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app.R
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app.R
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library(shiny)
ui <- fluidPage(
titlePanel("Probability Distribution Functions"),
sidebarPanel(
selectInput(
inputId = "selection",
label = "Choose a distribution: ",
choices = c("Beta", "Cauchy", "Chi Square", "Exponential", "Gamma",
"Gosset (T)", "Logistic", "Normal", "Snedecor (F)",
"Weibull", "Lindley", "Uniform", "Binomial", "Geometric",
"Hypergeometric", "Poisson", "Negative Binomial", "Discrete Lindley", "ZIP")),
checkboxInput(inputId = "MEAN", label = "Show first mmoment", value = TRUE),
conditionalPanel("input.selection == 'Weibull'",
sliderInput(inputId = "weibull.shape", label = "Shape",
min = 0.5, max = 8, value = 1,
step = 0.5),
sliderInput(inputId = "weibull.scale", label = "Scale",
min = 0.5, max = 8, value = 1)),
conditionalPanel("input.selection == 'Chi Square'",
sliderInput(inputId = "chisq.df", label = "DF",
min = 1, max = 5, value = 1,
step = 0.5)),
conditionalPanel("input.selection == 'Normal'",
sliderInput(inputId = "norm.mean", label = "Mean",
min = -4, max = 4, value = 0,
step = 0.5),
sliderInput(inputId = "norm.sd", label = "SD",
min = 0.1, max = 3, value = 1,
step = 0.1)),
conditionalPanel("input.selection == 'Uniform'",
sliderInput(inputId = "unif.min", label = "Min.",
min = -3, max = 0, value = -1,
step = 0.1),
sliderInput(inputId = "unif.max", label = "Máx.",
min = 0.1, max = 3, value = 1,
step = 0.1)),
conditionalPanel("input.selection == 'Exponential'",
sliderInput(inputId = "exp.rate", label = "Rate",
min = 0.1, max = 10, value = 1,
step = 0.5)),
conditionalPanel("input.selection == 'Cauchy'",
sliderInput(inputId = "cauchy.location",
label = "Location", min = -5, max = 5,
value = 0, step = 1),
sliderInput(inputId = "cauchy.scale",
label = "Scale", min = 0.1, max = 5,
value = 1, step = 0.5)),
conditionalPanel("input.selection == 'Snedecor (F)'",
sliderInput(inputId = "f.df1", label = "DF1",
min = 3, max = 10, value = 3,
step = 1),
sliderInput(inputId = "f.df2", label = "DF2",
min = 2, max = 10, value = 2,
step = 1),
sliderInput(inputId = "f.ncp", label = "NCP",
min = 1, max = 10, value = 1,
step = 1,)),
conditionalPanel("input.selection == 'Gamma'",
sliderInput(inputId = "gamma.shape",
label = "Shape", min = 0.05, max = 5,
value = 2, step = 0.05),
sliderInput(inputId = "gamma.rate", label = "Rate",
min = 0.05, max = 5, value = 3,
step = 0.05)),
conditionalPanel("input.selection == 'Beta'",
sliderInput(inputId = "beta.shape1",
label = "Shape 1",
min = 1, max = 5, value = 2,
step = 0.05),
sliderInput(inputId = "beta.shape2",
label = "Shape 2",
min = 1, max = 5, value = 3,
step = 0.05),
sliderInput(inputId = "beta.ncp", label = "NCP",
min = 0, max = 10, value = 0,
step = 1)),
conditionalPanel("input.selection == 'Logistic'",
sliderInput(inputId = "logis.location",
label = "Location", min = -2, max = 2,
value = 0, step = 0.05),
sliderInput(inputId = "logis.scale",
label = "Scale", min = 1, max = 5,
value = 1, step = 0.5)),
conditionalPanel("input.selection == 'Gosset (T)'",
sliderInput(inputId = "t.df", label = "DF", min = 1,
max = 20, value = 1, step = 1),
sliderInput(inputId = "t.ncp", label = "NCP",
min = -5, max = 5, value = 0,
step = 1)),
conditionalPanel("input.selection == 'Binomial'",
sliderInput(inputId = "binom.size", label = "Size",
min = 1, max = 20, value = 10,
step = 1),
sliderInput(inputId = "binom.prob",
label = "Probability", min = 0, max = 1,
value = 0.5, step = 0.05)),
conditionalPanel("input.selection == 'Poisson'",
sliderInput(inputId = "pois.lambda",
label = "Lambda", min = 0, max = 10,
value = 1, step = 1)),
conditionalPanel("input.selection == 'Geometric'",
