Interactive: Mean and variance of exponential distribution

Summary

Interactive diagram for seeing how the mean and variance affect the shape of the exponential distribution.

#| '!! shinylive warning !!': |
#|   shinylive does not work in self-contained HTML documents.
#|   Please set `embed-resources: false` in your metadata.
#| standalone: true
#| viewerHeight: 770

library(shiny)
library(bslib)
library(ggplot2)

ui <- page_fluid(
  title = "Exponential distribution visualizer",
  
  # Plot at the top
  card(
    card_header("Exponential distribution plot"),
    card_body(
      plotOutput("distPlot", height = "500px")
    )
  ),
  
  # Parameters below
  card(
    card_header("Distribution parameters"),
    card_body(
      sliderInput("rate", "Rate parameter (λ):", 
                 min = 0.1, max = 3, value = 1, step = 0.1)
    )
  )
)

server <- function(input, output, session) {
  
  # Generate the exponential distribution plot
  output$distPlot <- renderPlot({
    # Fixed range for x-axis to show consistent scale
    x_min <- 0
    x_max <- 10
    
    # Create data frame for plotting
    x <- seq(x_min, x_max, length.out = 500)
    y <- dexp(x, rate = input$rate)
    df <- data.frame(x = x, y = y)
    
    # Calculate mean and variance for display
    mean_val <- 1 / input$rate
    variance_val <- 1 / (input$rate^2)
    
    # Create plot with fixed axes
    p <- ggplot(df, aes(x = x, y = y)) +
      geom_line(color = "#3F6BB6", size = 1.2) +
      labs(x = "X", y = "Density",
           title = sprintf("Exponential distribution: Exp(λ = %.1f)\nMean = %.2f, Variance = %.2f", 
                          input$rate, mean_val, variance_val)) +
      theme_minimal() +
      theme(
        panel.grid.minor = element_blank(),
        plot.title = element_text(hjust = 0.5, size = 16),
        axis.title = element_text(size = 14),
        axis.text = element_text(size = 12)
      ) +
      # Fixed axis limits
      xlim(x_min, x_max) +
      ylim(0, 3) +
      # Add reference line at mean
      geom_vline(xintercept = mean_val, linetype = "dashed", color = "#DB4315", alpha = 0.7) +
      annotate("text", x = mean_val + 0.5, y = 2.5, label = "Mean", color = "#DB4315", size = 4)
    
    return(p)
  })
}

shinyApp(ui = ui, server = server)

Further reading

This interactive element appears in Guide: Expected value, variance, standard deviation. Please click this link to go to the guide.

Version history

v1.0: initial version created 08/24 by tdhc.

This work is licensed under CC BY-NC-SA 4.0.