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app.R
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library(shiny)
library(bslib)
# Probability Calcuator Shiny App
# Author: Evangelidakis Leandros
# Contact: [email protected]
ui <- navbarPage("Probability Calculator",
theme = bs_theme(version=3,bootswatch = "flatly"),
navbarMenu("Discrete Distributions",
tabPanel("Binomial",
fluidRow(
h2("Binomial Distribution"),
withMathJax(),
helpText('$$X \\sim {\\sf Binom}(n, p)$$'),
helpText(' $$P[X=x]= \\binom{n}{x}p^k(1-p)^{n-x}$$ '),
helpText('$$E[X]=np, Var[X]=npq$$'),
),
sidebarLayout(
sidebarPanel(
numericInput("binom_n",
"Number of trials (n)",
min = 1,
max = 1000,
value=20)
,
numericInput("binom_x",
"Number of successfull outcomes (x)",
min = 0,
max = 1000,
value=5),
numericInput("binom_p",
"Probability of success (p)",
min = 0,
max = 1,
value=0.5),
radioButtons("binom_checkbox","Options",choices =list("Single Value, P[X=x]"="1",
"Cumulative probability P[X<=x]"="2"),
selected="1"),
actionButton("binom_btn","Calculate",class = "btn-success")
)
,
mainPanel(
verbatimTextOutput("binomial_prob",placeholder = T),
plotOutput(outputId = "binom_plot")
)
)
),
#----------------------------------------------------------------------------------------------------------------------
tabPanel("Geometric",
fluidRow(
h2("Geometric Distribution"),
withMathJax(),
helpText('$$X \\sim {\\sf Geom}(p)$$'),
helpText('$$P[X=x]=(1-p)^{x}p$$'),
helpText('$$E[X]=\\frac{1}{p}, Var[X]=\\frac{1-p}{p}$$')
),
sidebarLayout(
sidebarPanel(
numericInput("geom_x",
"Number of trials until success (x)",
min = 1,
max = 1000,
value=20)
,
numericInput("geom_p",
"Probability of success (p)",
min = 0,
max = 1,
value=0.5),
radioButtons("geom_checkbox","Options",choices = list("Single Value, P[X=x]"="1",
"Cumulative probability P[X<=x]"="2"),
selected="1"),
actionButton("geom_btn","Calculate",class = "btn-success")
),
mainPanel(
verbatimTextOutput("geom_prob",placeholder = T),
plotOutput(outputId = "geom_plot")
)
)
) ,
#----------------------------------------------------------------------------------------------------------------------
tabPanel("Negative Binomial ",
fluidRow(
h2("Negative Binomial Distribution"),
withMathJax(),
helpText('$$X \\sim {\\sf NB}(r,p)$$'),
helpText('$$P[X=k]=\\binom{k+r-1}{r-1}(1-p)^{k}p^r$$'),
helpText('$$E[X]=\\frac{pr}{1-p}, Var[X]=\\frac{pr}{(1-p)^2}$$')
),
sidebarLayout(
sidebarPanel(
numericInput("neg_binom_k",
"Number of successes (k)",
min = 0,
max = 1000,
value=5)
,
numericInput("neg_binom_r",
"Number of failures (r)",
min = 1,
max = 1000,
value=10)
,
numericInput("neg_binom_p",
"Probability of success (p)",
min = 0,
max = 1,
value=0.6),
radioButtons("neg_binom_checkbox","Options",choices = list("Single Value, P[X=k]"="1",
"Cumulative probability P[X<=k]"="2"),
selected="1"),
actionButton("neg_binom_btn","Calculate",class = "btn-success")
),
mainPanel(
verbatimTextOutput("neg_binom_prob",placeholder = T),
plotOutput(outputId = "neg_binom_plot")
)
)
) ,
#----------------------------------------------------------------------------------------------------------------------
tabPanel("Poisson ",
fluidRow(
h2("Poisson Distribution"),
