distributions added (bbaf74bc) · Commits · Johannes Bleher / SBDA_public

02_code/R/binomial_app.R

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		###################################################################
		# Binomial Distribution
		###################################################################

		# The following script serves as a visualization of the binomial
		# distribution. For this purpose we use the shiny "library". If you
		# run this code in your own R-environment make sure that the library
		# is installed. When you run this on the jupyerhub the shiny app
		# start in a separate window of your browser.

		# Load the shiny library
		library(shiny)

		# Definition of the user interface (ui)
		ui <- fluidPage(

		# Title of the shiny app
		titlePanel("Binomial Distribution"),

		# A panel on the left side of the page
		sidebarLayout(

		# Elements within the panel on the left side
		sidebarPanel(

		# Dropdown menü
		selectInput("typ", "Functions:",
		choices=c("Distribution function" = 0,
		"Probability mass function" = 1)),
		helpText("What function should be displayed?"),


		# Slider for the number of repetitions
		sliderInput(inputId = "repetitions",
		label = "Number of repetitions:",
		min = 1,
		max = 150,
		value = 75),

		# Slider of the probability of success
		sliderInput(inputId = "probability",
		label = "Probability of success:",
		min = 0,
		max = 1,
		value = 0.5)

		),

		# Main panel on the right side of the page
		mainPanel(

		# Links to the functions defined in the code below
		# Display the distribution
		plotOutput(outputId = "binomial")

		)
		)
		)

		# Here comes the definition of the server function:
		# The input to this function is always the function values of the above
		# page elements. For example, if a user choses in the dropdown menu
		# the option "Distribution function" then the set value can be used
		# within the server function below by using the inputId. The server function
		# essentially is a endless loop that constantly checks the input elements
		# from the UI for updates.

		server <- function(input, output) {

		# Function for dynamic visualization
		output$binomial <- renderPlot({

		# Parameters
		n <- input$repetitions
		p <- input$probability

		# The probability of x successes given that one has observed a Bernoulli experiment n
		# times with probabiliy of successes p
		x <- seq(0, n, by = 1)
		y <- dbinom(x, n, p)

		# 10000 draws from the binomial distribution with n and p
		r <- rbinom(10000, n, p)

		if (input$typ == 0) {

		FFemp <- ecdf(r)
		xx <- knots(FFemp)
		xxlag <- c(xx)
		FFemplag <- head(c(0,FFemp(xx)),-1)
		par(mar=c(4, 4.5, 2, 4)+0.1)

		plot(FFemp,
		xlab="Number of successes",
		ylab="Cumulated relative frequency",
		main=sprintf("Distribution function with n=%s and p=%s", n, p),
		cex.axis=1.2,
		cex.lab=1.2,
		cex.main=1.2,
		lwd=2,
		cex=1.3,
		pch=16)

		points(xxlag,
		FFemplag,
		type="o",
		lt=0,
		cex=1.3,
		col="black")

		# Comparision of the distribution function with the normal distribution
		curve(pnorm(x, np, sqrt(np*(1-p))),
		col="coral3",
		lwd=2,
		add=TRUE,
		yaxt="n")
		}
		else {

		# Presentation of the probability mass function via a stick diagram
		plot(x,
		y,
		type="h",
		lwd=2,
		ylim=c(0,max(y)),
		col="black",
		main=sprintf("Probability mass function with n=%s and p=%s", n, p),
		ylab="Frequency",
		xlab="Number of successes",
		cex.axis=1.2,
		cex.lab=1.2,
		cex.main=1.2)

		# Density function of the normal distribution with mu = np and sigma = sqrt(np*(1-p))
		curve(dnorm(x, np, sqrt(np*(1-p))),
		col="coral3",
		lwd=2,
		add=TRUE,
		yaxt="n")

		}

		})

		}

		# Compile the elements in the shiny app
		shinyApp(ui = ui, server = server)
		No newline at end of file

02_code/R/exponential_app.R

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		###################################################################
		# Exponential Distribution
		###################################################################

		# The following script serves as a visualization of the exponential
		# distribution. For this purpose we use the shiny "library". If you
		# run this code in your own R-environment make sure that the library
		# is installed. When you run this on the jupyerhub the shiny app
		# start in a separate window of your browser.

