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--- b:head_first_statistics:visualization [2024/09/04 08:49] – [Scatter plot] hkimscil
+++ b:head_first_statistics:visualization [2025/09/08 08:22] (current) – [Histogram Modality] hkimscil
@@ Line 91: / Line 91: @@
 </code>
 {{:b:head_first_statistics:pasted:20240904-082258.png}}
+<code>
+dat.iq <- rnorm(1000, 100, 15)
+head(dat.iq)
+tail(dat.iq)
+head(dat.iq, n=12)
+tail(dat.iq, n=12)
+mean(dat.iq)
+sd(dat.iq)
+hist(dat.iq)
+hist(dat.iq, breaks=30, col='lightblue')
+set.seed(101)
+dat.iq <- rnorm(1000, 100, 15)
+head(dat.iq)
+tail(dat.iq)
+head(dat.iq, n=12)
+tail(dat.iq, n=12)
+mean(dat.iq)
+sd(dat.iq)
+hist(dat.iq)
+hist(dat.iq, breaks=30, col='lightblue')
+</code>
 ====== Scatter plot ======
 <code>
@@ Line 156: / Line 183: @@
 <WRAP clear />
-A bit more fancy line
-<code># Enhanced Scatterplot of MPG vs. Weight
-# by Number of Car Cylinders
-library(car)
-scatterplot(mpg ~ wt | cyl, data=mtcars,
-   xlab="Weight of Car", ylab="Miles Per Gallon",
-   main="Enhanced Scatter Plot",
-   labels=row.names(mtcars))</code>
-{{:c:ps1-1:2019:pasted:20190909-080032.png}}
-<WRAP clear />
 ====== Presentation ======
@@ Line 176: / Line 191: @@
 <WRAP clear/>
 ====== Histogram skewedness ======
+<WRAP column half>
+<code>
+####
+# left-skewed distribution
+# 1.
+set.seed(1)
+data <- rbeta(500, shape1 = 10, shape2 = 2)
+hist(data, probability = TRUE,
+     main = "Histogram with Left-skewed data",
+     xlab = "Value", ylab = "Density",
+     col = "lightblue", border = "white")
+# 2.
+# install.packages("fitdistrplus")
+library(fitdistrplus)
-[{{:c:ps1-1:2019:pasted:20190909-111117.png|skewness}}]
+fit <- fitdist(data, "beta")
-<WRAP clear/>.
+alpha_est <- fit$estimate["shape1"]
-[{{:c:ps1-1:2019:pasted:20190909-111001.png|modality}}]
+beta_est <- fit$estimate["shape2"]
-<WRAP clear/>.
-====== box plot ======
+# 3.
+curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est),
+      add = TRUE, col = "red", lwd = 2)
+</code>
+</WRAP>
+<WRAP column half>
+{{:b:head_first_statistics:pasted:20250903-074821.png}}
+</WRAP>
+<WRAP clear/>
+<WRAP column half>
+<code>
+set.seed(1)
+data <- rbeta(500, shape1 = 10, shape2 = 10)
+hist(data, probability = TRUE,
+     main = "Histogram with Normal Distribution Data",
+     xlab = "Value", ylab = "Density",
+     col = "lightblue", border = "white")
+# 2.
+# install.packages("fitdistrplus")
+library(fitdistrplus)
+fit <- fitdist(data, "beta")
+alpha_est <- fit$estimate["shape1"]
+beta_est <- fit$estimate["shape2"]
+# 3.
+curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est),
+      add = TRUE, col = "red", lwd = 2)
+</code>
+</WRAP>
+<WRAP column half>
+{{:b:head_first_statistics:pasted:20250903-074830.png}}
+</WRAP>
+<WRAP clear/>
+<WRAP column half>
+<code>
+##
+# right-skewed distribution
+# 1.