withMathJax(),
helpText('$$X \\sim {\\sf Poisson}(\\lambda)$$'),
helpText('$$P[X=x]=\\frac{\\lambda^xe^{-\\lambda}}{x!}$$'),
helpText('$$E[X]=\\lambda, Var[X]=\\lambda$$')
),
sidebarLayout(
sidebarPanel(
numericInput("poisson_x",
"Number of occurrences (x)",
min = 0,
max = 1000,
value=5)
,
numericInput("poisson_l",
"Parameter (l)",
min = 0.0000001,
max = 1000,
value=10),
radioButtons("poisson_checkbox","Options",choices = list("Single Value, P[X=x]"="1",
"Cumulative probability P[X<=x]"="2"),
selected="1"),
actionButton("poisson_btn","Calculate",class = "btn-success")
),
mainPanel(
verbatimTextOutput("poisson_prob",placeholder = T),
plotOutput(outputId = "poisson_plot")
)
)
) ,
#----------------------------------------------------------------------------------------------------------------------
tabPanel("Hypergeometric ",
fluidRow(
h2("Hypergeometric Distribution"),
withMathJax(),
helpText('$$X \\sim {\\sf Hypergeometric}(N,K,n)$$'),
helpText('$$P[X=k]=\\frac{\\binom{K}{k}\\binom{N-K}{n-k}}{\\binom{N}{n}}$$'),
helpText('$$E[X]=n\\frac{K}{N}, Var[X]=n\\frac{K}{N}\\frac{N-K}{N}\\frac{N-n}{N-1}$$'),
),
sidebarLayout(
sidebarPanel(
numericInput("hgeom_N",
"Population size (N)",
min = 0,
max = 1000,
value=500)
,
numericInput("hgeom_K",
"Number of success states in population (K)",
min = 0,
max = 1000,
value=50)
,
numericInput("hgeom_n",
"Number of quantities drawn in each trial (n)",
min = 0,
max = 1000,
value=100)
,
numericInput("hgeom_k",
"Number of observed successes (k)",
min = 0,
max = 1000,
value=20),
radioButtons("hgeom_checkbox","Options",choices = list("Single Value, P[X=x]"="1",
"Cumulative probability P[X<=x]"="2"),
selected="1"),
actionButton("hgeom_btn","Calculate",class = "btn-success")
),
mainPanel(
verbatimTextOutput("hgeom_prob",placeholder = T),
plotOutput(outputId = "hgeom_plot")
)
)
)),
#----------------------------------------------------------------------------------------------------------------------
navbarMenu("Continuous Distributions",
tabPanel("Normal",
fluidRow(
h2("Normal Distribution"),
withMathJax(),
helpText('$$X \\sim {\\sf N}(\\mu,\\sigma^2)$$'),
helpText('$$f(x)=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}e^{-{\\frac{(x-\\mu)^2}{2\\sigma^2}}}$$'),
helpText('$$E[X]=\\mu, Var[X]=\\sigma^2$$'),
),
sidebarLayout(
sidebarPanel(
numericInput("normal_x",
"Input value (x)",
min = 0,
max = 1000,
value=175)
,
numericInput("normal_mu",
"Mean (mu)",
min = 0,
max = 1000,
value=180)
,
numericInput("normal_sigma",
"Standard Deviation (sigma)",
min = 0.0001,
max = 1000,
value=20)
,
radioButtons("normal_checkbox","Options",choices = list("Density function, f(x)"="1",
"Cumulative probability P[X<=x]"="2"),
selected="1"),
actionButton("normal_btn","Calculate",class = "btn-success")
),
mainPanel(
verbatimTextOutput("normal_prob",placeholder = T),
plotOutput(outputId = "normal_plot")
)
)
) ,
#----------------------------------------------------------------------------------------------------------------------
tabPanel("Exponential",
fluidRow(
h2("Exponential Distribution"),
withMathJax(),
helpText('$$X \\sim {\\sf Exp}(\\lambda)$$'),
helpText('$$f(x)=\\lambda e^{-\\lambda x}$$'),
