Estimasi Distribusi dan Parameter Model
Febriana Dwi Rahayu
2026-03-09
par(mfrow=c(3,1))
library(probs)## Warning: package 'probs' was built under R version 4.4.3##
## Attaching package: 'probs'## The following objects are masked from 'package:base':
##
## intersect, setdiff, unionhampiran normal terhadap geometrik
set.seed(16)
populasi = rgeom(20, 0.1)
n1 = 2
contoh_geo1 = urnsamples(populasi, size = 2, replace = F, ordered = F)
mean_geo1 = matrix(apply(contoh_geo1, 1, mean))
n2 = 5
contoh_geo2 = urnsamples(populasi, size = 5, replace = F, ordered = F)
mean_geo2 = matrix(apply(contoh_geo2, 1, mean))
n3 = 10
contoh_geo3 = urnsamples(populasi, size = 10, replace = F, ordered = F)
mean_geo3 = matrix(apply(contoh_geo3, 1, mean))hist(mean_geo1,main = paste("Hampiran Normal Terhadap Geometrik (n = 2)"),xlab = "xbar")
hist(mean_geo2,main = paste("Hampiran Normal Terhadap Geometrik (n = 5)"),xlab = "xbar")
hist(mean_geo3,main = paste("Hampiran Normal Terhadap Geometrik (n = 10)"),xlab = "xbar")
hampiran normal terhadap eksponensial
set.seed(123)
populasi = rexp(20)
n1 = 2
contoh_exp1 = urnsamples(populasi, size = 2, replace = F, ordered = F)
mean_exp1 = matrix(apply(contoh_exp1, 1, mean))
n2 = 5
contoh_exp2 = urnsamples(populasi, size = 5, replace = F, ordered = F)
mean_exp2 = matrix(apply(contoh_exp2, 1, mean))
n3 = 10
contoh_exp3 = urnsamples(populasi, size = 10, replace = F, ordered = F)
mean_exp3 = matrix(apply(contoh_exp3, 1, mean))hist(mean_exp1,main = paste("Hampiran Normal Terhadap Eksponensial (n = 2)"),xlab = "xbar")
hist(mean_exp2,main = paste("Hampiran Normal Terhadap Eksponensial (n = 5)"),xlab = "xbar")
hist(mean_exp3,main = paste("Hampiran Normal Terhadap Eksponensial (n = 10)"),xlab = "xbar")
hampiran normal terhadap seragam
par(mfrow=c(3,1))
set.seed(42)
populasi = runif(20)
n1 = 2
contoh_unif1 = urnsamples(populasi, size = 2, replace = F, ordered = F)
mean_unif1 = matrix(apply(contoh_unif1, 1, mean))
n2 = 5
contoh_unif2 = urnsamples(populasi, size = 5, replace = F, ordered = F)
mean_unif2 = matrix(apply(contoh_unif2, 1, mean))
n3 = 10
contoh_unif3 = urnsamples(populasi, size = 10, replace = F, ordered = F)
mean_unif3 = matrix(apply(contoh_unif3, 1, mean))hist(mean_unif1,main = paste("Hampiran Normal Terhadap Seragam (n = 2)"),xlab = "xbar")
hist(mean_unif2,main = paste("Hampiran Normal Terhadap Seragam (n = 5)"),xlab = "xbar")
hist(mean_unif3,main = paste("Hampiran Normal Terhadap Seragam (n = 10)"),xlab = "xbar")
sebaran percontohan sebaran normal
set.seed(123)
populasi = rnorm(20,5,sqrt(12)) # membangkitkan bil. acak ~ normal (miu = 5, sigma2 =12)
n1 = 3
contoh_norm1 = urnsamples(populasi, size = 3, replace = F, ordered = F)
contoh_norm1## X1 X2 X3
## 1 3.0584554 4.2026418 10.3995240
## 2 3.0584554 4.2026418 5.2442482
## 3 3.0584554 4.2026418 5.4478659
## 4 3.0584554 4.2026418 10.9411594
## 5 3.0584554 4.2026418 6.5966606
## 6 3.0584554 4.2026418 0.6176993
## 7 3.0584554 4.2026418 2.6206719
## 8 3.0584554 4.2026418 3.4561816
## 9 3.0584554 4.2026418 9.2403437
## 10 3.0584554 4.2026418 6.2464317
## 11 3.0584554 4.2026418 6.3883130
## 12 3.0584554 4.2026418 5.3834162
## 13 3.0584554 4.2026418 3.0745098
## 14 3.0584554 4.2026418 11.1900487
## 15 3.0584554 4.2026418 6.7246046
## 16 3.0584554 4.2026418 -1.8125617
## 17 3.0584554 4.2026418 7.4295681
## 18 3.0584554 4.2026418 3.3622025
## 19 3.0584554 10.3995240 5.2442482
## 20 3.0584554 10.3995240 5.4478659
## 21 3.0584554 10.3995240 10.9411594
## 22 3.0584554 10.3995240 6.5966606
## 23 3.0584554 10.3995240 0.6176993
## 24 3.0584554 10.3995240 2.6206719
## 25 3.0584554 10.3995240 3.4561816
## 26 3.0584554 10.3995240 9.2403437
## 27 3.0584554 10.3995240 6.2464317
## 28 3.0584554 10.3995240 6.3883130
## 29 3.0584554 10.3995240 5.3834162
## 30 3.0584554 10.3995240 3.0745098
## 31 3.0584554 10.3995240 11.1900487
## 32 3.0584554 10.3995240 6.7246046
## 33 3.0584554 10.3995240 -1.8125617
## 34 3.0584554 10.3995240 7.4295681
## 35 3.0584554 10.3995240 3.3622025
## 36 3.0584554 5.2442482 5.4478659
## 37 3.0584554 5.2442482 10.9411594
## 38 3.0584554 5.2442482 6.5966606
## 39 3.0584554 5.2442482 0.6176993
## 40 3.0584554 5.2442482 2.6206719
## 41 3.0584554 5.2442482 3.4561816
## 42 3.0584554 5.2442482 9.2403437
## 43 3.0584554 5.2442482 6.2464317
## 44 3.0584554 5.2442482 6.3883130
## 45 3.0584554 5.2442482 5.3834162
## 46 3.0584554 5.2442482 3.0745098
## 47 3.0584554 5.2442482 11.1900487
## 48 3.0584554 5.2442482 6.7246046
## 49 3.0584554 5.2442482 -1.8125617
## 50 3.0584554 5.2442482 