		# Load the shiny library
		library(shiny)

		# Definition of the user interface (ui)
		ui <- fluidPage(

		# Title of the shiny app
		titlePanel("Exponential Distribution"),

		# A panel on the left side of the page
		sidebarLayout(

		# Elements within the panel on the left side
		sidebarPanel(

		# Dropdown menü
		selectInput("typ", "Functions:",
		choices=c("Distribution function" = 0,
		"Probability mass function" = 1)),
		helpText("What function should be displayed?"),


		# Slider for the selection of the parameter lambda of the exponential distribution
		sliderInput(inputId = "lambda",
		label = "lambda",
		min = 0.00000001,
		max = 0.5,
		value = 0.25)
		),

		# Main panel on the right side of the page
		mainPanel(

		# Links to the functions defined in the code below
		# Display the distribution
		plotOutput(outputId = "exponential")

		)
		)
		)

		# Here comes the definition of the server function:
		# The input to this function is always the function values of the above
		# page elements. For example, if a user choses in the dropdown menu
		# the option "Distribution function" then the set value can be used
		# within the server function below by using the inputId. The server function
		# essentially is a endless loop that constantly checks the input elements
		# from the UI for updates.

		server <- function(input, output) {

		# Function for dynamic visualization
		output$exponential <- renderPlot({

		# Parameter
		lambda <- input$lambda

		if (input$typ == 0) {

		# Comparison with the distribution function of the theoretical exponential distribution
		curve(pexp(x, lambda),
		from=0,
		to=50,
		xlab="x",
		ylab="Distribution function",
		main=sprintf("Distribution function with lambda=%s", lambda),
		cex.axis=1.2,
		cex.lab=1.2,
		cex.main=1.2,
		col="coral3",
		lwd=3)
		}
		else {

		# Comparison with the density function of the exponential distribution
		curve(dexp(x, lambda),
		from=0,
		to=50,
		xlab="x",
		ylab="Density function",
		main=sprintf("Density function with lambda=%s", lambda),
		cex.axis=1.2,
		cex.lab=1.2,
		cex.main=1.2,
		col="coral3",
		lwd=3)

		}

		})

		}

		# Compile the elements in the shiny app
		shinyApp(ui = ui, server = server)
		No newline at end of file

02_code/R/normal_app.R

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		###################################################################
		# Normal distribution
		###################################################################

		# The following script serves as a visualization of the normal
		# distribution. For this purpose we use the shiny "library". If you
		# run this code in your own R-environment make sure that the library
		# is installed. When you run this on the jupyerhub the shiny app
		# start in a separate window of your browser.

		# Load the shiny library
		library(shiny)

		# Definition of the user interface (ui)
		ui <- fluidPage(

		# Title of the shiny app
		titlePanel("Normal Distribution"),

		# A panel on the left side of the page
		sidebarLayout(

		# Elements within the panel on the left side
		sidebarPanel(

		# Dropdown menü
		selectInput("typ", "Functions:",
		choices=c("Distribution function" = 0,
		"Probability mass function" = 1)),
		helpText("What function should be displayed?"),

		# Slider for the selection of the expected value mu of the normal distribution
		sliderInput(inputId = "mu",
		label = "mu",
		min = -5,
		max = 5,
		value = 0,
		step=0.01),

		# Slider for the selection of the standard deviation sigma of the normal distribution
		sliderInput(inputId = "sigma",
		label = "sigma",
		min = 0.1,
		max = 5,
		value = 1,
		step=0.01)

		),


		# Main panel on the right side of the page
		mainPanel(

		# Links to the functions defined in the code below
		# Display the distribution
		plotOutput(outputId = "normal")

		)
		)
		)

		# Here comes the definition of the server function:
		# The input to this function is always the function values of the above
		# page elements. For example, if a user choses in the dropdown menu
		# the option "Distribution function" then the set value can be used
		# within the server function below by using the inputId. The server function
		# essentially is a endless loop that constantly checks the input elements
		# from the UI for updates.
		server <- function(input, output) {

