Tugas RMarkdown Week 12
Alyaa Nabiilah Afiifah
2025-05-23
Generate Data
Simulasikan 1000 data dengan 80% berdistribusi Gamma dan 20% berdistribusi Weibull
# Simulasi data Gamma
n_gamma <- 0.8 * 1000
data_gamma <- rgamma(n = n_gamma, shape = 2, rate = 0.5)
# Simulasi data Weibull
n_weibull <- 0.2 * 1000
data_weibull <- rweibull(n = n_weibull, shape = 2, scale = 8)
# Gabungkan data
curah_hujan <- c(data_gamma, data_weibull)
curah_hujan## [1] 10.60154071 4.93000435 1.23886549 1.19004010 2.96078601 1.13638147
## [7] 3.39704559 0.80023330 3.91811000 7.31522682 3.05044876 2.29715380
## [13] 3.80355238 6.25462159 2.68069293 12.06370066 3.46924234 5.97798425
## [19] 3.23593678 4.78281761 5.30731378 1.71147754 2.57262685 2.08916414
## [25] 0.80880854 6.27288907 2.05075577 1.53167309 1.24085359 4.45475058
## [31] 3.16589149 8.52900392 1.06797287 0.26470412 5.09321445 0.78010271
## [37] 4.96861669 8.54009008 4.16907301 5.78755240 4.02163960 6.88046256
## [43] 0.38889227 3.85430785 5.63906463 0.17444953 0.57431093 0.57771306
## [49] 5.10627577 0.70648085 1.45089283 5.02951400 3.72032299 2.94136399
## [55] 5.38328392 0.96670565 3.24225565 2.78733953 2.61599364 0.44871821
## [61] 4.67200330 4.54398987 0.50790215 5.62199919 7.75608665 3.09829075
## [67] 2.05954825 0.31412045 3.00556461 5.56702773 4.63255383 2.43527164
## [73] 2.65666856 3.17001916 5.72634846 7.02513992 6.50734232 6.90439529
## [79] 0.35555846 2.15174872 2.17837577 4.13192644 0.63360761 6.34923510
## [85] 1.41689988 4.89597091 1.84941976 6.55013841 2.12558844 1.99027560
## [91] 3.86738738 4.49690660 0.37234289 0.50418179 3.19770214 2.74165387
## [97] 3.13115130 3.36612400 8.77243623 0.47669069 6.53194141 4.33428203
## [103] 4.70898637 2.09609375 1.87180669 1.62911667 0.74539155 4.49652266
## [109] 3.91666299 1.38318334 4.92061776 4.69073578 5.56939223 3.13025493
## [115] 3.91302634 5.19685163 7.90603424 2.98175222 6.43521847 2.26596310
## [121] 8.08990992 3.97719201 0.70216150 4.19769341 0.71697116 4.11452344
## [127] 3.58239082 1.98984854 3.11051376 3.35407132 2.20690755 4.01342001
## [133] 2.86758953 4.45918383 0.99898183 2.06042448 5.23174542 2.21371473
## [139] 5.93496097 4.80777343 6.62294528 1.09660606 2.08546178 0.90094633
## [145] 5.41744686 5.76259790 0.40377080 4.70529593 1.66645383 2.72296783
## [151] 5.60640021 5.93521115 3.01443809 2.34226162 1.94816338 4.03757393
## [157] 5.61996265 1.99372813 1.43285349 11.40278934 0.93795009 3.54648204
## [163] 2.01660828 8.26465346 8.48159846 5.84017576 4.13280364 1.08065387
## [169] 3.65799439 5.80765243 7.12684623 4.07029506 8.83085492 3.00964111
## [175] 7.02627028 7.12199281 1.21839676 7.77642496 5.11449110 2.21080030
## [181] 4.58193869 7.89957288 5.72437093 1.64062955 6.13924920 3.78984308
## [187] 7.25012256 1.18459105 2.71316906 4.11769311 5.82467099 5.36912742
## [193] 1.86818034 6.56627912 12.38591036 6.43921695 1.57113303 2.70300240
## [199] 1.36238100 5.05296257 2.21762056 3.49240263 2.70994803 3.62219337
## [205] 3.19096832 0.97218738 1.86950668 3.64409443 0.90510766 6.08386509
## [211] 4.08805168 3.01215615 1.07723317 3.51216836 10.52492588 14.14410514
## [217] 0.80609974 3.26943996 2.03295606 9.41425923 3.34071728 11.69710360
## [223] 3.93979271 6.31221086 13.50364191 2.46069099 