helpText('$$E[X]=\\frac{1}{\\lambda}, Var[X]=\\frac{1}{\\lambda^2}$$'),
),
sidebarLayout(
sidebarPanel(
numericInput("exp_x",
"Input value (x)",
min = 0,
max = 100000,
value= 175)
,
numericInput("exp_lambda",
"Parameter (l)",
min = 0.0001,
max = 100000,
value= 0.2)
,
radioButtons("exp_checkbox","Options",choices = list("Density function, f(x)"="1",
"Cumulative probability P[X<=x]"="2"),
selected="1"),
actionButton("exp_btn","Calculate",class = "btn-success")
),
mainPanel(
verbatimTextOutput("exp_prob",placeholder = T),
plotOutput(outputId = "exp_plot")
)
)
),
#----------------------------------------------------------------------------------------------------------------------
tabPanel("Uniform",
fluidRow(
h2("Uniform Distribution"),
withMathJax(),
helpText('$$X \\sim {\\sf U}(\\alpha,\\beta)$$'),
helpText('$$f(x)=\\frac{1}{b-a}, a<x<b$$'),
helpText('$$E[X]=\\frac{1}{2}, Var[X]=\\frac{1}{12}$$'),
),
sidebarLayout(
sidebarPanel(
numericInput("uniform_x",
"Input value (x)",
min = 0,
max = 100000,
value= 50)
,
numericInput("uniform_a",
"Parameter (a)",
min = 0,
max = 100000,
value= 20)
,
numericInput("uniform_b",
"Parameter (b)",
min = 0.0001,
max = 100000,
value= 60)
,
radioButtons("uniform_checkbox","Options",choices = list("Density function, f(x)"="1",
"Cumulative probability P[X<=x]"="2"),
selected="1"),
actionButton("uniform_btn","Calculate",class = "btn-success")
),
mainPanel(
verbatimTextOutput("uniform_prob",placeholder = T),
plotOutput(outputId = "uniform_plot")
)
)
) ,
tabPanel("Gamma",
fluidRow(
h2("Gamma Distribution"),
withMathJax(),
helpText('$$X \\sim {\\sf Gamma}(k,\\theta)$$'),
helpText('$$f(x)=\\frac{x^{k-1}e^{-x/\\theta}}{\\theta^k \\Gamma(k)}$$'),
helpText('$$E[X]=k\\theta, Var[X]=k\\theta^2$$'),
),
sidebarLayout(
sidebarPanel(
numericInput("gamma_x",
"Input value (x)",
min = 0.000001,
max = 100000,
value= 4)
,
numericInput("gamma_shape",
"Shape Parameter (k)",
min = 0.000001,
max = 100000,
value= 9)
,
numericInput("gamma_scale",
"Scale Parameter (theta)",
min = 0.000001,
max = 100000,
value= 0.5)
,
radioButtons("gamma_checkbox","Options",choices = list("Density function, f(x)"="1",
"Cumulative probability P[X<=x]"="2"),
selected="1"),
actionButton("gamma_btn","Calculate",class = "btn-success")
),
mainPanel(
verbatimTextOutput("gamma_prob",placeholder = T),
plotOutput(outputId = "gamma_plot")
)
)
)
)
#----------------------------------------------------------------------------------------------------------------------
)
server <- function(input, output) {
binomial_prob <- eventReactive(input$binom_btn,
switch( input$binom_checkbox,
"1" = paste("P[X=",input$binom_x,'] = ',dbinom(input$binom_x,size=input$binom_n,prob=input$binom_p),sep = ""),
"2" = paste("P[X<=",input$binom_x,'] = ',pbinom(input$binom_x,size=input$binom_n,prob=input$binom_p),sep = "")
)
)
output$binomial_prob <- renderText({
binomial_prob()
})
binom_plot <- reactive({
plot(seq(0,input$binom_n,by = 1),dbinom(seq(0,input$binom_n,by = 1),input$binom_n,input$binom_p),
col='red',type='b',pch=20,main='Binomial Distribution',
xlab='Number of successes', ylab='Probability'
)
grid()
})
output$binom_plot <- renderPlot({
binom_plot()
})
