Chi2 und t-Test

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#                Chi-Square Distribution - Shiny App

#           (PDF/CDF + df slider + parameter display)

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library(shiny)

# ------------------- User Interface -------------------

ui <- fluidPage(

  titlePanel("Chi-Square Distribution"),

  sidebarLayout(

    sidebarPanel(

      selectInput("typ", "Function:",

                  choices = c("Distribution function (CDF)" = 0,

                              "Density function (PDF)" = 1)),

      helpText("Select which function you want to visualize."),

      sliderInput("df", "Degrees of freedom (ν):",

                  min = 1, max = 60, value = 5, step = 1),

      hr(),

      h4("Current Parameters:"),

      verbatimTextOutput("paramText")

    ),

    mainPanel(

      plotOutput("chisqPlot")

    )

  )

)

# ------------------- Server Logic -------------------

server <- function(input, output) {

  output$chisqPlot <- renderPlot({

    df <- input$df

    # Dynamic x-range: cover almost all probability mass

    xmax <- qchisq(0.999, df = df)

    x <- seq(0, xmax, length.out = 400)

    pdf_vals <- dchisq(x, df = df)

    cdf_vals <- pchisq(x, df = df)

    if (input$typ == 1) {

      # ---- PDF ----

      plot(x, pdf_vals, type = "l", lwd = 3, col = "coral3",

           main = sprintf("Chi-Square (df = %d) - Density (PDF)", df),

           xlab = "x", ylab = "Density",

           cex.lab = 1.2, cex.axis = 1.2, cex.main = 1.2)

      abline(h = 0, lty = 2)

    } else {

      # ---- CDF ----

      plot(x, cdf_vals, type = "l", lwd = 3, col = "steelblue",

           main = sprintf("Chi-Square (df = %d) - Distribution (CDF)", df),

           xlab = "x", ylab = "Cumulative probability",

           cex.lab = 1.2, cex.axis = 1.2, cex.main = 1.2)

      abline(h = c(0, 1), lty = 2)

    }

  })

  output$paramText <- renderText({

    df <- input$df

    paste0("Degrees of freedom (ν): ", df,

           "\nMean = ν = ", df,

           "\nVariance = 2ν = ", 2 * df)

  })

}

# ------------------- Run App -------------------

shinyApp(ui = ui, server = server)

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#              Student's t Distribution - Shiny App

#           (PDF/CDF + df slider + optional Normal overlay)

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library(shiny)

ui <- fluidPage(

  titlePanel("Student's t Distribution"),

  sidebarLayout(

    sidebarPanel(

      selectInput("typ", "Function:",

                  choices = c("Distribution function (CDF)" = 0,

                              "Density function (PDF)" = 1)),

      helpText("Select which function you want to visualize."),

      sliderInput("df", "Degrees of freedom (ν):",

                  min = 1, max = 100, value = 5, step = 1),

      checkboxInput("showNormal", "Overlay Standard Normal (N(0,1))", value = TRUE),

      hr(),

      h4("Current Parameters:"),

      verbatimTextOutput("paramText")

    ),

    mainPanel(

      plotOutput("tPlot")

    )

  )

)

server <- function(input, output) {

  output$tPlot <- renderPlot({

    df <- input$df

    # Dynamic x-range: central 99.9% interval

    xlim <- qt(0.9995, df = df)

    x <- seq(-xlim, xlim, length.out = 600)

    pdf_vals <- dt(x, df = df)

    cdf_vals <- pt(x, df = df)

    if (input$typ == 1) {

      # ---- PDF ----

      plot(x, pdf_vals, type = "l", lwd = 3, col = "coral3",

           main = sprintf("Student's t (df = %d) - Density (PDF)", df),

           xlab = "x", ylab = "Density",

           cex.lab = 1.2, cex.axis = 1.2, cex.main = 1.2)

      abline(h = 0, lty = 2)

      if (isTRUE(input$showNormal)) {

        lines(x, dnorm(x), lwd = 2, lty = 2, col = "gray30")

        legend("topright",

               legend = c(sprintf("t (df = %d)", df), "N(0,1)"),

               lty = c(1, 2), lwd = c(3, 2),

               col = c("coral3", "gray30"),

               bty = "n")

      }

    } else {

      # ---- CDF ----

      plot(x, cdf_vals, type = "l", lwd = 3, col = "steelblue",

           main = sprintf("Student's t (df = %d) - Distribution (CDF)", df),

           xlab = "x", ylab = "Cumulative probability",

           cex.lab = 1.2, cex.axis = 1.2, cex.main = 1.2)

      abline(h = c(0, 1), lty = 2)

    }

  })

  output$paramText <- renderText({

    df <- input$df

    mean_txt <- if (df > 1) "0" else "undefined (df ≤ 1)"

    var_txt  <- if (df > 2) sprintf("%g", df / (df - 2)) else "infinite (df ≤ 2)"

    paste0("Degrees of freedom (ν): ", df,

           "\nMean = ", mean_txt,

           "\nVariance = ", var_txt)

  })

}

shinyApp(ui = ui, server = server)