		# Function for dynamic visualization
		output$normal <- renderPlot({

		# Distribution parameters
		mu <- input$mu
		sigma <- input$sigma

		if (input$typ == 0) {

		# Comparison with the distribution function of the normal distribution
		curve(pnorm(x, mean=mu, sd=sigma),
		from=-10,
		to=10,
		xlab="x",
		ylim=c(0,1),
		xlim=c(-10,10),
		ylab="Distribution function",
		main=sprintf("Distribution function with mu=%s and sigma=%s", mu, sigma),
		col="coral3",
		lwd=3)

		# Comparison with the distribution function of the standard normal distribution
		curve(pnorm(x, mean=0, sd=1),
		ylim=c(0,1),
		xlim=c(-10,10),
		from=-10,
		to=10,
		col="black",
		cex.axis=1.2,
		cex.lab=1.2,
		add=TRUE,
		cex.main=1.2,
		lwd=3)

		}
		else {

		# Comparison with the density function of the normal distribution
		curve(dnorm(x, mean=mu, sd=sigma),
		from=-10,
		to=10,
		xlab="x",
		xlim=c(-10,10),
		ylab="Dichtefunktion",
		main=sprintf("Density function with mu=%s and sigma=%s", mu, sigma),
		col="coral3",
		lwd=3)

		# Comparison with the density function of the standard normal distribution
		curve(dnorm(x, mean=0, sd=1),
		xlim=c(-10,10),
		from=-10,
		to=10,
		col="black",
		add=TRUE,
		cex.axis=1.2,
		cex.lab=1.2,
		cex.main=1.2,
		lwd=3)




		}

		})

		}

		# Compile the elements in the shiny app
		shinyApp(ui = ui, server = server)
		No newline at end of file

02_code/R/poisson_app.R

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		###################################################################
		# Poisson distribution
		###################################################################

		# The following script serves as a visualization of the Poisson
		# distribution. For this purpose we use the shiny "library". If you
		# run this code in your own R-environment make sure that the library
		# is installed. When you run this on the jupyerhub the shiny app
		# start in a separate window of your browser.


		# Load the shiny library
		library(shiny)

		# Definition of the user interface (ui)
		ui <- fluidPage(

		# Title of the shiny app
		titlePanel("Poisson Distribution"),

		# A panel on the left side of the page
		sidebarLayout(

		# Elements within the panel on the left side
		sidebarPanel(

		# Dropdown menü
		selectInput("typ", "Functions:",
		choices=c("Distribution function" = 0,
		"Probability mass function" = 1)),
		helpText("What function should be displayed?"),


		# Slider for the selection of lambda
		sliderInput(inputId = "lambda",
		label = "Parameter lambda:",
		min = 1,
		max = 50,
		value = 25)

		),

		# Main panel on the right side of the page
		mainPanel(

		# Links to the functions defined in the code below
		# Display the distribution
		plotOutput(outputId = "poisson")

		)
		)
		)

		# Here comes the definition of the server function:
		# The input to this function is always the function values of the above
		# page elements. For example, if a user choses in the dropdown menu
		# the option "Distribution function" then the set value can be used
		# within the server function below by using the inputId. The server function
		# essentially is a endless loop that constantly checks the input elements
		# from the UI for updates.
		server <- function(input, output) {

		# Function for dynamic visualization
		output$poisson <- renderPlot({

		# Poisson Parameter lambda
		lambda <- input$lambda

		# Sequence of events
		x <- seq(0, 100, by = 1)

		# Proability of x events with the given lambda
		y <- dpois(x, lambda)

		# 1000 draws from the poisson distribution
		r <- rpois(1000, lambda)


		if (input$typ == 0) {

		FFemp <- ecdf(r)
		xx <- knots(FFemp)
		xxlag <- c(xx)
		FFemplag <- head(c(0,FFemp(xx)),-1)
		par(mar=c(4, 4.5, 2, 4)+0.1)

		# Presentation of the empirical distribution function
		plot(FFemp,
		xlab="Number of events",
		ylab="Cumulated relative frequency",
		main=sprintf("Distribution function with lambda=%s", lambda),
		cex.axis=1.2,
		cex.lab=1.2,
		cex.main=1.2,
		lwd=2,
		cex=1.3,
		pch=16,
		xlim=c(1,100))