7.4295681
## 51 3.0584554 5.2442482 3.3622025
## 52 3.0584554 5.4478659 10.9411594
## 53 3.0584554 5.4478659 6.5966606
## 54 3.0584554 5.4478659 0.6176993
## 55 3.0584554 5.4478659 2.6206719
## 56 3.0584554 5.4478659 3.4561816
## 57 3.0584554 5.4478659 9.2403437
## 58 3.0584554 5.4478659 6.2464317
## 59 3.0584554 5.4478659 6.3883130
## 60 3.0584554 5.4478659 5.3834162
## 61 3.0584554 5.4478659 3.0745098
## 62 3.0584554 5.4478659 11.1900487
## 63 3.0584554 5.4478659 6.7246046
## 64 3.0584554 5.4478659 -1.8125617
## 65 3.0584554 5.4478659 7.4295681
## 66 3.0584554 5.4478659 3.3622025
## 67 3.0584554 10.9411594 6.5966606
## 68 3.0584554 10.9411594 0.6176993
## 69 3.0584554 10.9411594 2.6206719
## 70 3.0584554 10.9411594 3.4561816
## 71 3.0584554 10.9411594 9.2403437
## 72 3.0584554 10.9411594 6.2464317
## 73 3.0584554 10.9411594 6.3883130
## 74 3.0584554 10.9411594 5.3834162
## 75 3.0584554 10.9411594 3.0745098
## 76 3.0584554 10.9411594 11.1900487
## 77 3.0584554 10.9411594 6.7246046
## 78 3.0584554 10.9411594 -1.8125617
## 79 3.0584554 10.9411594 7.4295681
## 80 3.0584554 10.9411594 3.3622025
## 81 3.0584554 6.5966606 0.6176993
## 82 3.0584554 6.5966606 2.6206719
## 83 3.0584554 6.5966606 3.4561816
## 84 3.0584554 6.5966606 9.2403437
## 85 3.0584554 6.5966606 6.2464317
## 86 3.0584554 6.5966606 6.3883130
## 87 3.0584554 6.5966606 5.3834162
## 88 3.0584554 6.5966606 3.0745098
## 89 3.0584554 6.5966606 11.1900487
## 90 3.0584554 6.5966606 6.7246046
## 91 3.0584554 6.5966606 -1.8125617
## 92 3.0584554 6.5966606 7.4295681
## 93 3.0584554 6.5966606 3.3622025
## 94 3.0584554 0.6176993 2.6206719
## 95 3.0584554 0.6176993 3.4561816
## 96 3.0584554 0.6176993 9.2403437
## 97 3.0584554 0.6176993 6.2464317
## 98 3.0584554 0.6176993 6.3883130
## 99 3.0584554 0.6176993 5.3834162
## 100 3.0584554 0.6176993 3.0745098
## 101 3.0584554 0.6176993 11.1900487
## 102 3.0584554 0.6176993 6.7246046
## 103 3.0584554 0.6176993 -1.8125617
## 104 3.0584554 0.6176993 7.4295681
## 105 3.0584554 0.6176993 3.3622025
## 106 3.0584554 2.6206719 3.4561816
## 107 3.0584554 2.6206719 9.2403437
## 108 3.0584554 2.6206719 6.2464317
## 109 3.0584554 2.6206719 6.3883130
## 110 3.0584554 2.6206719 5.3834162
## 111 3.0584554 2.6206719 3.0745098
## 112 3.0584554 2.6206719 11.1900487
## 113 3.0584554 2.6206719 6.7246046
## 114 3.0584554 2.6206719 -1.8125617
## 115 3.0584554 2.6206719 7.4295681
## 116 3.0584554 2.6206719 3.3622025
## 117 3.0584554 3.4561816 9.2403437
## 118 3.0584554 3.4561816 6.2464317
## 119 3.0584554 3.4561816 6.3883130
## 120 3.0584554 3.4561816 5.3834162
## 121 3.0584554 3.4561816 3.0745098
## 122 3.0584554 3.4561816 11.1900487
## 123 3.0584554 3.4561816 6.7246046
## 124 3.0584554 3.4561816 -1.8125617
## 125 3.0584554 3.4561816 7.4295681
## 126 3.0584554 3.4561816 3.3622025
## 127 3.0584554 9.2403437 6.2464317
## 128 3.0584554 9.2403437 6.3883130
## 129 3.0584554 9.2403437 5.3834162
## 130 3.0584554 9.2403437 3.0745098
## 131 3.0584554 9.2403437 11.1900487
## 132 3.0584554 9.2403437 6.7246046
## 133 3.0584554 9.2403437 -1.8125617
## 134 3.0584554 9.2403437 7.4295681
## 135 3.0584554 9.2403437 3.3622025
## 136 3.0584554 6.2464317 6.3883130
## 137 3.0584554 6.2464317 5.3834162
## 138 3.0584554 6.2464317 3.0745098
## 139 3.0584554 6.2464317 11.1900487
## 140 3.0584554 6.2464317 6.7246046
## 141 3.0584554 6.2464317 -1.8125617
## 142 3.0584554 6.2464317 7.4295681
## 143 3.0584554 6.2464317 3.3622025
## 144 3.0584554 6.3883130 5.3834162
## 145 3.0584554 6.3883130 3.0745098
## 146 3.0584554 6.3883130 11.1900487
## 147 3.0584554 6.3883130 6.7246046
## 148 3.0584554 6.3883130 -1.8125617
## 149 3.0584554 6.3883130 7.4295681
## 150 3.0584554 6.3883130 3.3622025
## 151 3.0584554 5.3834162 3.0745098
## 152 3.0584554 5.3834162 11.1900487
## 153 3.0584554 5.3834162 6.7246046
## 154 3.0584554 5.3834162 -1.8125617
## 155 3.0584554 5.3834162 7.4295681
## 156 3.0584554 5.3834162 3.3622025
## 157 3.0584554 3.0745098 11.1900487
## 158 3.0584554 3.0745098 6.7246046
## 159 3.0584554 3.0745098 -1.8125617
## 160 3.0584554 3.0745098 7.4295681
## 161 3.0584554 3.0745098 3.3622025
## 162 3.0584554 11.1900487 6.7246046
## 163 3.0584554 11.1900487 -1.8125617
## 164 3.0584554 11.1900487 7.4295681
## 165 3.0584554 11.1900487 3.3622025
## 166 3.0584554 6.7246046 -1.8125617
## 167 3.0584554 6.7246046 7.4295681
## 168 3.0584554 6.7246046 3.3622025
## 169 3.0584554 -1.8125617 7.4295681
## 170 3.0584554 -1.8125617 3.3622025
## 171 3.0584554 7.4295681 3.3622025
## 172 4.2026418 10.3995240 5.2442482