4.43684715 0.22315606
## [229] 5.28554488 1.48009527 4.67613036 3.52558445 2.12500188 1.81458165
## [235] 3.51668710 3.56663081 3.79704291 2.11962541 1.35167598 2.39521857
## [241] 10.46391085 3.39748591 4.12360623 6.92011178 1.72959523 5.52565592
## [247] 7.14457565 2.03432465 7.47586539 7.97182458 4.19450513 8.26879151
## [253] 2.84018205 5.74103967 8.72339534 1.37022853 8.06724673 2.55327709
## [259] 1.79731786 6.26684489 6.15971463 3.22374667 2.45461409 7.51719336
## [265] 2.41182488 10.77899617 1.68368706 4.87093146 6.08762962 5.34706243
## [271] 3.44781346 0.28275540 9.30358212 4.03954432 4.99410102 1.44328485
## [277] 8.47737633 3.81027775 2.17062602 5.73392462 4.54740188 2.53362825
## [283] 4.19578029 1.10180326 6.86387342 1.61102062 1.67193580 2.90295948
## [289] 9.24400555 1.12649222 3.08934870 1.68526641 6.11212526 3.32795151
## [295] 11.73861915 0.27293069 1.10036215 11.46777032 0.85825174 6.84915402
## [301] 1.94127590 1.34535822 1.53669961 6.15038655 1.80997230 3.06080398
## [307] 1.03458431 5.69884958 4.41432603 4.47516303 8.15105790 4.25573014
## [313] 3.45041831 1.56736348 2.84601506 0.84458829 4.77824916 2.41055046
## [319] 3.78169449 2.35290356 2.56658598 1.16225607 4.84966069 1.44708481
## [325] 3.80423671 3.19933008 1.81243764 1.33051836 1.01774397 1.90507167
## [331] 3.28716211 5.58947961 5.03071150 3.68390493 1.63917200 5.98786401
## [337] 3.60498355 1.85307865 2.51282739 5.33394259 1.23573032 2.91914965
## [343] 2.13407937 4.30977659 2.22581290 2.68994361 4.18973445 5.32293893
## [349] 2.43054315 2.68616322 0.85361203 4.93125408 4.15236257 4.23942076
## [355] 1.10193243 0.25987107 6.88848962 2.94217911 1.92863366 6.44770781
## [361] 1.43301278 2.64534537 2.05082621 6.49962359 13.11628903 2.84440827
## [367] 3.72339417 0.96990672 10.88967779 2.15264323 6.64987420 3.04624938
## [373] 4.27808293 1.26013591 2.34887814 3.27454874 7.28945990 1.04442963
## [379] 4.67517708 3.38511138 9.11838216 2.68360643 4.97412546 0.43028595
## [385] 8.58864380 2.82438195 1.75128707 2.14356708 7.75264629 3.13802266
## [391] 1.23708982 7.05985426 3.77133020 3.90711115 5.74620236 2.62419475
## [397] 2.21310739 4.25914277 4.82967489 2.69946835 6.78792415 2.95412417
## [403] 5.76579677 2.55249694 1.67635723 1.09585063 4.77958984 8.85653086
## [409] 1.98676158 4.22587891 5.61636331 0.68971059 5.72233684 3.41633006
## [415] 3.55793448 1.75014802 2.31166855 4.09555468 2.64893402 2.82787737
## [421] 0.64947917 4.74313643 4.02305671 0.67068633 3.11463781 2.54155301
## [427] 1.66565944 5.10583846 6.37422804 8.70347846 11.73953076 4.73396393
## [433] 6.07286557 7.06123525 11.58284556 5.30907067 12.05873076 1.33196288
## [439] 3.17435271 3.21211236 5.37570566 0.34018188 1.73635471 2.57260600
## [445] 0.32748457 2.23316466 5.22040156 4.10830252 5.35656470 3.53363004
## [451] 5.28537180 3.45771212 2.24782413 10.63954251 4.46458463 3.78218644
## [457] 3.24710487 4.07890225 2.57483505 1.14951946 5.02904565 8.14202295
## [463] 4.32379945 9.03136709 4.98989223 1.11612772 3.12345664 3.84476949
## [469] 2.62549682 10.34495373 3.26795119 2.67026967 1.95766043 1.60424007
## [475] 1.30935547 3.54821125 4.18030922 7.61540462 2.64874850 2.71318294
## [481] 1.47914414 4.76937088 5.62349984 5.28704511 0.74407550 5.01994149