#----------------------------------------------------------------------------------------------------------------------
geom_prob <- eventReactive(input$geom_btn,
switch (input$geom_checkbox,
"1" = paste("P[X=" ,input$geom_x,'] = ',dgeom(input$geom_x,prob=input$geom_p),sep = ""),
"2" = paste("P[X<=",input$geom_x,'] = ',pgeom(input$geom_x,prob=input$geom_p),sep = "")
)
)
output$geom_prob <- renderText({
geom_prob()
})
geom_plot <- reactive({
plot(seq(0,input$geom_x,by = 1),dgeom(seq(0,input$geom_x,by = 1),input$binom_p),
col='red',type='b',pch=20,main='Geometric Distribution',
xlab='Number of trials until success', ylab='Probability'
)
grid()
})
output$geom_plot <- renderPlot({
geom_plot()
})
#----------------------------------------------------------------------------------------------------------------------
neg_binom_prob <- eventReactive(input$neg_binom_btn,
switch (input$neg_binom_checkbox,
"1" = paste("P[X=" ,input$neg_binom_k,'] = ',dnbinom(input$neg_binom_k,size=input$neg_binom_r,prob=input$neg_binom_p),sep = ""),
"2" = paste("P[X<=",input$neg_binom_k,'] = ',pnbinom(input$neg_binom_k,size=input$neg_binom_r,prob=input$neg_binom_p),sep = "")
)
)
output$neg_binom_prob <- renderText({
neg_binom_prob()
})
neg_binom_plot <- reactive({
plot(seq(0,input$neg_binom_k,by = 1),dnbinom(seq(0,input$neg_binom_k,by = 1),input$neg_binom_r,input$neg_binom_p),
col='red',type='b',pch=20,main='Negative Binomial Distribution',
xlab='Number of successes', ylab='Probability'
)
grid()
})
output$neg_binom_plot <- renderPlot({
neg_binom_plot()
})
#----------------------------------------------------------------------------------------------------------------------
poisson_prob <- eventReactive(input$poisson_btn,
switch (input$poisson_checkbox,
"1" = paste("P[X=" ,input$poisson_x,'] = ',ppois(input$poisson_x,lambda=input$poisson_l),sep = ""),
"2" = paste("P[X<=",input$poisson_x,'] = ',dpois(input$poisson_x,lambda=input$poisson_l),sep = "")
)
)
output$poisson_prob <- renderText({
poisson_prob()
})
poisson_plot <- reactive({
plot(seq(0,input$poisson_x,by = 1),ppois(seq(0,input$poisson_x,by = 1),input$poisson_l),
col='red',type='b',pch=20,main='Poisson Distribution',
xlab='Number of occurrences', ylab='Probability'
)
grid()
})
output$poisson_plot <- renderPlot({
poisson_plot()
})
#----------------------------------------------------------------------------------------------------------------------
hgeom_prob <- eventReactive(input$hgeom_btn,
switch (input$hgeom_checkbox,
"1" = paste("P[X=" ,input$hgeom_k,'] = ',dhyper(input$hgeom_k,m=input$hgeom_K,n=input$hgeom_N-input$hgeom_K,k=input$hgeom_n),sep = ""),
"2" = paste("P[X<=",input$hgeom_k,'] = ',phyper(input$hgeom_k,m=input$hgeom_K,n=input$hgeom_N-input$hgeom_K,k=input$hgeom_n),sep = "")
)
)
output$hgeom_prob <- renderText({
hgeom_prob()
})
hgeom_plot <- reactive({
plot(seq(0,input$hgeom_k,by = 1),dhyper(seq(0,input$hgeom_k,by = 1),m=input$hgeom_K,n=input$hgeom_N-input$hgeom_K,k=input$hgeom_n),
col='red',type='b',pch=20,main='Hypergeometric Distribution',
xlab='Number of occurrences', ylab='Probability'
)
grid()
})
output$hgeom_plot <- renderPlot({
hgeom_plot()
})