## 173 4.2026418 10.3995240 5.4478659
## 174 4.2026418 10.3995240 10.9411594
## 175 4.2026418 10.3995240 6.5966606
## 176 4.2026418 10.3995240 0.6176993
## 177 4.2026418 10.3995240 2.6206719
## 178 4.2026418 10.3995240 3.4561816
## 179 4.2026418 10.3995240 9.2403437
## 180 4.2026418 10.3995240 6.2464317
## 181 4.2026418 10.3995240 6.3883130
## 182 4.2026418 10.3995240 5.3834162
## 183 4.2026418 10.3995240 3.0745098
## 184 4.2026418 10.3995240 11.1900487
## 185 4.2026418 10.3995240 6.7246046
## 186 4.2026418 10.3995240 -1.8125617
## 187 4.2026418 10.3995240 7.4295681
## 188 4.2026418 10.3995240 3.3622025
## 189 4.2026418 5.2442482 5.4478659
## 190 4.2026418 5.2442482 10.9411594
## 191 4.2026418 5.2442482 6.5966606
## 192 4.2026418 5.2442482 0.6176993
## 193 4.2026418 5.2442482 2.6206719
## 194 4.2026418 5.2442482 3.4561816
## 195 4.2026418 5.2442482 9.2403437
## 196 4.2026418 5.2442482 6.2464317
## 197 4.2026418 5.2442482 6.3883130
## 198 4.2026418 5.2442482 5.3834162
## 199 4.2026418 5.2442482 3.0745098
## 200 4.2026418 5.2442482 11.1900487
## 201 4.2026418 5.2442482 6.7246046
## 202 4.2026418 5.2442482 -1.8125617
## 203 4.2026418 5.2442482 7.4295681
## 204 4.2026418 5.2442482 3.3622025
## 205 4.2026418 5.4478659 10.9411594
## 206 4.2026418 5.4478659 6.5966606
## 207 4.2026418 5.4478659 0.6176993
## 208 4.2026418 5.4478659 2.6206719
## 209 4.2026418 5.4478659 3.4561816
## 210 4.2026418 5.4478659 9.2403437
## 211 4.2026418 5.4478659 6.2464317
## 212 4.2026418 5.4478659 6.3883130
## 213 4.2026418 5.4478659 5.3834162
## 214 4.2026418 5.4478659 3.0745098
## 215 4.2026418 5.4478659 11.1900487
## 216 4.2026418 5.4478659 6.7246046
## 217 4.2026418 5.4478659 -1.8125617
## 218 4.2026418 5.4478659 7.4295681
## 219 4.2026418 5.4478659 3.3622025
## 220 4.2026418 10.9411594 6.5966606
## 221 4.2026418 10.9411594 0.6176993
## 222 4.2026418 10.9411594 2.6206719
## 223 4.2026418 10.9411594 3.4561816
## 224 4.2026418 10.9411594 9.2403437
## 225 4.2026418 10.9411594 6.2464317
## 226 4.2026418 10.9411594 6.3883130
## 227 4.2026418 10.9411594 5.3834162
## 228 4.2026418 10.9411594 3.0745098
## 229 4.2026418 10.9411594 11.1900487
## 230 4.2026418 10.9411594 6.7246046
## 231 4.2026418 10.9411594 -1.8125617
## 232 4.2026418 10.9411594 7.4295681
## 233 4.2026418 10.9411594 3.3622025
## 234 4.2026418 6.5966606 0.6176993
## 235 4.2026418 6.5966606 2.6206719
## 236 4.2026418 6.5966606 3.4561816
## 237 4.2026418 6.5966606 9.2403437
## 238 4.2026418 6.5966606 6.2464317
## 239 4.2026418 6.5966606 6.3883130
## 240 4.2026418 6.5966606 5.3834162
## 241 4.2026418 6.5966606 3.0745098
## 242 4.2026418 6.5966606 11.1900487
## 243 4.2026418 6.5966606 6.7246046
## 244 4.2026418 6.5966606 -1.8125617
## 245 4.2026418 6.5966606 7.4295681
## 246 4.2026418 6.5966606 3.3622025
## 247 4.2026418 0.6176993 2.6206719
## 248 4.2026418 0.6176993 3.4561816
## 249 4.2026418 0.6176993 9.2403437
## 250 4.2026418 0.6176993 6.2464317
## 251 4.2026418 0.6176993 6.3883130
## 252 4.2026418 0.6176993 5.3834162
## 253 4.2026418 0.6176993 3.0745098
## 254 4.2026418 0.6176993 11.1900487
## 255 4.2026418 0.6176993 6.7246046
## 256 4.2026418 0.6176993 -1.8125617
## 257 4.2026418 0.6176993 7.4295681
## 258 4.2026418 0.6176993 3.3622025
## 259 4.2026418 2.6206719 3.4561816
## 260 4.2026418 2.6206719 9.2403437
## 261 4.2026418 2.6206719 6.2464317
## 262 4.2026418 2.6206719 6.3883130
## 263 4.2026418 2.6206719 5.3834162
## 264 4.2026418 2.6206719 3.0745098
## 265 4.2026418 2.6206719 11.1900487
## 266 4.2026418 2.6206719 6.7246046
## 267 4.2026418 2.6206719 -1.8125617
## 268 4.2026418 2.6206719 7.4295681
## 269 4.2026418 2.6206719 3.3622025
## 270 4.2026418 3.4561816 9.2403437
## 271 4.2026418 3.4561816 6.2464317
## 272 4.2026418 3.4561816 6.3883130
## 273 4.2026418 3.4561816 5.3834162
## 274 4.2026418 3.4561816 3.0745098
## 275 4.2026418 3.4561816 11.1900487
## 276 4.2026418 3.4561816 6.7246046
## 277 4.2026418 3.4561816 -1.8125617
## 278 4.2026418 3.4561816 7.4295681
## 279 4.2026418 3.4561816 3.3622025
## 280 4.2026418 9.2403437 6.2464317
## 281 4.2026418 9.2403437 6.3883130
## 282 4.2026418 9.2403437 5.3834162
## 283 4.2026418 9.2403437 3.0745098
## 284 4.2026418 9.2403437 11.1900487
## 285 4.2026418 9.2403437 6.7246046
## 286 4.2026418 9.2403437 -1.8125617
## 287 4.2026418 9.2403437 7.4295681
## 288 4.2026418 9.2403437 3.3622025
## 289 4.2026418 6.2464317 6.3883130
## 290 4.2026418 6.2464317 5.3834162
## 291 4.2026418 6.2464317 3.0745098
## 292 4.2026418 6.2464317 11.1900487
## 293 4.2026418 6.2464317 