## [487] 8.51111760 4.15296544 2.03585006 3.29584422 4.05288423 6.30312372
## [493] 7.22282343 5.55519379 6.39679462 3.09188792 2.23440606 9.99829080
## [499] 5.05030405 1.41090299 4.84179026 1.54090492 2.42372547 5.80440289
## [505] 2.14567396 3.00429885 5.94956202 9.48784393 4.18260747 4.25071817
## [511] 3.37863067 3.09696245 6.58799829 5.79742982 5.19255923 7.43452906
## [517] 4.33853246 3.67548915 6.16916717 5.33637860 1.07616439 0.71293861
## [523] 0.50109320 0.48012880 3.40007632 0.83150711 7.61349438 0.93849039
## [529] 3.42371009 2.94554662 1.77019204 4.26261194 0.45796838 5.83215885
## [535] 3.94856272 4.58388485 0.93745584 2.03710912 12.72781563 5.75513114
## [541] 0.99853772 3.52847455 1.34699786 6.33761777 4.35538658 3.23422361
## [547] 1.19486177 1.84455704 0.46271553 1.55005501 2.68775208 1.03539002
## [553] 0.52917691 0.91812577 2.16961354 0.95300046 4.08735701 2.50636246
## [559] 6.64308894 2.62912598 3.16259217 1.54192173 9.84519535 1.34777708
## [565] 0.55247711 9.57547703 3.95654356 4.32635382 2.63949378 12.94095560
## [571] 1.63094490 5.98795420 4.82216012 2.22529784 3.55496848 5.23252941
## [577] 2.99203207 6.96041118 6.34136892 2.08771939 2.05556534 1.82561442
## [583] 4.69725999 1.12550152 3.16948804 3.25824131 1.88197127 10.37191231
## [589] 2.59125499 5.79736628 1.82335926 4.98553687 0.44132332 0.33453194
## [595] 2.03626272 4.42562853 7.92743292 10.15837794 3.21826772 2.37388260
## [601] 1.85615521 1.56312093 2.64290709 3.51697393 2.29221888 1.26581200
## [607] 5.11860828 5.71332803 4.01858773 3.07549959 0.97521184 8.04443770
## [613] 2.15418733 4.08864414 4.80188663 1.76777330 1.41866054 4.02472006
## [619] 2.33160272 4.86272461 4.07991367 4.63852549 4.24306429 2.61805061
## [625] 4.22714480 1.85339373 7.33478451 1.67375141 3.40888318 8.50894278
## [631] 6.24775901 0.52531847 3.97021937 9.86610133 3.07462200 1.87281567
## [637] 4.35702568 6.52326970 8.13075657 7.93328936 0.80075078 5.04586118
## [643] 0.68891566 6.15081258 1.61200513 1.86308303 6.58228988 1.79447669
## [649] 7.77491269 1.66199285 1.91043843 3.20573056 2.65706487 3.38905827
## [655] 3.92683424 4.76047401 1.69412152 1.99457416 2.64887045 0.35268105
## [661] 1.22834986 0.70884075 6.04794099 3.11737959 4.56455126 1.66964954
## [667] 3.45620891 3.64369220 1.99142142 4.38807361 1.42698049 1.67759657
## [673] 7.41964330 2.92676344 7.54918543 4.43064423 9.36855489 8.21872456
## [679] 0.62845575 4.25886760 3.94376020 6.12581585 1.08530634 0.84984967
## [685] 5.17468011 3.58323769 1.39571142 0.04951099 2.79549594 0.63699191
## [691] 4.44385027 4.13658894 3.79922951 2.54901706 10.88634624 2.66810428
## [697] 1.75779738 3.86708584 1.64502471 4.02551262 12.97473966 6.67577808
## [703] 6.04874182 3.10174272 3.99271053 3.28075314 3.98817335 1.40310929
## [709] 1.07872010 10.25668393 3.42462136 7.67160105 6.14752413 1.59849260
## [715] 2.54862444 2.80138813 4.29382262 3.33561866 11.00387879 3.45662705
## [721] 1.94883614 6.32588225 2.51778925 2.07948263 2.09998749 1.14085565
## [727] 6.78425673 2.99703743 5.18232530 4.48530192 4.38719736 3.75498376
## [733] 5.25468279 10.07528337 4.75570337 11.49386188 2.92045989 0.76924122
## [739] 4.04285867 1.46674790 12.03200717 0.56581747 0.97015319 4.62856133
## [745] 3.99097709 