#----------------------------------------------------------------------------------------------------------------------
normal_prob <- eventReactive(input$normal_btn,
switch (input$normal_checkbox,
"1" = paste("f(" ,input$normal_x,') = ',dnorm(x=input$normal_x,mean=input$normal_mu,sd=input$normal_sigma),sep = ""),
"2" = paste("P[X<=",input$normal_x,'] = ',pnorm(input$normal_x,mean=input$normal_mu,sd=input$normal_sigma),sep = "")
))
output$normal_prob <- renderText({
normal_prob()
})
normal_plot <- reactive({
plot(seq(input$normal_mu-4*input$normal_sigma,input$normal_mu+4*input$normal_sigma,by = .1),dnorm(seq(input$normal_mu-4*input$normal_sigma,input$normal_mu+4*input$normal_sigma,by = .1),mean=input$normal_mu,sd=input$normal_sigma),
col='red',type='b',pch=20,main='Normal Distribution',
xlab='x', ylab='f(x)'
)
grid()
})
output$normal_plot <- renderPlot({
normal_plot()
})
#----------------------------------------------------------------------------------------------------------------------
exp_prob <- eventReactive(input$exp_btn,
switch (input$exp_checkbox,
"1" = paste("f(" ,input$exp_x,') = ',dexp(x=input$exp_x,rate=input$exp_lambda),sep = ""),
"2" = paste("P[X<=",input$exp_x,'] = ',pexp(q=input$exp_x,rate=input$exp_lambda),sep = "")
))
output$exp_prob <- renderText({
exp_prob()
})
exp_plot <- reactive({
plot(seq(0,input$exp_x,by = .1),dexp(seq(0,input$exp_x,by = .1),rate=input$exp_lambda),
col='red',type='b',pch=20,main='Exponential Distribution',
xlab='x', ylab='f(x)'
)
grid()
})
output$exp_plot <- renderPlot({
exp_plot()
})
#----------------------------------------------------------------------------------------------------------------------
uniform_prob <- eventReactive(input$uniform_btn,
switch (input$uniform_checkbox,
"1" = paste("f(" ,input$uniform_x,') = ',dunif(input$uniform_x,input$uniform_a,input$uniform_b),sep = ""),
"2" = paste("P[X<=",input$uniform_x,'] = ',punif(input$uniform_x,input$uniform_a,input$uniform_b),sep = "")
))
output$uniform_prob <- renderText({
uniform_prob()
})
uniform_plot <- reactive({
plot(seq(0,2*input$uniform_b,by = .5),dunif(seq(0,2*input$uniform_b,by = .5),input$uniform_a,input$uniform_b),
col='red',type='b',pch=20,main='Uniform Distribution',
xlab='x', ylab='f(x)'
)
grid()
})
output$uniform_plot <- renderPlot({
uniform_plot()
})
#----------------------------------------------------------------------------------------------------------------------
gamma_prob <- eventReactive(input$gamma_btn,
switch (input$gamma_checkbox,
"1" = paste("f(" ,input$gamma_x,') = ',dgamma(input$gamma_x,shape=input$gamma_shape,scale=input$gamma_scale),sep = ""),
"2" = paste("P[X<=",input$gamma_x,'] = ',pgamma(input$gamma_x,shape=input$gamma_shape,scale=input$gamma_scale),sep = "")
))
output$gamma_prob <- renderText({
gamma_prob()
})
gamma_plot <- reactive({
plot(seq(0,2*input$gamma_x,by = .5),dgamma(seq(0,2*input$gamma_x,by = .5),shape=input$gamma_shape,scale=input$gamma_scale),
col='red',type='b',pch=20,main='Gamma Distribution',
xlab='x', ylab='f(x)'
)
grid()
})
output$gamma_plot <- renderPlot({
gamma_plot()
})
#----------------------------------------------------------------------------------------------------------------------
}
shinyApp(ui = ui, server = server)