		# Points on the left end of the stairs of the empirical distribution function
		points(xxlag,
		FFemplag,
		type="o",
		lt=0,
		cex=1.3,
		col="black")
		}
		else {

		# Presentation of the probability function via a stick diagram
		plot(x,
		y,
		type="h",
		lwd=2,
		ylim=c(0,max(y)),
		col="black",
		main=sprintf("Probability mass function with lambda=%s", lambda),
		ylab="Frequency",
		xlab="Number of events",
		cex.axis=1.2,
		cex.lab=1.2,
		cex.main=1.2)

		}

		})

		}

		# Zusammenführen der Elemente zu einer shiny app
		shinyApp(ui = ui, server = server)
		No newline at end of file

02_code/R/uniform_app.R

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		###################################################################
		# Uniform (Rectangular) Distribution
		###################################################################

		# The following script serves as a visualization of the Uniform (rectengular)
		# distribution. For this purpose we use the shiny "library". If you
		# run this code in your own R-environment make sure that the library
		# is installed. When you run this on the jupyerhub the shiny app
		# start in a separate window of your browser.

		# Load the shiny library
		library(shiny)

		# Definition of the user interface (ui)
		ui <- fluidPage(

		# Title of the shiny app
		titlePanel("Uniform Distribution"),

		# A panel on the left side of the page
		sidebarLayout(

		# Elements within the panel on the left side
		sidebarPanel(


		# Dropdown menü
		selectInput("typ", "Functions:",
		choices=c("Distribution function" = 0,
		"Probability mass function" = 1)),
		helpText("What function should be displayed?"),


		# Selection slider for the distribution parameter a of the uniform distribution
		sliderInput(inputId = "a",
		label = "a",
		min = 0,
		max = 1,
		value = 0.25),

		# Selection slider for the distribution parameter b of the uniform distribution
		sliderInput(inputId = "b",
		label = "b",
		min = 0,
		max = 1,
		value = 0.75)
		),

		# Main panel on the right side of the page
		mainPanel(

		# Links to the functions defined in the code below
		# Display the distribution
		plotOutput(outputId = "uniform")

		)
		)
		)

		# Here comes the definition of the server function:
		# The input to this function is always the function values of the above
		# page elements. For example, if a user choses in the dropdown menu
		# the option "Distribution function" then the set value can be used
		# within the server function below by using the inputId. The server function
		# essentially is a endless loop that constantly checks the input elements
		# from the UI for updates.
		server <- function(input, output, session) {

		# Function for dynamic visualization
		output$uniform <- renderPlot({

		# Distribution parameters
		a <- input$a
		b <- input$b

		updateSliderInput(session, "a", value = a,
		min = 0, max = b-0.01, step=0.01)

		updateSliderInput(session, "b", value = b,
		min = a+0.01, max = 1, step=0.01)

		if (input$typ == 0) {

		# Chosen uniform distribution function
		curve(punif(x, min=a, max=b),
		from=0,
		to=1,
		xlab="x",
		ylab="Distribution Function",
		main=sprintf("Distribution Function with a=%s and b=%s", a, b),
		cex.axis=1.2,
		cex.lab=1.2,
		cex.main=1.2,
		col="coral3",
		lwd=3)
		}
		else {

		# Chosen uniform density function
		curve(dunif(x, min=a, max=b),
		from=a,
		to=b,
		xlab="x",
		ylab="Density Function",
		main=sprintf("Density Function with a=%s and b=%s", a, b),
		xlim=c(0,1),
		ylim=c(0,1/(b-a)+0.1/(b-a)),
		cex.axis=1.2,
		cex.lab=1.2,
		cex.main=1.2,
		col="coral3",
		lwd=3)

		curve(0*x,
		from=0,
		to=a,
		col="coral3",
		lwd=3,
		add=TRUE)

		curve(0*x,
		from=b,
		to=1,
		col="coral3",
		lwd=3,
		add=TRUE)

		}

		})

		}

		# Compile the elements to a shiny app
		shinyApp(ui = ui, server = server)
		No newline at end of file