3.03863011 3.40302721 3.28271373 7.09026625 0.72937210
## [751] 7.19754110 3.69595477 2.14883257 4.18580770 7.51059577 4.03604187
## [757] 3.08889348 7.36056809 4.23888109 10.71775001 0.78319155 3.26103746
## [763] 2.71010188 5.23525298 1.43220165 2.07876726 0.51144913 0.91950171
## [769] 3.49504848 1.10713472 9.28753141 6.38701206 9.59848504 2.57749138
## [775] 9.48817134 6.51948576 1.83692683 2.36013056 5.89330923 1.42996884
## [781] 4.09317909 10.75216984 0.90261222 1.60744523 7.34539162 1.24353927
## [787] 5.44659084 4.86079483 4.38643251 7.76135339 2.97745086 3.38910838
## [793] 1.22329389 0.56318608 3.89210603 9.99851142 6.20036054 5.59123888
## [799] 5.17868979 2.05652379 5.40471029 1.22645796 2.65756089 9.83631602
## [805] 13.70008163 1.23503305 8.02180576 3.11063722 8.75128182 15.08794929
## [811] 9.92007996 14.29374455 8.23614273 2.52367195 9.36426860 8.86424630
## [817] 11.32174413 11.63413135 3.56568645 15.14393290 2.17856890 7.96190252
## [823] 9.50894343 4.88295131 2.47449558 11.56419783 7.52333356 6.25794415
## [829] 10.69890256 2.54673406 5.62780347 10.51863297 1.57352941 4.38722666
## [835] 1.27966365 6.33670020 5.40395712 5.48505484 5.39425461 5.18318453
## [841] 7.17357422 4.58739294 11.45559205 10.01379712 3.33400003 7.78365992
## [847] 6.40527500 5.58606237 5.88920575 0.96358742 9.48440833 2.49157240
## [853] 2.59152097 4.40161356 6.86665232 10.36955432 6.03893049 0.68797335
## [859] 4.30093177 4.32178648 10.83890394 9.87952656 6.37653958 8.28857992
## [865] 4.45944222 4.41859834 5.99892825 9.80991511 8.48704258 5.07690118
## [871] 6.86886027 5.51520333 8.37773226 9.44990884 1.61406054 5.43417749
## [877] 14.69016644 14.21269581 3.74774952 3.61699409 4.87372237 8.60391697
## [883] 5.21585803 13.68054274 2.36801760 7.28640165 14.00637525 9.46663183
## [889] 5.15620702 13.85775525 6.75812819 4.74982075 2.48067816 10.32281256
## [895] 6.26986370 6.47240295 7.98539916 4.02855509 3.10266614 2.17676290
## [901] 5.79372808 3.52888930 12.42663682 12.52122580 9.91117848 3.54419893
## [907] 4.17173323 7.35523371 14.93206834 5.60555348 8.44776205 3.16463144
## [913] 11.18164288 7.91007949 3.13997795 14.40500278 8.79349196 7.13135790
## [919] 2.46351237 2.83866827 8.67913531 1.64567126 6.21845378 11.15823904
## [925] 10.29492138 5.92144051 9.16054643 1.80594249 8.57515925 3.39471732
## [931] 4.75325214 3.50648945 2.51290659 9.11697531 4.77812928 5.67919926
## [937] 12.63330594 1.97653520 12.13304282 7.01412710 9.83883041 4.62152012
## [943] 7.63017010 9.44620683 5.41757667 7.19315229 5.59872416 15.43412207
## [949] 10.29658826 5.12535304 9.18997567 11.12183499 3.81089957 2.96594768
## [955] 8.20456784 8.71867257 3.31027790 4.85780839 2.27104694 12.15716942
## [961] 5.27485607 6.67804233 9.57215352 3.26435226 6.49764022 8.09703582
## [967] 4.56355185 10.01322553 3.43751890 4.80191879 9.86862851 5.86296359
## [973] 2.45916098 7.59694049 3.45850596 2.16434787 6.44910573 8.34205889
## [979] 4.25618087 4.39337910 13.31697446 1.77417901 6.46534282 3.72088600
## [985] 1.28022860 2.96608283 7.44435063 5.95158334 6.99110665 16.92276324
## [991] 5.48555224 11.63706695 2.64995320 1.71075067 15.53555268 8.39145232
## [997] 7.19005478 3.92970186 3.84797676 1.83902049Summary
summary(curah_hujan)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.04951 2.15380 3.91739 4.53284 6.11555 16.92276Histogram