6.7246046
## 294 4.2026418 6.2464317 -1.8125617
## 295 4.2026418 6.2464317 7.4295681
## 296 4.2026418 6.2464317 3.3622025
## 297 4.2026418 6.3883130 5.3834162
## 298 4.2026418 6.3883130 3.0745098
## 299 4.2026418 6.3883130 11.1900487
## 300 4.2026418 6.3883130 6.7246046
## 301 4.2026418 6.3883130 -1.8125617
## 302 4.2026418 6.3883130 7.4295681
## 303 4.2026418 6.3883130 3.3622025
## 304 4.2026418 5.3834162 3.0745098
## 305 4.2026418 5.3834162 11.1900487
## 306 4.2026418 5.3834162 6.7246046
## 307 4.2026418 5.3834162 -1.8125617
## 308 4.2026418 5.3834162 7.4295681
## 309 4.2026418 5.3834162 3.3622025
## 310 4.2026418 3.0745098 11.1900487
## 311 4.2026418 3.0745098 6.7246046
## 312 4.2026418 3.0745098 -1.8125617
## 313 4.2026418 3.0745098 7.4295681
## 314 4.2026418 3.0745098 3.3622025
## 315 4.2026418 11.1900487 6.7246046
## 316 4.2026418 11.1900487 -1.8125617
## 317 4.2026418 11.1900487 7.4295681
## 318 4.2026418 11.1900487 3.3622025
## 319 4.2026418 6.7246046 -1.8125617
## 320 4.2026418 6.7246046 7.4295681
## 321 4.2026418 6.7246046 3.3622025
## 322 4.2026418 -1.8125617 7.4295681
## 323 4.2026418 -1.8125617 3.3622025
## 324 4.2026418 7.4295681 3.3622025
## 325 10.3995240 5.2442482 5.4478659
## 326 10.3995240 5.2442482 10.9411594
## 327 10.3995240 5.2442482 6.5966606
## 328 10.3995240 5.2442482 0.6176993
## 329 10.3995240 5.2442482 2.6206719
## 330 10.3995240 5.2442482 3.4561816
## 331 10.3995240 5.2442482 9.2403437
## 332 10.3995240 5.2442482 6.2464317
## 333 10.3995240 5.2442482 6.3883130
## 334 10.3995240 5.2442482 5.3834162
## 335 10.3995240 5.2442482 3.0745098
## 336 10.3995240 5.2442482 11.1900487
## 337 10.3995240 5.2442482 6.7246046
## 338 10.3995240 5.2442482 -1.8125617
## 339 10.3995240 5.2442482 7.4295681
## 340 10.3995240 5.2442482 3.3622025
## 341 10.3995240 5.4478659 10.9411594
## 342 10.3995240 5.4478659 6.5966606
## 343 10.3995240 5.4478659 0.6176993
## 344 10.3995240 5.4478659 2.6206719
## 345 10.3995240 5.4478659 3.4561816
## 346 10.3995240 5.4478659 9.2403437
## 347 10.3995240 5.4478659 6.2464317
## 348 10.3995240 5.4478659 6.3883130
## 349 10.3995240 5.4478659 5.3834162
## 350 10.3995240 5.4478659 3.0745098
## 351 10.3995240 5.4478659 11.1900487
## 352 10.3995240 5.4478659 6.7246046
## 353 10.3995240 5.4478659 -1.8125617
## 354 10.3995240 5.4478659 7.4295681
## 355 10.3995240 5.4478659 3.3622025
## 356 10.3995240 10.9411594 6.5966606
## 357 10.3995240 10.9411594 0.6176993
## 358 10.3995240 10.9411594 2.6206719
## 359 10.3995240 10.9411594 3.4561816
## 360 10.3995240 10.9411594 9.2403437
## 361 10.3995240 10.9411594 6.2464317
## 362 10.3995240 10.9411594 6.3883130
## 363 10.3995240 10.9411594 5.3834162
## 364 10.3995240 10.9411594 3.0745098
## 365 10.3995240 10.9411594 11.1900487
## 366 10.3995240 10.9411594 6.7246046
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## 783 6.5966606 0.6176993 3.0745098
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## 785 6.5966606 0.6176993 6.7246046
## 786 6.5966606 0.6176993 -1.8125617
## 787 6.5966606 0.6176993 7.4295681
## 788 6.5966606 0.6176993 3.3622025
## 789 6.5966606 2.6206719 3.4561816
## 790 6.5966606 2.6206719 9.2403437
## 791 6.5966606 2.6206719 6.2464317
## 792 6.5966606 2.6206719 6.3883130
## 793 6.5966606 2.6206719 5.3834162
## 794 6.5966606 2.6206719 3.0745098
## 795 6.5966606 2.6206719 11.1900487
## 796 6.5966606 2.6206719 6.7246046
## 797 6.5966606 2.6206719 -1.8125617
## 798 6.5966606 2.6206719 7.4295681
## 799 6.5966606 2.6206719 3.3622025
## 800 6.5966606 3.4561816 9.2403437
## 801 6.5966606 3.4561816 6.2464317
## 802 6.5966606 3.4561816 6.3883130
## 803 6.5966606 3.4561816 5.3834162
## 804 6.5966606 3.4561816 3.0745098
## 805 6.5966606 3.4561816 11.1900487
## 806 6.5966606 3.4561816 6.7246046
## 807 6.5966606 3.4561816 -1.8125617
## 808 6.5966606 3.4561816 7.4295681
## 809 6.5966606 3.4561816 3.3622025
## 810 6.5966606 9.2403437 6.2464317
## 811 6.5966606 9.2403437 6.3883130
## 812 6.5966606 9.2403437 5.3834162
## 813 6.5966606 9.2403437 3.0745098
## 814 6.5966606 9.2403437 11.1900487
## 815 6.5966606 9.2403437 6.7246046
## 816 6.5966606 9.2403437 -1.8125617
## 817 6.5966606 9.2403437 7.4295681
## 818 6.5966606 9.2403437 3.3622025
## 819 6.5966606 6.2464317 6.3883130
## 820 6.5966606 6.2464317 5.3834162
## 821 6.5966606 6.2464317 3.0745098
## 822 6.5966606 6.2464317 11.1900487
## 823 6.5966606 6.2464317 6.7246046
## 824 6.5966606 6.2464317 -1.8125617
## 825 6.5966606 6.2464317 7.4295681
## 826 6.5966606 6.2464317 3.3622025
## 827 6.5966606 6.3883130 