シーケンスデータ
- seq(from, to): fromからtoまでの数値シーケンスを生成
- seq(1, 10) 出力: 1 2 3 4 5 6 7 8 9 10
- seq(from, to, by): fromからtoまでbyのステップで数値シーケンスを生成
- seq(1, 10, by = 2) 出力: 1 3 5 7 9
- seq(from, to, length.out): fromからtoまでlength.out個の等間隔で生成
- seq(0, 1, length.out = 11) 出力: 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.9 1.0
> #---------------------------------------
> # -3から3まで、長さ100のシーケンスを生成
> z <- seq(-3, 3, length.out = 100)
>
> # dnorm関数を使用して確率密度を計算(z-->density)
> density <- dnorm(z)
>
> # pnorm関数を使用して累積確率を計算(z-->probability)
> cumulative_probability <- pnorm(z)
>
> # qnorm関数を使用して分位点を計算（probability-->z)
> probabilities <- seq(0, 1, length.out = 100)
> quantiles <- qnorm(probabilities) #mean=0,sd=1省略
>
> # dnormの視覚化
> pdf_data <- data.frame(z = z, density = density)
> ggplot(pdf_data, aes(x = z, y = density)) +
+ #stat_ecdf(geom = "step", color = "blue") +
+ geom_line() +
+ labs(title = "Probability Density Function", x = "z-value", y = "Density")
> # pnormの視覚化
> cdf_data <- data.frame(z = z, cumulative_probability = cumulative_probability)
> ggplot(cdf_data, aes(x = z, y = cumulative_probability)) +
+ #stat_ecdf(geom = "step", color = "blue") +
+ geom_line() +
+ labs(title = "Cumulative Distribution Function", x = "z-value", y = "Cumulative Probability")
> # qnormの視覚化
> quantile_data <- data.frame(p = probabilities, quantile = quantiles)
> ggplot(quantile_data, aes(x = p, y = quantile)) +
+ #stat_ecdf(geom = "step", color = "blue") +
+ geom_line() +
+ labs(title = "Quantile Function", x = "Probability", y = "z-value")
ランダムデータ
- random_numbers <- rnorm(n = 100, mean = 0, sd = 1)
- n: 生成する乱数の数
- mean: 平均
- sd: 標準偏差
> # ランダムサンプルデータの生成１
> data1 <- rnorm(1000, mean = 0, sd = 1)
> data2 <- rnorm(1000, mean = 1, sd = 2)
> data3 <- rnorm(1000, mean = 50, sd = 10)
>
> # 25, 50, 75パーセンタイルの計算(c()の数はいくらでもOK）
> percentiles1 <- quantile(data1, probs = c(0.25, 0.5, 0.75))
> percentiles2 <- quantile(data2, probs = c(0.25, 0.5, 0.75))
> percentiles3 <- quantile(data3, probs = c(0.25, 0.5, 0.75))
>
> # 2.5, 50, 97.5パーセンタイルの計算（c()の数分、出力される）
> percentiles4 <- quantile(data3, probs = c(0.025, 0.5, 0.975))
>
> # 25, 50, 75パーセンタイルの計算
> probability_below_60_1 <- pnorm(0, mean = 0, sd = 1)
> probability_below_60_2 <- pnorm(10, mean = 1, sd = 10)
> probability_below_60_3 <- pnorm(70, mean = 50, sd = 10)
>
> # ↓が分かりやすい四分位数95%の信頼区間をZスコア換算
> # z_score <- qnorm(.975,mean=0,sd=1)
>
>
> # ヒストグラムの相対密度プロット
> ggplot(data.frame(value = data1), aes(x = value)) +
+ geom_histogram(aes(y = after_stat(density)), bins = 30, fill = "blue", alpha = 0.2) +
+ geom_density(color="red") +
+ labs(title = "Histogram and Kernel Density Estimation with Relative Density", x = "Value", y = "Relative Density")
> # 累積確率のプロット
> ggplot(data.frame(value = data3), aes(x = value)) +
+ stat_ecdf(geom = "step", color = "blue") +
+ geom_vline(xintercept = 60, color = "red", linetype = "dashed", linewidth = 1) +
+ annotate("text", x = 60 , y = 0, label = paste0("P(X <= 60) = ", round(pnorm(60, mean = 50, sd = 10), 2)), vjust = -1) +
+ labs(title = "ECDF with Probability", x = "Value", y = "Cumulative Probability") +
+ theme_minimal()
> # データフレームの作成
> dataF <- data.frame(
+ value = c(data1, data2,data3),
+ group = factor(rep(c("Group 1", "Group 2","Group 3"), each = 1000))
+ )
> #dataF
>
> # カーネル密度推定の相対密度プロット
> ggplot(dataF, aes(x = value, color = group)) +
+ geom_density() +
+ labs(title = "Kernel Density Estimation with Relative Density", x = "Value", y = "Relative Density")
> # ヒストグラムにパーセンタイル線を追加
> ggplot(data.frame(value = data1), aes(x = value)) +
+ geom_histogram(fill = "blue", alpha = 0.2) +
+ geom_vline(aes(xintercept = percentiles1[1]), color = "red", linetype = "dashed", linewidth = 1) +
+ geom_vline(aes(xintercept = percentiles1[2]), color = "green", linetype = "dashed", linewidth = 1) +
+ geom_vline(aes(xintercept = percentiles1[3]), color = "purple", linetype = "dashed", linewidth = 1) +
+ annotate("text", x = percentiles1[1], y = 0, label = paste0("Lo = ", round(percentiles1[1], 3))) +
+ annotate("text", x = percentiles1[3], y = 0, label = paste0("Up = ", round(percentiles1[3], 3))) +
+ labs(title = "Histogram with Percentiles", x = "Value", y = "Frequency") +
+ theme_minimal()
> # カーネル密度プロットにパーセンタイル線を追加
> ggplot(data.frame(value = data2), aes(x = value)) +
+ geom_density(fill = "blue", alpha = 0.2) +
+ geom_vline(aes(xintercept = percentiles2[1]), color = "red", linetype = "dashed", linewidth = 1) +
+ geom_vline(aes(xintercept = percentiles2[2]), color = "green", linetype = "dashed", linewidth = 1) +
+ geom_vline(aes(xintercept = percentiles2[3]), color = "purple", linetype = "dashed", linewidth = 1) +
+ annotate("text", x = percentiles2[1], y = 0, label = paste0("Lo = ", round(percentiles2[1], 3))) +
+ annotate("text", x = percentiles2[3], y = 0, label = paste0("Up = ", round(percentiles2[3], 3))) +
+ labs(title = "Kernel Density Plot with Percentiles", x = "Value", y = "Density") +
+ theme_minimal()
> # カーネル密度プロットにパーセンタイル線を追加
> ggplot(data.frame(value = data3), aes(x = value)) +
+ geom_density(fill = "blue", alpha = 0.2) +
+ geom_vline(aes(xintercept = percentiles4[1]), color = "red", linetype = "dashed", linewidth = 1) +
+ geom_vline(aes(xintercept = percentiles4[2]), color = "green", linetype = "dashed", linewidth = 1) +
+ geom_vline(aes(xintercept = percentiles4[3]), color = "purple", linetype = "dashed", linewidth = 1) +
+ annotate("text", x = percentiles4[1], y = 0, label = paste0("Lower = ", round(percentiles4[1], 3))) +
+ annotate("text", x = percentiles4[3], y = 0, label = paste0("Upper = ", round(percentiles4[3], 3))) +
+ labs(title = "Kernel Density Plot with Percentiles", x = "Value", y = "Density") +
+ theme_minimal()