hist(curah_hujan,
main = "Histogram Curah Hujan",
xlab = "Curah Hujan",
col = "lavender",
border = "purple")
Data banyak terpusat di sebelah kiri
Boxplot
boxplot(curah_hujan,
main = "Boxplot Curah Hujan",
ylab = "Curah Hujan",
col = "pink",
border = "black",
outcol = "red")
Rentang data cukup kecil dan memiliki banyak outlier atas
Fitting Distribution
# FITDISTRPLUS
library(fitdistrplus)## Warning: package 'fitdistrplus' was built under R version 4.3.3## Loading required package: MASS## Loading required package: survival## Warning: package 'survival' was built under R version 4.3.3library(logspline)## Warning: package 'logspline' was built under R version 4.3.3x = curah_hujan
## Fitting
wei_ = fitdist(x, "weibull")
gamma_ = fitdist(x, "gamma")
lnorm_ = fitdist(x, "lnorm")
plot(wei_)
plot(gamma_)
plot(lnorm_)
## Estimate parameters
print(wei_)## Fitting of the distribution ' weibull ' by maximum likelihood
## Parameters:
## estimate Std. Error
## shape 1.511269 0.03695305
## scale 5.035287 0.11113078print(gamma_)## Fitting of the distribution ' gamma ' by maximum likelihood
## Parameters:
## estimate Std. Error
## shape 2.009211 0.08347012
## rate 0.443210 0.02089939print(lnorm_)## Fitting of the distribution ' lnorm ' by maximum likelihood
## Parameters:
## estimate Std. Error
## meanlog 1.2423432 0.02553616
## sdlog 0.8075243 0.01805667## Summary Model
summary(wei_)## Fitting of the distribution ' weibull ' by maximum likelihood
## Parameters :
## estimate Std. Error
## shape 1.511269 0.03695305
## scale 5.035287 0.11113078
## Loglikelihood: -2395.007 AIC: 4794.013 BIC: 4803.829
## Correlation matrix:
## shape scale
## shape 1.0000000 0.3184947
## scale 0.3184947 1.0000000summary(gamma_)## Fitting of the distribution ' gamma ' by maximum likelihood
## Parameters :
## estimate Std. Error
## shape 2.009211 0.08347012
## rate 0.443210 0.02089939
## Loglikelihood: -2394.054 AIC: 4792.109 BIC: 4801.924
## Correlation matrix:
## shape rate
## shape 1.000000 0.881004
## rate 0.881004 1.000000summary(lnorm_)## Fitting of the distribution ' lnorm ' by maximum likelihood
## Parameters :
## estimate Std. Error
## meanlog 1.2423432 0.02553616
## sdlog 0.8075243 0.01805667
## Loglikelihood: -2447.5 AIC: 4898.999 BIC: 4908.815
## Correlation matrix:
## meanlog sdlog
## meanlog 1 0
## sdlog 0 1Distribusi Terbaik
# AIC
aic_values <- c(weibull = wei_$aic, gamma = gamma_$aic, lognormal = lnorm_$aic)
sorted_aic <- sort(aic_values); sorted_aic## gamma weibull lognormal
## 4792.109 4794.013 4898.999Gamma merupakan distribusi yang paling sesuai
# BIC
bic_values <- c(weibull = wei_$bic, gamma = gamma_$bic, lognormal = lnorm_$bic)
sorted_bic <- sort(bic_values); sorted_bic## gamma weibull lognormal
## 4801.924 4803.829 4908.815Gamma merupakan distribusi yang paling sesuai
# loglik
loglik_values <- c(weibull = wei_$loglik, gamma = gamma_$loglik, lognormal = lnorm_$loglik)
sorted_loglik <- sort(loglik_values, decreasing = TRUE); sorted_loglik## gamma weibull lognormal
## -2394.054 -2395.007 -2447.500Gamma merupakan distribusi yang paling sesuai
Kesimpulan akhir : Gamma merupakan distribusi yang paling fit dengan data