Commit dad78736 authored by jbleher's avatar jbleher
Browse files

New apps

parent 8eb032bf

02_code/R/Bernoulli_app.R

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############################################################

#                 Bernoulli Distribution - Shiny App

############################################################



library(shiny)



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

ui <- fluidPage(

  

  # Title

  titlePanel("Bernoulli Distribution"),

  

  sidebarLayout(

    

    sidebarPanel(

      # Auswahl: PMF oder CDF

      selectInput("typ", "Function:",

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

                              "Probability mass function (PMF)" = 1)),

      

      helpText("The Bernoulli distribution models a single trial with outcome 0 or 1."),

      

      # Parameter p

      sliderInput("p", "Success probability (p):",

                  min = 0, max = 1, value = 0.4, step = 0.01)

    ),

    

    mainPanel(

      plotOutput("bernPlot")

    )

  )

)



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

server <- function(input, output) {

  

  output$bernPlot <- renderPlot({

    

    p <- input$p

    x <- 0:1

    

    if (input$typ == 1) {

      # PMF

      pmf <- dbinom(x, size = 1, prob = p)

      plot(x, pmf, type = "h", lwd = 3,

           ylim = c(0, 1),

           main = sprintf("Bernoulli PMF (p = %.2f)", p),

           xlab = "x", ylab = "Probability",

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

      points(x, pmf, pch = 19)

      text(x, pmf + 0.05, labels = round(pmf, 3))

      

    } else {

      # CDF

      cdf <- pbinom(x, size = 1, prob = p)

      plot(x, cdf, type = "s", lwd = 3,

           ylim = c(0, 1),

           main = sprintf("Bernoulli CDF (p = %.2f)", p),

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

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

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

      points(x, cdf, pch = 19)

    }

  })

}



# ------------------- Start App -------------------

shinyApp(ui = ui, server = server)

02_code/R/Beta_app.R

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############################################################

#                 Beta Distribution - Shiny App

############################################################



library(shiny)



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

ui <- fluidPage(

  

  # Title

  titlePanel("Beta Distribution"),

  

  sidebarLayout(

    

    sidebarPanel(

      

      # Auswahl: CDF oder PDF

      selectInput("typ", "Function:",

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

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

      

      helpText("The Beta distribution is defined on [0,1] with two shape parameters."),

      

      # Parameter alpha (shape1) und beta (shape2)

      sliderInput("alpha", "Shape parameter α (shape1):",

                  min = 0.1, max = 10, value = 2, step = 0.1),

      

      sliderInput("beta", "Shape parameter β (shape2):",

                  min = 0.1, max = 10, value = 3, step = 0.1)

    ),

    

    mainPanel(

      plotOutput("betaPlot")

    )

  )

)



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

server <- function(input, output) {

  

  output$betaPlot <- renderPlot({

    

    alpha <- input$alpha

    beta  <- input$beta

    

    # x-Werte im Intervall [0,1]

    x <- seq(0, 1, length.out = 400)

    

    if (input$typ == 1) {

      # PDF

      y <- dbeta(x, shape1 = alpha, shape2 = beta)

      

      plot(x, y, type = "l", lwd = 3,

           main = sprintf("Beta PDF (α = %.2f, β = %.2f)", alpha, beta),

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

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

      abline(h = 0, lwd = 2)

      

    } else {

      # CDF

      y <- pbeta(x, shape1 = alpha, shape2 = beta)

      

      plot(x, y, type = "l", lwd = 3,

           main = sprintf("Beta CDF (α = %.2f, β = %.2f)", alpha, beta),

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

           cex.lab = 1.2, cex.main = 1.2,

           ylim = c(0, 1))

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

    }

  })

}



# ------------------- Start App -------------------

shinyApp(ui = ui, server = server)

02_code/R/Cauchy_app.R

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############################################################

#                 Cauchy Distribution - Shiny App

############################################################



library(shiny)



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

ui <- fluidPage(

  

  titlePanel("Cauchy Distribution"),

  

  sidebarLayout(

    

    sidebarPanel(

      

      selectInput("typ", "Function:",

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

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

      

      helpText("The Cauchy distribution is a heavy-tailed distribution with undefined mean and variance."),

      

      sliderInput("x0", "Location parameter (x0):",

                  min = -10, max = 10, value = 0, step = 0.5),

      

      sliderInput("gamma", "Scale parameter (γ):",

                  min = 0.1, max = 10, value = 1, step = 0.1)

    ),

    

    mainPanel(

      plotOutput("cauchyPlot")

    )

  )

)



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

server <- function(input, output) {

  

  output$cauchyPlot <- renderPlot({

    

    x0    <- input$x0

    gamma <- input$gamma

    

    # x-range around x0

    x <- seq(x0 - 10 * gamma, x0 + 10 * gamma, length.out = 400)