5.3834162
## 828 6.5966606 6.3883130 3.0745098
## 829 6.5966606 6.3883130 11.1900487
## 830 6.5966606 6.3883130 6.7246046
## 831 6.5966606 6.3883130 -1.8125617
## 832 6.5966606 6.3883130 7.4295681
## 833 6.5966606 6.3883130 3.3622025
## 834 6.5966606 5.3834162 3.0745098
## 835 6.5966606 5.3834162 11.1900487
## 836 6.5966606 5.3834162 6.7246046
## 837 6.5966606 5.3834162 -1.8125617
## 838 6.5966606 5.3834162 7.4295681
## 839 6.5966606 5.3834162 3.3622025
## 840 6.5966606 3.0745098 11.1900487
## 841 6.5966606 3.0745098 6.7246046
## 842 6.5966606 3.0745098 -1.8125617
## 843 6.5966606 3.0745098 7.4295681
## 844 6.5966606 3.0745098 3.3622025
## 845 6.5966606 11.1900487 6.7246046
## 846 6.5966606 11.1900487 -1.8125617
## 847 6.5966606 11.1900487 7.4295681
## 848 6.5966606 11.1900487 3.3622025
## 849 6.5966606 6.7246046 -1.8125617
## 850 6.5966606 6.7246046 7.4295681
## 851 6.5966606 6.7246046 3.3622025
## 852 6.5966606 -1.8125617 7.4295681
## 853 6.5966606 -1.8125617 3.3622025
## 854 6.5966606 7.4295681 3.3622025
## 855 0.6176993 2.6206719 3.4561816
## 856 0.6176993 2.6206719 9.2403437
## 857 0.6176993 2.6206719 6.2464317
## 858 0.6176993 2.6206719 6.3883130
## 859 0.6176993 2.6206719 5.3834162
## 860 0.6176993 2.6206719 3.0745098
## 861 0.6176993 2.6206719 11.1900487
## 862 0.6176993 2.6206719 6.7246046
## 863 0.6176993 2.6206719 -1.8125617
## 864 0.6176993 2.6206719 7.4295681
## 865 0.6176993 2.6206719 3.3622025
## 866 0.6176993 3.4561816 9.2403437
## 867 0.6176993 3.4561816 6.2464317
## 868 0.6176993 3.4561816 6.3883130
## 869 0.6176993 3.4561816 5.3834162
## 870 0.6176993 3.4561816 3.0745098
## 871 0.6176993 3.4561816 11.1900487
## 872 0.6176993 3.4561816 6.7246046
## 873 0.6176993 3.4561816 -1.8125617
## 874 0.6176993 3.4561816 7.4295681
## 875 0.6176993 3.4561816 3.3622025
## 876 0.6176993 9.2403437 6.2464317
## 877 0.6176993 9.2403437 6.3883130
## 878 0.6176993 9.2403437 5.3834162
## 879 0.6176993 9.2403437 3.0745098
## 880 0.6176993 9.2403437 11.1900487
## 881 0.6176993 9.2403437 6.7246046
## 882 0.6176993 9.2403437 -1.8125617
## 883 0.6176993 9.2403437 7.4295681
## 884 0.6176993 9.2403437 3.3622025
## 885 0.6176993 6.2464317 6.3883130
## 886 0.6176993 6.2464317 5.3834162
## 887 0.6176993 6.2464317 3.0745098
## 888 0.6176993 6.2464317 11.1900487
## 889 0.6176993 6.2464317 6.7246046
## 890 0.6176993 6.2464317 -1.8125617
## 891 0.6176993 6.2464317 7.4295681
## 892 0.6176993 6.2464317 3.3622025
## 893 0.6176993 6.3883130 5.3834162
## 894 0.6176993 6.3883130 3.0745098
## 895 0.6176993 6.3883130 11.1900487
## 896 0.6176993 6.3883130 6.7246046
## 897 0.6176993 6.3883130 -1.8125617
## 898 0.6176993 6.3883130 7.4295681
## 899 0.6176993 6.3883130 3.3622025
## 900 0.6176993 5.3834162 3.0745098
## 901 0.6176993 5.3834162 11.1900487
## 902 0.6176993 5.3834162 6.7246046
## 903 0.6176993 5.3834162 -1.8125617
## 904 0.6176993 5.3834162 7.4295681
## 905 0.6176993 5.3834162 3.3622025
## 906 0.6176993 3.0745098 11.1900487
## 907 0.6176993 3.0745098 6.7246046
## 908 0.6176993 3.0745098 -1.8125617
## 909 0.6176993 3.0745098 7.4295681
## 910 0.6176993 3.0745098 3.3622025
## 911 0.6176993 11.1900487 6.7246046
## 912 0.6176993 11.1900487 -1.8125617
## 913 0.6176993 11.1900487 7.4295681
## 914 0.6176993 11.1900487 3.3622025
## 915 0.6176993 6.7246046 -1.8125617
## 916 0.6176993 6.7246046 7.4295681
## 917 0.6176993 6.7246046 3.3622025
## 918 0.6176993 -1.8125617 7.4295681
## 919 0.6176993 -1.8125617 3.3622025
## 920 0.6176993 7.4295681 3.3622025
## 921 2.6206719 3.4561816 9.2403437
## 922 2.6206719 3.4561816 6.2464317
## 923 2.6206719 3.4561816 6.3883130
## 924 2.6206719 3.4561816 5.3834162
## 925 2.6206719 3.4561816 3.0745098
## 926 2.6206719 3.4561816 11.1900487
## 927 2.6206719 3.4561816 6.7246046
## 928 2.6206719 3.4561816 -1.8125617
## 929 2.6206719 3.4561816 7.4295681
## 930 2.6206719 3.4561816 3.3622025
## 931 2.6206719 9.2403437 6.2464317
## 932 2.6206719 9.2403437 6.3883130
## 933 2.6206719 9.2403437 5.3834162
## 934 2.6206719 9.2403437 3.0745098
## 935 2.6206719 9.2403437 11.1900487
## 936 2.6206719 9.2403437 6.7246046
## 937 2.6206719 9.2403437 -1.8125617
## 938 2.6206719 9.2403437 7.4295681
## 939 2.6206719 9.2403437 3.3622025
## 940 2.6206719 6.2464317 6.3883130
## 941 2.6206719 6.2464317 5.3834162
## 942 2.6206719 6.2464317 3.0745098
## 943 2.6206719 6.2464317 11.1900487
## 944 2.6206719 6.2464317 6.7246046
## 945 2.6206719 6.2464317 -1.8125617
## 946 2.6206719 6.2464317 7.4295681
## 947 2.6206719 6.2464317 3.3622025
## 948 2.6206719 6.3883130 