SMWR_Ch3
박선희
2018년 4월 18일
3.1
ex_3_1 = c(6.0, 0.5, 0.4, 0.7, 0.8, 6.0,
5.0, 0.6, 1.2, 0.3, 0.2, 0.5,
0.5, 10, 0.2, 0.2, 1.7, 3.0)
ex_3_1 = ex_3_1[order(ex_3_1)]
ex_3_1## [1] 0.2 0.2 0.2 0.3 0.4 0.5 0.5 0.5 0.6 0.7 0.8 1.2 1.7 3.0
## [15] 5.0 6.0 6.0 10.0n = length(ex_3_1)
p = 0.5
# nonparametric
non_p_Rl = (n - 1.96 * sqrt(n))/2
non_p_Rl## [1] 4.842212non_p_Ru = (n + 1.96 * sqrt(n))/2 +1
non_p_Ru## [1] 14.15779non_p_Rl = quantile(ex_3_1, probs = non_p_Rl/n)
non_p_Ru = quantile(ex_3_1, probs = non_p_Ru/n)
# parametric
p_Rl = exp(mean(log(ex_3_1)) - 2.064 * sqrt(var(log(ex_3_1)) / n))
p_Ru = exp(mean(log(ex_3_1)) + 2.064 * sqrt(var(log(ex_3_1)) / n))
library("ggplot2")
ggplot() +
geom_boxplot(aes(x = "ex_3_1",
y = ex_3_1)) +
geom_hline(yintercept = c(non_p_Rl, non_p_Ru),
size = 2, color = "blue") +
geom_hline(yintercept = c(p_Rl, p_Ru),
size = 2, color = "red")
Parametric confidence interval seems more appropriate in this case.
3-2
ex_3_2 = c(1.0, 0.2, 1.2, 1.0, 0.3, 0.1,
0.1, 0.4, 3.2, 0.3, 0.4, 1.8,
0.9, 0.1, 0.2, 0.3, 0.5)
ex_3_2 = ex_3_2[order(ex_3_2)]
n = length(ex_3_2)
CI_mean_l = mean(ex_3_2) - 2.064 * sqrt(var(ex_3_2) / n)
CI_mean_u = mean(ex_3_2) + 2.064 * sqrt(var(ex_3_2) / n)
CI_mean_l## [1] 0.3060061CI_mean_u## [1] 1.105759mean(ex_3_2)## [1] 0.7058824exp(mean(log(ex_3_2)))## [1] 0.4277575ggplot() +
geom_boxplot(aes(x = "ex_3_2",
y = ex_3_2)) +
geom_hline(yintercept = mean(ex_3_2),
size = 2, color = "blue") +
geom_hline(yintercept = exp(mean(log(ex_3_2))),
size = 2, color = "red")
Lognormal mean seems more appropriate in this case. Because given data shows skewde distribution.
3-3
ex_3_3 = c(0.001, 0.030, 0.10, 0.003, 0.040, 0.454,
0.007, 0.041, 0.49, 0.020, 0.077, 1.02)
boxplot(ex_3_3)
ex_3_3 = ex_3_3[order(ex_3_3)]
ex_3_3## [1] 0.001 0.003 0.007 0.020 0.030 0.040 0.041 0.077 0.100 0.454 0.490
## [12] 1.020n = length(ex_3_3)
n## [1] 12# nonparametric
non_p_Rl = (n - 1.96 * sqrt(n))/2
non_p_Rl## [1] 2.60518non_p_Ru = (n + 1.96 * sqrt(n))/2 +1
non_p_Ru## [1] 10.39482non_p_Rl = quantile(ex_3_3, probs = non_p_Rl/n)
non_p_Ru = quantile(ex_3_3, probs = non_p_Ru/n)
# parametric
p_Rl = exp(mean(log(ex_3_3)) - 2.064 * sqrt(var(log(ex_3_3)) / n))
p_Ru = exp(mean(log(ex_3_3)) + 2.064 * sqrt(var(log(ex_3_3)) / n))
library("ggplot2")
ggplot() +
geom_boxplot(aes(x = "ex_3_3",
y = ex_3_3)) +
geom_hline(yintercept = c(non_p_Rl, non_p_Ru),
size = 2, color = "blue") +
geom_hline(yintercept = c(p_Rl, p_Ru),
size = 2, color = "red") +
geom_point(aes(x = "ex_3_3",
y = 0.85),
size = 5,
color = "green")
- Yes, it does.
- Parametric confidence interval seems more appropriate than non-parametric confidence interval. Because later values are located out of inter quantile range.
3-4
ex_3_4 = read.csv("c2.csv")
ex_3_4## 癤풷ear Flow..cfs.
