos:", num_outliers_global, "\n")## Número de valores atípicos: 11cat("Ubicación más extrema (Min/Sur):", if(!is.na(minimooutliers_global)) paste(format(minimooutliers_global, big.mark=","), "°") else "Ninguno", "\n")## Ubicación más extrema (Min/Sur): 63.42546 °cat("Ubicación más extrema (Max/Norte):", if(!is.na(maximooutliers_global)) paste(format(maximooutliers_global, big.mark=","), "°") else "Ninguno", "\n")## Ubicación más extrema (Max/Norte): 70.26126 °8 Conclusión
La variable continua Latitud del Accidente fluctúa entre 18.44801° y 70.26126°, con valores que giran en torno a una mediana de 34.93°, presentando una desviación estándar de 5.65° y, a diferencia de las variables de impacto, muestra un comportamiento marcadamente homogéneo (CV del 15.74%). Se identifican apenas 11 valores atípicos (anomalías espaciales) que se ubican a partir de los 63.42546° hacia el extremo norte; asimismo, la distribución exhibe una asimetría positiva (1.06) y una curtosis de 2.97 (prácticamente mesocúrtica o de concentración normal), lo cual indica que la gran mayoría de los siniestros se acumulan en latitudes medias. Este resultado refleja un comportamiento geográfico lógico y esperado, ya que evidencia que el núcleo de los derrames ocurre dentro de la densa red de oleoductos del territorio contiguo de EE. UU., dejando los siniestros en zonas remotas (como Alaska) como eventos espacialmente marginales.