+set.seed(1)
+data <- rbeta(500, shape1 = 2, shape2 = 10)
+hist(data, probability = TRUE,
+     main = "Histogram with Right-skewed Distribution",
+     xlab = "Value", ylab = "Density",
+     col = "lightblue", border = "white")
+# install.packages("fitdistrplus")
+library(fitdistrplus)
+fit <- fitdist(data, "beta")
+alpha_est <- fit$estimate["shape1"]
+beta_est <- fit$estimate["shape2"]
+#
+curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est),
+      add = TRUE, col = "red", lwd = 2)
+</code>
+</WRAP>
+<WRAP column half>
+{{:b:head_first_statistics:pasted:20250903-082513.png}}
+</WRAP>
+<WRAP clear/>
+====== Histogram Modality======
+<WRAP column half>
+Unimodal
+<code>
+### unimodal data
+set.seed(1)
+d.1 <- rnorm(500, 10, 2)
+hist(d.1, breaks = 30, probability = T,
+     main = "Hist with Unimodal distrib",
+     xlab = "Value", ylab = "Density",
+     col = "lightblue", border = "black")
+lines(density(d.1),
+      col = "darkred", lwd = 2)
+</code>
+</WRAP>
+<WRAP column half>
+{{:b:head_first_statistics:pasted:20250903-083409.png}}
+</WRAP>
+<WRAP clear/>
+Bimodal distribution
+<WRAP column half>
+<code>
+### bimodal data
+set.seed(1)
+d.1 <- rnorm(500, 10, 2)
+d.2 <- rnorm(500, 20, 2)
+d.all <- c(d.1, d.2)
+hist(d.all, breaks = 30, probability = T,
+     main = "Hist with bimodal distrib",
+     xlab = "Value", ylab = "Density",
+     col = "lightblue", border = "black")
+lines(density(d.all),
+      col = "darkred", lwd = 2)
+</code>
+</WRAP>
+<WRAP column half>
+{{:b:head_first_statistics:pasted:20250903-083524.png}}
+</WRAP>
+<WRAP clear/>
+<WRAP column half>
+<code>
+### multi-modal data
+# Parameters for the first normal distribution (Mode 1)
+m.1 <- 50
+sd.1 <- 5
+# Parameters for the second normal distribution (Mode 2)
+m.2 <- 100
+sd.2 <- 15
+m.3 <- 160
+sd.3 <- 6
+# Mixing proportion for Mode 1
+prop.1 <- 0.3
+# Mixing proportion for Mode 2
+prop.2 <- 0.6 # This is 1 - prop1
+# Mixing proportion for Mode 2
+prop.3 <- 1.0 # This is 1 - prop1
+# Number of samples to generate
+n.sam <- 1000
+# Create an empty vector to store the combined samples
+mm.dist <- numeric(n.sam)
+set.seed(1)
+for (i in 1:n.sam) {
+  # Randomly choose which distribution to sample from
+  tmp <- runif(1)
+  if (tmp < prop.1) {
+    mm.dist[i] <- rnorm(1, mean = m.1, sd = sd.1)
+  } else if (tmp < prop.2) {
+    mm.dist[i] <- rnorm(1, mean = m.2, sd = sd.2)
+  } else {
+    mm.dist[i] <- rnorm(1, mean = m.3, sd = sd.3)
+  }
+}
+hist(mm.dist, breaks = 30,
+     main = "Multimodal Distribution",
+     xlab = "Value", ylab = "Density",
+     freq = FALSE, probability = T,
+     col = "lightblue", border = "black")
+lines(density(mm.dist),
+      col = "darkred", lwd = 2)
+</code>
+</WRAP>
+<WRAP column half>
+{{:b:head_first_statistics:pasted:20250908-082219.png}}
+</WRAP>
+<WRAP clear/>
+====== box plot ======
+<WRAP column half>
 <code>
 # Boxplot of MPG by Car Cylinders
@@ Line 191: / Line 388: @@
     ylab="Miles Per Gallon")
 </code>
-{{:c:ps1-1:2019:pasted:20190909-111438.png}}
+</WRAP>
+<WRAP column half>
+{{:c:ps1-1:2019:pasted:20190909-111438.png}}
+</WRAP>
+<WRAP clear/>
+====== see also ======
+https://r-graph-gallery.com/