## 1 1941 369
## 2 1942 683
## 3 1943 923
## 4 1944 1193
## 5 1945 413
## 6 1946 1025
## 7 1947 894
## 8 1948 859
## 9 1949 1157
## 10 1950 524
## 11 195l 327
## 12 1952 574
## 13 1953 762
## 14 1954 578
## 15 1955 379
## 16 1956 374
## 17 1957 581
## 18 1958 581
## 19 1959 530
## 20 1960 929n = nrow(ex_3_4)
n## [1] 20boxplot(ex_3_4[, 2])
ex_3_4 = ex_3_4[, 2]
# nonparametric - mean
mean_Rl = mean(ex_3_4) - 2.064 * sqrt(var(ex_3_4) / n)
mean_Ru = mean(ex_3_4) + 2.064 * sqrt(var(ex_3_4) / n)
# nonparametric - median
non_p_Rl = (n - 1.96 * sqrt(n))/2
non_p_Rl## [1] 5.617307non_p_Ru = (n + 1.96 * sqrt(n))/2 +1
non_p_Ru## [1] 15.38269non_p_Rl = quantile(ex_3_4, probs = non_p_Rl/n)
non_p_Ru = quantile(ex_3_4, probs = non_p_Ru/n)
ggplot() +
geom_boxplot(aes(x = "ex_3_4",
y = ex_3_4)) +
geom_hline(yintercept = c(mean_Rl, mean_Ru),
size = 2, color = "blue") + # mean
geom_hline(yintercept = c(non_p_Rl, non_p_Ru),
size = 2, color = "red") # median
3-5
ex_3_5 = read.csv("c3.csv", header = FALSE)
ex_3_5 = as.numeric(unlist(ex_3_5))
ex_3_5 = ex_3_5[!is.na(ex_3_5)]
ex_3_5 = ex_3_5[order(ex_3_5)]
ex_3_5## [1] 1 2 3 4 5 6 7 8 9 10
## [11] 11 12 13 14 15 16 17 18 19 20
## [21] 21 22 23 24 25 26 27 28 29 30
## [31] 31 32 33 34 35 36 37 1730 1750 1770
## [41] 1810 1940 1940 1960 1960 1980 2010 2010 2030 2050
## [51] 2050 2050 2080 2080 2100 2170 2190 2190 2260 2290
## [61] 2290 2290 2290 2320 2360 2390 2390 2390 2430 2460
## [71] 2490 2490 2490 2600 2620 2680 2680 2700 2700 2700
## [81] 2700 2760 2790 2810 2840 2840 2840 2840 2840 2840
## [91] 2870 2950 3040 3040 3100 3130 3220 3220 3220 3310
## [101] 3370 3410 3440 3440 3470 3500 3570 3600 3630 3630
## [111] 3660 3660 3700 3700 3700 3760 3760 3760 3900 3900
## [121] 4000 4000 4040 4040 4140 4210 4320 4460 4500 4540
## [131] 4570 4610 4610 4680 4840 4960 5000 5120 5200 5280
## [141] 5360 5500 5690 5900 5900 5900 5900 5900 5900 6120
## [151] 6120 6120 6120 6120 6340 6340 6800 6800 6800 6800
## [161] 6800 7040 7040 7280 7280 7280 7280 7280 7280 7530
## [171] 7530 7530 7780 7780 7780 7780 7780 8040 8040 8040
## [181] 8040 8040 8040 8040 8040 8300 8300 8300 8580 8580
## [191] 8580 8580 8580 8850 8850 8850 8850 8850 9120 9120
## [201] 9120 9120 9400 9400 9400 9400 9400 9400 9700 9700
## [211] 9700 9700 9700 9700 9700 9700 9700 10000 10000 10000
## [221] 10000 10000 10300 10300 10300 10300 10300 10300 10300 10600
## [231] 10600 10600 10600 10600 10600 10900 10900 10900 10900 11200
## [241] 11200 11500 11500 11500 11500 11500 11500 11800 11800 11800
## [251] 12200 12200 12200 12500 12500 12800 12800 12800 13200 13200
## [261] 13600 13900 13900 13900 13900 13900 14300 14300 14300 14300
## [271] 14600 14600 15000 15000 15000 15000 15400 15400 15400 15400
## [281] 15800 15800 16200 16200 16200 16200 16700 17100 17100 17500
## [291] 17500 17500 18000 18000 18000 18400 18800 18800 19300 19300
## [301] 19800 19800 19800 20200 20200 20700 20700 22100 22100 22100
## [311] 22100 22100 22100 23100 23100 23600 23600 24100 24100 24500
## [321] 25100 25600 25600 26200 26200 27200 27800 27800 27800 27800
## [331] 27800 27800 27900 28900 31100 31100 31100 32300 35900 35900
## [341] 37100 37100 38300 38300 39500 39500 40700 42000 47200 49800
## [351] 49800 50400 55000 60600 64800 73300 73300 77800 77800 80800
## [361] 86800 91300 168000 250000 309999Rl = exp(mean(log(ex_3_5)) + 0.898 * sd(log(ex_3_5)))
Rl## [1] 32322.55Ru = exp(mean(log(ex_3_5)) + 1.838 * sd(log(ex_3_5)))
Ru## [1] 246013.8ggplot() +
geom_boxplot(aes(x = "ex_3_5",
y = ex_3_5)) +
geom_hline(yintercept = c(Rl, Ru),
size = 2, color = "blue") 