sliderInput(inputId = "geom.prob",
label = "Probability", min = 0.05,
max = 1, value = 0.5, step = 0.05)),
conditionalPanel("input.selection == 'Hypergeometric'",
sliderInput(inputId = "hyper.m", label = "m",
min = 0, max = 30, value = 5,
step = 1)),
conditionalPanel("input.selection == 'Negative Binomial'",
sliderInput(inputId = "nbinom.size",
label = "Size",
min = 1, max = 10, value = 5,
step = 1),
sliderInput(inputId = "nbinom.prob",
label = "Probability", min = 0,
max = 1, value = 0.5, step = 0.05)),
conditionalPanel("input.selection == 'Lindley'",
sliderInput(inputId = "theta.lindley",
label = "theta",
min = 0.01, max = 10, value = 1,
step = 0.05)),
conditionalPanel("input.selection == 'Discrete Lindley'",
sliderInput(inputId = "discrete.lindley.lambda",
label = "Lambda",
min = 0, max = 1, value = 0.5,
step = 0.05)),
conditionalPanel("input.selection == 'ZIP'",
sliderInput(inputId = "zip.lambda",
label = "Lambda",
min = 0, max = 20, value = 0.5,
step = 0.5),
sliderInput(inputId = "zip.pi",
label = "Pi",
min = 0, max = 1, value = 0.1,
step = 0.05))),
mainPanel(
plotOutput(outputId = "distPlot")
),
hr(),
h5(actionButton("exit", "Exit"), br(), br(), hr(),
"Created by:"),
tags$a("Vinicius Riffel", href = "https://github.com/vriffel")
)
server <- function(input, output) {
funcInput <- reactive({
par(mfrow = c(1, 2))
switch(input$selection,
"Weibull" = {
curve(dweibull(x, scale = input$weibull.scale,
shape = input$weibull.shape), from = 0,
to = 15, xlab = "x", ylab = "y", main = "Density")
if (input$MEAN) {
exp.weibull <- function(x) {
return(x * dweibull(x, shape = input$weibull.shape,
scale = input$weibull.scale))
}
xinter <- integrate(exp.weibull, 0, Inf)$value
abline(v = xinter, col = "red")
}
curve(pweibull(x, scale = input$weibull.scale,
shape = input$weibull.shape), xlab = "x",
ylab = "y", from = 0, to = 15, main = "Distribution")
},
"Chi Square" = {
curve(dchisq(x, df = input$chisq.df), from = 0,
to = 15, xlab = "x", ylab = "y", main = "Density")
if (input$MEAN) {
exp.chisq <- function(x) {
return(x * dchisq(x, df = input$chisq.df))
}
xinter <- integrate(exp.chisq, 0, Inf)$value
abline(v = xinter, col = "red")
}
curve(pchisq(x, df = input$chisq.df), from = 0,
to = 15, xlab = "x", ylab = "y",
main = "Distribution")},
"Normal" = {
curve(dnorm(x, mean = input$norm.mean,
sd = input$norm.sd), from = -7, to = 7,
xlab = "x", ylab = "y", main = "Density")
if (input$MEAN) {
exp.norm <- function(x) {
return(x * dnorm(x, mean = input$norm.mean,
sd = input$norm.sd))
}
xinter <- integrate(exp.norm, -Inf, Inf)$value
abline(v = xinter, col = "red")
}
curve(pnorm(x, mean = input$norm.mean,
sd = input$norm.sd), from = -7, to = 7,
xlab = "x", ylab = "y", main = "Distribution")},
"Uniform" = {
curve(dunif(x, min = input$unif.min,
max = input$unif.max), from = -4, to = 4,
xlab = "x", ylab = "y", main = "Density")
if (input$MEAN) {
exp.unif <- function(x) {
return(x * dunif(x, min = input$unif.min,
max = input$unif.max))
}
xinter <- integrate(exp.unif, -Inf, Inf)$value
abline(v = xinter, col = "red")
}
curve(punif(x, min = input$unif.min,
max = input$unif.max), from = -4, to = 4,
xlab = "x", ylab = "y", main = "Distribution")},
"Exponential" ={
curve(dexp(x, rate = input$exp.rate), from = 0,
to = 3, xlab = "x", ylab = "y", main = "Density")
if (input$MEAN) {
exp.exp <- function(x) {
return(x * dexp(x, rate = input$exp.rate))
}
xinter <- integrate(exp.exp, -Inf, Inf)$value
abline(v = xinter, col = "red")
}
curve(pexp(x, rate = input$exp.rate), from = 0,
to = 3, xlab = "x", ylab = "y", main = "Distribution")},
"Cauchy" = {
curve(dcauchy(x, location = input$cauchy.location,
scale = input$cauchy.scale), from = -4,
to = 4, xlab = "x", ylab = "y", main = "Density")
curve(pcauchy(x, location = input$cauchy.location,
