Calculator: Normal distribution
Summary
A calculator to work out cdfs for the normal distribution \(N(\mu,\sigma^2)\).
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#| viewerHeight: 700
library(shiny)
library(bslib)
library(ggplot2)
ui <- page_fluid(
title = "Normal distribution calculator",
layout_columns(
col_widths = c(4, 8),
# Left column - Inputs
card(
card_header("Parameters"),
card_body(
numericInput("mean", "Mean (μ):", value = 0),
numericInput("sd", "Standard deviation (σ):", value = 1, min = 0.01),
hr(),
radioButtons("prob_type", "Probability to calculate:",
choices = list("P(X ≤ x)" = "less",
"P(X ≥ x)" = "greater",
"P(x ≤ X ≤ y)" = "between"),
selected = "less"),
conditionalPanel(
condition = "input.prob_type == 'less' || input.prob_type == 'greater'",
numericInput("x_value", "x value:", value = 0)
),
conditionalPanel(
condition = "input.prob_type == 'between'",
numericInput("x_lower", "Lower bound (x):", value = -1),
numericInput("x_upper", "Upper bound (y):", value = 1)
)
)
),
# Right column - Plot
card(
card_header("Normal distribution plot"),
card_body(
uiOutput("plot_title"),
plotOutput("distPlot", height = "300px")
)
)
),
# Bottom row - Results
card(
card_header("Results"),
card_body(
# Removed the LaTeX formula display
textOutput("explanation")
)
)
)
server <- function(input, output, session) {
# Display the plot title with distribution parameters
output$plot_title <- renderUI({
title <- sprintf("N(μ = %.2f, σ = %.2f)", input$mean, input$sd)
tags$h4(title, style = "text-align: center; margin-bottom: 15px;")
})
# Calculate the probability based on user selection
probability <- reactive({
if (input$prob_type == "less") {
prob <- pnorm(input$x_value, mean = input$mean, sd = input$sd)
explanation <- sprintf("P(X ≤ %.2f) = %.4f or %.2f%%",
input$x_value, prob, prob * 100)
return(list(prob = prob, explanation = explanation, type = "less", x = input$x_value))
} else if (input$prob_type == "greater") {
prob <- 1 - pnorm(input$x_value, mean = input$mean, sd = input$sd)
explanation <- sprintf("P(X ≥ %.2f) = %.4f or %.2f%%",
input$x_value, prob, prob * 100)
return(list(prob = prob, explanation = explanation, type = "greater", x = input$x_value))
} else if (input$prob_type == "between") {
lower_prob <- pnorm(input$x_lower, mean = input$mean, sd = input$sd)
upper_prob <- pnorm(input$x_upper, mean = input$mean, sd = input$sd)
prob <- upper_prob - lower_prob
explanation <- sprintf("P(%.2f ≤ X ≤ %.2f) = %.4f or %.2f%%",
input$x_lower, input$x_upper, prob, prob * 100)
return(list(prob = prob, explanation = explanation, type = "between",
lower = input$x_lower, upper = input$x_upper))
}
})
# Display an explanation of the calculation
output$explanation <- renderText({
res <- probability()
return(res$explanation)
})
# Generate the normal distribution plot
output$distPlot <- renderPlot({
# Calculate range for x-axis (covering 99.7% of the distribution)
x_min <- input$mean - 3.5 * input$sd
x_max <- input$mean + 3.5 * input$sd
# Create data frame for plotting
x <- seq(x_min, x_max, length.out = 500)
y <- dnorm(x, mean = input$mean, sd = input$sd)
df <- data.frame(x = x, y = y)
# Create base plot
p <- ggplot(df, aes(x = x, y = y)) +
geom_line() +
labs(x = "X", y = "Density") +
theme_minimal() +
theme(panel.grid.minor = element_blank())
# Add bold line at X = 0
p <- p + geom_vline(xintercept = 0, linetype = "solid", color = "black", linewidth = 0.8)
# Add shaded area based on selected probability type
res <- probability()
if (res$type == "less") {
shade_x <- seq(x_min, res$x, length.out = 200)
shade_y <- dnorm(shade_x, mean = input$mean, sd = input$sd)
shade_df <- data.frame(x = shade_x, y = shade_y)
p <- p + geom_area(data = shade_df, aes(x = x, y = y), fill = "#3F6BB6", alpha = 0.6) +
geom_vline(xintercept = res$x, linetype = "dashed", color = "#db4315")
} else if (res$type == "greater") {
shade_x <- seq(res$x, x_max, length.out = 200)
shade_y <- dnorm(shade_x, mean = input$mean, sd = input$sd)
shade_df <- data.frame(x = shade_x, y = shade_y)
p <- p + geom_area(data = shade_df, aes(x = x, y = y), fill = "#3F6BB6", alpha = 0.6) +
geom_vline(xintercept = res$x, linetype = "dashed", color = "#db4315")
} else if (res$type == "between") {
shade_x <- seq(res$lower, res$upper, length.out = 200)
shade_y <- dnorm(shade_x, mean = input$mean, sd = input$sd)
shade_df <- data.frame(x = shade_x, y = shade_y)
p <- p + geom_area(data = shade_df, aes(x = x, y = y), fill = "#3F6BB6", alpha = 0.6) +
geom_vline(xintercept = res$lower, linetype = "dashed", color = "#db4315") +
geom_vline(xintercept = res$upper, linetype = "dashed", color = "#db4315")
}
return(p)
})
}
shinyApp(ui = ui, server = server)Further reading
This interactive element appears in Guide: PMFs, PDFs, CDFs and [Overview: Probability distributions.] Please click the relevant links to go to the guides.
Version history
v1.0: initial version created 04/24 by tdhc and Michelle Arnetta as part of a University of St Andrews VIP project.