5.3834162
## 949 2.6206719 6.3883130 3.0745098
## 950 2.6206719 6.3883130 11.1900487
## 951 2.6206719 6.3883130 6.7246046
## 952 2.6206719 6.3883130 -1.8125617
## 953 2.6206719 6.3883130 7.4295681
## 954 2.6206719 6.3883130 3.3622025
## 955 2.6206719 5.3834162 3.0745098
## 956 2.6206719 5.3834162 11.1900487
## 957 2.6206719 5.3834162 6.7246046
## 958 2.6206719 5.3834162 -1.8125617
## 959 2.6206719 5.3834162 7.4295681
## 960 2.6206719 5.3834162 3.3622025
## 961 2.6206719 3.0745098 11.1900487
## 962 2.6206719 3.0745098 6.7246046
## 963 2.6206719 3.0745098 -1.8125617
## 964 2.6206719 3.0745098 7.4295681
## 965 2.6206719 3.0745098 3.3622025
## 966 2.6206719 11.1900487 6.7246046
## 967 2.6206719 11.1900487 -1.8125617
## 968 2.6206719 11.1900487 7.4295681
## 969 2.6206719 11.1900487 3.3622025
## 970 2.6206719 6.7246046 -1.8125617
## 971 2.6206719 6.7246046 7.4295681
## 972 2.6206719 6.7246046 3.3622025
## 973 2.6206719 -1.8125617 7.4295681
## 974 2.6206719 -1.8125617 3.3622025
## 975 2.6206719 7.4295681 3.3622025
## 976 3.4561816 9.2403437 6.2464317
## 977 3.4561816 9.2403437 6.3883130
## 978 3.4561816 9.2403437 5.3834162
## 979 3.4561816 9.2403437 3.0745098
## 980 3.4561816 9.2403437 11.1900487
## 981 3.4561816 9.2403437 6.7246046
## 982 3.4561816 9.2403437 -1.8125617
## 983 3.4561816 9.2403437 7.4295681
## 984 3.4561816 9.2403437 3.3622025
## 985 3.4561816 6.2464317 6.3883130
## 986 3.4561816 6.2464317 5.3834162
## 987 3.4561816 6.2464317 3.0745098
## 988 3.4561816 6.2464317 11.1900487
## 989 3.4561816 6.2464317 6.7246046
## 990 3.4561816 6.2464317 -1.8125617
## 991 3.4561816 6.2464317 7.4295681
## 992 3.4561816 6.2464317 3.3622025
## 993 3.4561816 6.3883130 5.3834162
## 994 3.4561816 6.3883130 3.0745098
## 995 3.4561816 6.3883130 11.1900487
## 996 3.4561816 6.3883130 6.7246046
## 997 3.4561816 6.3883130 -1.8125617
## 998 3.4561816 6.3883130 7.4295681
## 999 3.4561816 6.3883130 3.3622025
## 1000 3.4561816 5.3834162 3.0745098
## 1001 3.4561816 5.3834162 11.1900487
## 1002 3.4561816 5.3834162 6.7246046
## 1003 3.4561816 5.3834162 -1.8125617
## 1004 3.4561816 5.3834162 7.4295681
## 1005 3.4561816 5.3834162 3.3622025
## 1006 3.4561816 3.0745098 11.1900487
## 1007 3.4561816 3.0745098 6.7246046
## 1008 3.4561816 3.0745098 -1.8125617
## 1009 3.4561816 3.0745098 7.4295681
## 1010 3.4561816 3.0745098 3.3622025
## 1011 3.4561816 11.1900487 6.7246046
## 1012 3.4561816 11.1900487 -1.8125617
## 1013 3.4561816 11.1900487 7.4295681
## 1014 3.4561816 11.1900487 3.3622025
## 1015 3.4561816 6.7246046 -1.8125617
## 1016 3.4561816 6.7246046 7.4295681
## 1017 3.4561816 6.7246046 3.3622025
## 1018 3.4561816 -1.8125617 7.4295681
## 1019 3.4561816 -1.8125617 3.3622025
## 1020 3.4561816 7.4295681 3.3622025
## 1021 9.2403437 6.2464317 6.3883130
## 1022 9.2403437 6.2464317 5.3834162
## 1023 9.2403437 6.2464317 3.0745098
## 1024 9.2403437 6.2464317 11.1900487
## 1025 9.2403437 6.2464317 6.7246046
## 1026 9.2403437 6.2464317 -1.8125617
## 1027 9.2403437 6.2464317 7.4295681
## 1028 9.2403437 6.2464317 3.3622025
## 1029 9.2403437 6.3883130 5.3834162
## 1030 9.2403437 6.3883130 3.0745098
## 1031 9.2403437 6.3883130 11.1900487
## 1032 9.2403437 6.3883130 6.7246046
## 1033 9.2403437 6.3883130 -1.8125617
## 1034 9.2403437 6.3883130 7.4295681
## 1035 9.2403437 6.3883130 3.3622025
## 1036 9.2403437 5.3834162 3.0745098
## 1037 9.2403437 5.3834162 11.1900487
## 1038 9.2403437 5.3834162 6.7246046
## 1039 9.2403437 5.3834162 -1.8125617
## 1040 9.2403437 5.3834162 7.4295681
## 1041 9.2403437 5.3834162 3.3622025
## 1042 9.2403437 3.0745098 11.1900487
## 1043 9.2403437 3.0745098 6.7246046
## 1044 9.2403437 3.0745098 -1.8125617
## 1045 9.2403437 3.0745098 7.4295681
## 1046 9.2403437 3.0745098 3.3622025
## 1047 9.2403437 11.1900487 6.7246046
## 1048 9.2403437 11.1900487 -1.8125617
## 1049 9.2403437 11.1900487 7.4295681
## 1050 9.2403437 11.1900487 3.3622025
## 1051 9.2403437 6.7246046 -1.8125617
## 1052 9.2403437 6.7246046 7.4295681
## 1053 9.2403437 6.7246046 3.3622025
## 1054 9.2403437 -1.8125617 7.4295681
## 1055 9.2403437 -1.8125617 3.3622025
## 1056 9.2403437 7.4295681 3.3622025
## 1057 6.2464317 6.3883130 5.3834162
## 1058 6.2464317 6.3883130 3.0745098
## 1059 6.2464317 6.3883130 11.1900487
## 1060 6.2464317 6.3883130 6.7246046
## 1061 6.2464317 6.3883130 -1.8125617
## 1062 6.2464317 6.3883130 7.4295681
## 1063 6.2464317 6.3883130 3.3622025
## 1064 6.2464317 5.3834162 3.0745098
## 1065 6.2464317 5.3834162 11.1900487
## 1066 6.2464317 5.3834162 6.7246046
## 1067 6.2464317 