Density Plot and Histogram

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Load the required library(s):

> library(ggplot2)

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Data

> set.seed(42)
> df <- data.frame(vals = round(c(rnorm(30, mean = 18, sd = 10))))
> head(df)

  vals
1   32
2   12
3   22
4   24
5   22
6   17

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Density Plot

> ggplot(df, aes(x = vals)) +
+   geom_density(alpha = 0.5, fill = "lightgreen") +
+   labs(title = "Density Plot", 
+        subtitle = "Kernal: Default (Gaussian)", x = "Values", y = "Density") +
+   theme_minimal()

Kimberly Fessel has explained with a visually understandable tutorial. See here: https://youtu.be/DCgPRaIDYXA

> # Generate 6 random data points from a normal distribution
> set.seed(45) # Setting seed for reproducibility
> data_points <- rnorm(6, mean = 50, sd = 10)
> 
> # Bandwidth estimation (Silverman's rule of thumb)
> bandwidth <- 1.06 * sd(data_points) * length(data_points)^(-1/5)
> 
> # sequence of x values for plotting the individual Gaussian curves
> x_values <- seq(min(data_points) - 3 * bandwidth, max(data_points) + 3 * bandwidth, length.out = 400)
> 
> # Function to create a data frame for scaled individual Gaussian distributions
> gaussian_curve <- function(x, mu) {
+   data.frame(x = x, y = dnorm(x, mean = mu, sd = bandwidth) / length(data_points))
+ }
> 
> # Create a list of data frames for each data point
> curves_list <- lapply(data_points, gaussian_curve, x = x_values)
> curves_df <- do.call(rbind, curves_list)
> curves_df$group <- rep(data_points, each = 400)
> 
> data_frame <- data.frame(x = data_points)
> 
> ggplot() +
+   geom_density(data = data_frame, aes(x = x, y = after_stat(density)), fill = "blue", alpha = 0.4) +
+   geom_line(data = curves_df, aes(x = x, y = y, group = group, col = as.factor(group))) +
+   geom_point(data = data_frame, aes(x = x, y = 0, col = as.factor(x)), size = 3) +
+   labs(title = "Kernal Density Estimation, and Individual Curves",
+        caption = "Kernal used: Gaussian",
+        x = "Data Values", 
+        y = "Density") +
+   theme_minimal() +
+   guides(color = "none")

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Different Kernal Estimation Techniques

Different Kernal Estimation Techniques

Refer to this link to know more: https://rdrr.io/r/stats/density.html

More reading materials: 1. Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988). The New S Language. Wadsworth & Brooks/Cole (for S version).

2. Scott, D. W. (1992). Multivariate Density Estimation. Theory, Practice and Visualization. New York: Wiley.

3. Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society series B, 53, 683–690. . https://www.jstor.org/stable/2345597.

4. Silverman, B. W. (1986). Density Estimation. London: Chapman and Hall.

5. Venables, W. N. and Ripley, B. D. (2002). Modern Applied Statistics with S. New York: Springer.

Gaussian Kernal

> ggplot(df, aes(x = vals)) +
+   geom_density(alpha = 0.5, kernel = "gaussian", fill = "lightgreen") +
+   labs(title = "Density Plot", 
+        subtitle = "Kernal: Gaussian", x = "Values", y = "Density") +
+   theme_minimal()

Epanechnikov Kernal

> ggplot(df, aes(x = vals)) +
+   geom_density(alpha = 0.5, kernel = "epanechnikov", fill = "lightgreen") +
+   labs(title = "Density Plot", 
+        subtitle = "Kernal: Epanechnikov", x = "Values", y = "Density") +
+   theme_minimal()

Rectangular Kernal

> ggplot(df, aes(x = vals)) +
+   geom_density(alpha = 0.5, kernel = "rectangular", fill = "lightgreen") +
+   labs(title = "Density Plot", 
+        subtitle = "Kernal: Rectangular", x = "Values", y = "Density") +
+   theme_minimal()

Triangular Kernal

> ggplot(df, aes(x = vals)) +
+   geom_density(alpha = 0.5, kernel = "triangular", fill = "lightgreen") +
+   labs(title = "Density Plot", 
+        subtitle = "Kernal: Triangular", x = "Values", y = "Density") +
+   theme_minimal()

Biweight Kernal

> ggplot(df, aes(x = vals)) +
+   geom_density(alpha = 0.5, kernel = "biweight", fill = "lightgreen") +
+   labs(title = "Density Plot", 
+        subtitle = "Kernal: Biweight", x = "Values", y = "Density") +
+   theme_minimal()

Cosine Kernal

> ggplot(df, aes(x = vals)) +
+   geom_density(alpha = 0.5, kernel = "cosine", fill = "lightgreen") +
+   labs(title = "Density Plot", 
+        subtitle = "Kernal: Cosine", x = "Values", y = "Density") +
+   theme_minimal()

Optcosine Kernal

> ggplot(df, aes(x = vals)) +
+   geom_density(alpha = 0.5, kernel = "optcosine", fill = "lightgreen") +
+   labs(title = "Density Plot", 
+        subtitle = "Kernal: Optcosine", x = "Values", y = "Density") +
+   theme_minimal()

Histogram and Density Plot Combined

> # Create the combined histogram and density plot
> ggplot(df, aes(x = vals)) +
+   geom_histogram(aes(y = after_stat(density)), bins = 30, fill = "lightblue", color = "black") +
+   geom_density(alpha = 0.5, fill = "lightgreen") +
+   labs(title = "Combined Histogram and Density Plot", x = "Value", y = "Density") +
+   theme_minimal()