    

    if (input$typ == 1) {

      # PDF

      y <- dcauchy(x, location = x0, scale = gamma)

      

      plot(x, y, type = "l", lwd = 3,

           main = sprintf("Cauchy PDF (x0 = %.2f, γ = %.2f)", x0, gamma),

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

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

      abline(h = 0, lwd = 2)

      

    } else {

      # CDF

      y <- pcauchy(x, location = x0, scale = gamma)

      

      plot(x, y, type = "l", lwd = 3,

           main = sprintf("Cauchy CDF (x0 = %.2f, γ = %.2f)", x0, gamma),

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

           cex.lab = 1.2, cex.main = 1.2,

           ylim = c(0, 1))

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

    }

  })

}



# ------------------- Start App -------------------

shinyApp(ui = ui, server = server)

02_code/R/Emxtreme_value_app.R

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############################################################

#          Extreme Value (Gumbel) Distribution - Shiny App

############################################################



library(shiny)



# -------- Gumbel PDF and CDF (Type I Extreme Value) --------

dgumbel <- function(x, mu = 0, beta = 1) {

  z <- (x - mu) / beta

  (1 / beta) * exp(-(z + exp(-z)))

}



pgumbel <- function(x, mu = 0, beta = 1) {

  z <- (x - mu) / beta

  exp(-exp(-z))

}



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

ui <- fluidPage(

  

  titlePanel("Extreme Value (Gumbel) Distribution"),

  

  sidebarLayout(

    

    sidebarPanel(

      

      selectInput("typ", "Function:",

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

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

      

      helpText("Gumbel distribution (Type I Extreme Value) for maxima."),

      

      sliderInput("mu", "Location parameter (μ):",

                  min = -10, max = 10, value = 0, step = 0.5),

      

      sliderInput("beta", "Scale parameter (β):",

                  min = 0.1, max = 10, value = 1, step = 0.1)

    ),

    

    mainPanel(

      plotOutput("gumbelPlot")

    )

  )

)



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

server <- function(input, output) {

  

  output$gumbelPlot <- renderPlot({

    

    mu   <- input$mu

    beta <- input$beta

    

    # x-range around mu

    x <- seq(mu - 10 * beta, mu + 10 * beta, length.out = 400)

    

    if (input$typ == 1) {

      # PDF

      y <- dgumbel(x, mu = mu, beta = beta)

      

      plot(x, y, type = "l", lwd = 3,

           main = sprintf("Gumbel PDF (μ = %.2f, β = %.2f)", mu, beta),

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

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

      abline(h = 0, lwd = 2)

      

    } else {

      # CDF

      y <- pgumbel(x, mu = mu, beta = beta)

      

      plot(x, y, type = "l", lwd = 3,

           main = sprintf("Gumbel CDF (μ = %.2f, β = %.2f)", mu, beta),

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

           cex.lab = 1.2, cex.main = 1.2,

           ylim = c(0, 1))

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

    }

  })

}



# ------------------- Start App -------------------

shinyApp(ui = ui, server = server)

02_code/R/Logit_app.R

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############################################################

#                 Logistic Distribution - Shiny App

############################################################



library(shiny)



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

ui <- fluidPage(

  

  titlePanel("Logistic Distribution"),

  

  sidebarLayout(

    

    sidebarPanel(

      

      selectInput("typ", "Function:",

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

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

      

      helpText("The logistic distribution is similar to the normal distribution but has heavier tails."),

      

      sliderInput("mu", "Location parameter (μ):",

                  min = -10, max = 10, value = 0, step = 0.5),

      

      sliderInput("s", "Scale parameter (s):",

                  min = 0.1, max = 10, value = 1, step = 0.1)

    ),

    

    mainPanel(

      plotOutput("logisPlot")

    )

  )

)



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

server <- function(input, output) {

  

  output$logisPlot <- renderPlot({

    

    mu <- input$mu

    s  <- input$s

    

    # x-range around mu

    x <- seq(mu - 10 * s, mu + 10 * s, length.out = 400)

    

    if (input$typ == 1) {

      # PDF

      y <- dlogis(x, location = mu, scale = s)

      

      plot(x, y, type = "l", lwd = 3,

           main = sprintf("Logistic PDF (μ = %.2f, s = %.2f)", mu, s),

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

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

      abline(h = 0, lwd = 2)

      

    } else {

      # CDF

      y <- plogis(x, location = mu, scale = s)

      

      plot(x, y, type = "l", lwd = 3,

           main = sprintf("Logistic CDF (μ = %.2f, s = %.2f)", mu, s),

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

           cex.lab = 1.2, cex.main = 1.2,

           ylim = c(0, 1))

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

    }

  })

}



# ------------------- Start App -------------------

shinyApp(ui = ui, server = server)