5.3834162 -1.8125617
## 1068 6.2464317 5.3834162 7.4295681
## 1069 6.2464317 5.3834162 3.3622025
## 1070 6.2464317 3.0745098 11.1900487
## 1071 6.2464317 3.0745098 6.7246046
## 1072 6.2464317 3.0745098 -1.8125617
## 1073 6.2464317 3.0745098 7.4295681
## 1074 6.2464317 3.0745098 3.3622025
## 1075 6.2464317 11.1900487 6.7246046
## 1076 6.2464317 11.1900487 -1.8125617
## 1077 6.2464317 11.1900487 7.4295681
## 1078 6.2464317 11.1900487 3.3622025
## 1079 6.2464317 6.7246046 -1.8125617
## 1080 6.2464317 6.7246046 7.4295681
## 1081 6.2464317 6.7246046 3.3622025
## 1082 6.2464317 -1.8125617 7.4295681
## 1083 6.2464317 -1.8125617 3.3622025
## 1084 6.2464317 7.4295681 3.3622025
## 1085 6.3883130 5.3834162 3.0745098
## 1086 6.3883130 5.3834162 11.1900487
## 1087 6.3883130 5.3834162 6.7246046
## 1088 6.3883130 5.3834162 -1.8125617
## 1089 6.3883130 5.3834162 7.4295681
## 1090 6.3883130 5.3834162 3.3622025
## 1091 6.3883130 3.0745098 11.1900487
## 1092 6.3883130 3.0745098 6.7246046
## 1093 6.3883130 3.0745098 -1.8125617
## 1094 6.3883130 3.0745098 7.4295681
## 1095 6.3883130 3.0745098 3.3622025
## 1096 6.3883130 11.1900487 6.7246046
## 1097 6.3883130 11.1900487 -1.8125617
## 1098 6.3883130 11.1900487 7.4295681
## 1099 6.3883130 11.1900487 3.3622025
## 1100 6.3883130 6.7246046 -1.8125617
## 1101 6.3883130 6.7246046 7.4295681
## 1102 6.3883130 6.7246046 3.3622025
## 1103 6.3883130 -1.8125617 7.4295681
## 1104 6.3883130 -1.8125617 3.3622025
## 1105 6.3883130 7.4295681 3.3622025
## 1106 5.3834162 3.0745098 11.1900487
## 1107 5.3834162 3.0745098 6.7246046
## 1108 5.3834162 3.0745098 -1.8125617
## 1109 5.3834162 3.0745098 7.4295681
## 1110 5.3834162 3.0745098 3.3622025
## 1111 5.3834162 11.1900487 6.7246046
## 1112 5.3834162 11.1900487 -1.8125617
## 1113 5.3834162 11.1900487 7.4295681
## 1114 5.3834162 11.1900487 3.3622025
## 1115 5.3834162 6.7246046 -1.8125617
## 1116 5.3834162 6.7246046 7.4295681
## 1117 5.3834162 6.7246046 3.3622025
## 1118 5.3834162 -1.8125617 7.4295681
## 1119 5.3834162 -1.8125617 3.3622025
## 1120 5.3834162 7.4295681 3.3622025
## 1121 3.0745098 11.1900487 6.7246046
## 1122 3.0745098 11.1900487 -1.8125617
## 1123 3.0745098 11.1900487 7.4295681
## 1124 3.0745098 11.1900487 3.3622025
## 1125 3.0745098 6.7246046 -1.8125617
## 1126 3.0745098 6.7246046 7.4295681
## 1127 3.0745098 6.7246046 3.3622025
## 1128 3.0745098 -1.8125617 7.4295681
## 1129 3.0745098 -1.8125617 3.3622025
## 1130 3.0745098 7.4295681 3.3622025
## 1131 11.1900487 6.7246046 -1.8125617
## 1132 11.1900487 6.7246046 7.4295681
## 1133 11.1900487 6.7246046 3.3622025
## 1134 11.1900487 -1.8125617 7.4295681
## 1135 11.1900487 -1.8125617 3.3622025
## 1136 11.1900487 7.4295681 3.3622025
## 1137 6.7246046 -1.8125617 7.4295681
## 1138 6.7246046 -1.8125617 3.3622025
## 1139 6.7246046 7.4295681 3.3622025
## 1140 -1.8125617 7.4295681 3.3622025mean_norm1 = matrix(apply(contoh_norm1, 1, mean))
mean_xbar1 = mean(mean_norm1)
var_xbar1 = var(mean_norm1)
n2 = 4
contoh_norm2 = urnsamples(populasi, size = 4, replace = F, ordered = F)
mean_norm2 = matrix(apply(contoh_norm2, 1, mean))
mean_xbar2 = mean(mean_norm2)
var_xbar2 = var(mean_norm2)
n3 = 15
contoh_norm3 = urnsamples(populasi, size = 15, replace = F, ordered = F)
mean_norm3 = matrix(apply(contoh_norm3, 1, mean))
mean_xbar3 = mean(mean_norm3)
var_xbar3 = var(mean_norm3)
hist(mean_norm1,main = paste("(n = 3)"),xlab = "xbar")
hist(mean_norm2,main = paste("(n = 4)"),xlab = "xbar")
hist(mean_norm3,main = paste("(n = 15)"),xlab = "xbar")
penerapan ketakbiasan penduga (mean)
#1. sebaran normal
set.seed(123)
n = 10
populasi1 = rnorm(20)
mean_pop1 = mean(populasi1)
sampel_normal1 = urnsamples(populasi1, size = 10, replace = F, ordered = F)
mean_normal1 = matrix(apply(sampel_normal1, 1, mean))
median_normal1 = matrix(apply(sampel_normal1, 1, median))
harapan_mean_norm1 = mean(mean_normal1)
harapan_median_norm1 = mean(median_normal1)
#2. sebaran eksponensial
library(probs)
set.seed(123)
n = 10
populasi2 = rexp(20)
mean_pop2 = mean(populasi2)
sampel_exp1 = urnsamples(populasi2, size = 10, replace = F, ordered = F)
mean_exp1 = matrix(apply(sampel_exp1, 1, mean))
median_exp1 = matrix(apply(sampel_exp1, 1, median))
harapan_mean_exp1 = mean(mean_exp1)
harapan_median_exp1 = mean(median_exp1)
#3. uniform
library(probs)
set.seed(123)
n = 10
populasi3 = runif(20)
mean_pop3 = mean(populasi3)
sampel_unif1 = urnsamples(populasi3, size = 10, replace = F, ordered = F)
mean_unif1 = matrix(apply(sampel_unif1, 1, mean))
median_unif1 = matrix(apply(sampel_unif1, 1, median))
harapan_mean_unif1 = mean(mean_unif1)
harapan_median_unif1 = mean(median_unif1)
hasil = data.frame("Hasil"=c("mean_populasi","harapan_mean_contoh","harapan_median_contoh"),"Sebaran Normal"=c(mean_pop1,harapan_mean_norm1,harapan_median_norm1),"Sebaran Eksponensial"=c(mean_pop2,harapan_mean_exp1,harapan_median_exp1),"Sebaran Seragam"=c(mean_pop3,harapan_mean_unif1,harapan_median_unif1))
hasil## Hasil Sebaran.Normal Sebaran.Eksponensial Sebaran.Seragam
## 1 mean_populasi 0.1416238 0.8111726 0.5508084
## 2 harapan_mean_contoh 0.1416238 0.8111726 0.5508084
## 3 harapan_median_contoh 0.1174878 0.4931612 0.5504018penerapan ketabiasan penduga (ragam)
#sebaran normal
set.seed(888)
n = 10
populasi = rnorm(20)
sigma2 = var(populasi)*(20-1)/20 #fungsi var pada R adalah varian contoh (penyebut n-1) sehingga perlu dikali (n-1)/n
library(probs)
sampel = urnsamples(populasi, size = 10, replace = F, ordered = F)
## pembagi (n-1)
s2.n1 = matrix(apply(sampel, 1, var))
E.s2.n1 = mean(s2.n1)
## pembagi (n)
s2.n = s2.n1*(10-1)/10
E.s2.n = mean(s2.n)
#sebaran eksponensial
set.seed(888)
n = 10
populasi2 = rexp(20)
sigma2.exp = var(populasi2)*(20-1)/20
library(probs)
sampel_exp = urnsamples(populasi2, size = 10, replace = F, ordered = F)
## pembagi (n-1)
s2.n1.exp = matrix(apply(sampel_exp, 1, var))
E.s2.n1.exp = mean(s2.n1.exp)
## pembagi (n)
s2.n.exp = s2.n1.exp*(10-1)/10
E.s2.n.exp = mean(s2.n.exp)
hasil = data.frame( "." = c("ragam populasi","nilai harapan ragam contoh (n-1)","nilai harapan ragam contoh (n)"),"Sebaran Normal" = c(sigma2, E.s2.n1, E.s2.n),"Sebaran Eksponensial" = c(sigma2.exp, E.s2.n1.exp, E.s2.n.exp))
hasil## . Sebaran.Normal Sebaran.Eksponensial
## 1 ragam populasi 1.298573 1.750903
## 2 nilai harapan ragam contoh (n-1) 1.366919 1.843056
## 3 nilai harapan ragam contoh (n) 1.230227 1.658750selang kepercayaan
Apa arti dari SK 95%?
SK 95% bagi \(\theta\) : Kita percaya 95% bahwa selang a sampai b memuat nilai parameter θ yang sebenarnya
SK 95%: Jika kita melakukan 100 kali percontohan acak dan setiap percontohan acak dibuat selang kepercayaannya, maka dari 100 SK yang terbentuk, ada 95 SK yang mencakup parameter sedangkan sisanya sebanyak 5 SK tidak mencakup parameter.
algoritme
Tentukan sebaran yang akan digunakan
Ulangi sebanyak k kali
- Bangkitkan n buah data dari sebaran yang sudah ditentukan
- Hitung nilai \(\bar{x}\) dan \(s^2\)
- Hitung \(\sigma^2_{\bar{x}}\) dan buat selang kepercayaan \((1-\alpha)\)%
Hitung proporsi banyaknya selang kepercayaan yang memuat \(\mu\), bandingkan dengan \((1-\alpha)\)
n1 = 10
k = 100 #ulangan
alpha = 0.05
mu = 50
std = 10
set.seed(123)
sampel.norm1 = matrix(rnorm(n1*k,mu,std),k)
xbar.norm1 = apply(sampel.norm1,1,mean)
s.norm1 = apply(sampel.norm1,1,sd)
SE.norm1 = s.norm1/sqrt(n1)
z.norm1 = qnorm(1-alpha/2)
SK.norm1 = (xbar.norm1-z.norm1*SE.norm1 < mu & mu < xbar.norm1+z.norm1*SE.norm1)
x.norm1 = sum(SK.norm1)/k #proporsi banyaknya SK yang memuat mu
n2 = 30
k = 100 #ulangan
alpha = 0.05
mu = 50
std = 10
set.seed(123)
sampel.norm2 = matrix(rnorm(n2*k,mu,std),k)
xbar.norm2 = apply(sampel.norm2,1,mean)
s.norm2 = apply(sampel.norm2,1,sd)
SE.norm2 = s.norm2/sqrt(n2)
z.norm2 = qnorm(1-alpha/2)
SK.norm2 = (xbar.norm2-z.norm2*SE.norm2 < mu & mu < xbar.norm2+z.norm2*SE.norm2)
x.norm2 = sum(SK.norm2)/k #proporsi banyaknya SK yang memuat mu
n3 = 100
k = 100 #ulangan
alpha = 0.05
mu = 50
std = 10
set.seed(123)
sampel.norm3 = matrix(rnorm(n3*k,mu,std),k)
xbar.norm3 = apply(sampel.norm3,1,mean)
s.norm3 = apply(sampel.norm3,1,sd)
SE.norm3 = s.norm3/sqrt(n3)
z.norm3 = qnorm(1-alpha/2)
SK.norm3 = (xbar.norm3-z.norm3*SE.norm3 < mu & mu < xbar.norm3+z.norm3*SE.norm3)
x.norm3 = sum(SK.norm3)/k
hasil = data.frame("n" =c(10,30,100),"Ketepatan SK Sebaran Normal"=c(x.norm1, x.norm2, x.norm3))
hasil## n Ketepatan.SK.Sebaran.Normal
## 1 10 0.93
## 2 30 0.93
## 3 100 0.96matplot(rbind (xbar.norm2-z.norm2*SE.norm2, xbar.norm2+z.norm2*SE.norm2), rbind(1:k,1:k), col=ifelse(SK.norm2,"darkmagenta","coral3"), type = "l", lty = 1,main='Selang Kepercayaan 95% (n=100)', xlab='SK', ylab='banyak ulangan')
abline(v=mu)
library(car)## Warning: package 'car' was built under R version 4.4.3## Loading required package: carData## Warning: package 'carData' was built under R version 4.4.3data("Prestige")
m <- mean(Prestige$income)
m## [1] 6797.902p <- dim(Prestige)[1]
se <- sd(Prestige$income)/sqrt(p)
se## [1] 420.4089tval <- qt(0.975, df=p-1)
cat(paste("KI: [", round(m-tval*se, 2),",",round(m+tval*se,2),"]"))## KI: [ 5963.92 , 7631.88 ]