scale = input$cauchy.scale), from = -4,
to = 4, xlab = "x", ylab = "y", main = "Distribution")},
"Snedecor (F)" = {
curve(df(x, df1 = input$f.df1, df2 = input$f.df2,
ncp = input$f.ncp), from = 0, to = 10,
xlab = "x", ylab = "y", main = "Density")
curve(pf(x, df1 = input$f.df1, df2 = input$f.df2,
ncp = input$f.ncp), from = 0, to = 10,
xlab = "x", ylab = "y", main = "Distribution")},
"Gamma" = {
curve(dgamma(x, shape = input$gamma.shape,
rate = input$gamma.rate), from = 0,
to = 15, xlab = "x", ylab = "y", main = "Density")
if (input$MEAN) {
exp.gamma <- function(x) {
return(x * dgamma(x, shape = input$gamma.shape,
rate = input$gamma.rate))
}
xinter <- integrate(exp.gamma, -Inf, Inf)$value
abline(v = xinter, col = "red")
}
curve(pgamma(x, shape = input$gamma.shape,
rate = input$gamma.rate), from = 0,
to = 15, xlab = "x", ylab = "y", main = "Distribution")},
"Beta" = {
curve(dbeta(x, shape1 = input$beta.shape1,
shape2 = input$beta.shape2,
ncp = input$beta.ncp), from = 0, to = 1,
xlab = "x", ylab = "y", main = "Density")
if (input$MEAN) {
exp.beta <- function(x) {
return(x * dbeta(x, shape1 = input$beta.shape1,
shape2 = input$beta.shape2,
ncp = input$beta.ncp))
}
xinter <- integrate(exp.beta, -Inf, Inf)$value
abline(v = xinter, col = "red")
}
curve(pbeta(x, shape1 = input$beta.shape1,
shape2 = input$beta.shape2,
ncp = input$beta.ncp), from = 0, to = 1,
xlab = "x", ylab = "y", main = "Distribution")},
"Logistic" = {
curve(dlogis(x, location = input$logis.location,
scale = input$logis.scale), from = 5,
to = -5, xlab = "x", ylab = "y", main = "Density")
if (input$MEAN) {
exp.logis <- function(x) {
return(x * dlogis(x, location = input$logis.location,
scale = input$logis.scale))
}
xinter <- integrate(exp.logis, -Inf, Inf)$value
abline(v = xinter, col = "red")
}
curve(plogis(x, location = input$logis.location,
scale = input$logis.scale), from = 5,
to = -5, xlab = "x", ylab = "y",
main = "Distribution")},
"Gosset (T)" = {
curve(dt(x, df = input$t.df, ncp = input$t.ncp),
from = -5, to = 5, xlab = "x", ylab = "y",
main = "Density")
if (input$MEAN) {
exp.t <- function(x) {
return(x * dt(x, df = input$t.df,
ncp = input$t.ncp))
}
xinter <- integrate(exp.t, -Inf, Inf)$value
abline(v = xinter, col = "red")
}
curve(pt(x, df = input$t.df, ncp = input$t.ncp),
from = -5, to = 5, xlab = "x", ylab = "y",
main = "Distribution")},
"Binomial" = {
curve(dbinom(x, size = input$binom.size,
prob = input$binom.prob), n = 21,
type = "h", from = 0, to = 15, xlab = "x",
ylab = "y", main = "Probability Function")
if (input$MEAN) {
abline(v = input$binom.size * input$binom.prob, col = "red")
}
curve(pbinom(x, size = input$binom.size,
prob = input$binom.prob), n = 21,
type = "h", from = 0, to = 15, xlab = "x",
ylab = "y", main = "Distribution")},
"Poisson" = {
curve(dpois(x, lambda = input$pois.lambda), from = 0,
to = 15, type = "h", xlab = "x", ylab = "y",
main = "Probability Function")
if (input$MEAN) {
abline(v = input$pois.lambda, col = "red")
}
curve(ppois(as.integer(x), lambda = input$pois.lambda),
from = 0, to = 15, xlab = "x", ylab = "y",
main = "Distribution")},
"Geometric" = {
curve(dgeom(x, prob = input$geom.prob), from = 0,
to = 20, type = "h", xlab = "x", ylab = "y",
main = "Probability Function")
if (input$MEAN) {
abline(v = (1 - input$geom.prob)/input$geom.prob, col = "red")
}
curve(pgeom(x, prob = input$geom.prob), from = 0,
to = 20, xlab = "x", ylab = "y",
main = "Distribution")},
"Hypergeometric" = {
curve(dhyper(x, m = input$hyper.m, n = 10, k = 10),
type = "h", from = 0, to = 10, xlab = "x",
ylab = "y", main = "Probability Function")
curve(phyper(x, m = input$hyper.m, n = 10, k = 10), from = 0,
to = 10, xlab = "x", ylab = "y",
main = "Distribution")},
"Negative Binomial" = {
curve(dnbinom(x, size = input$nbinom.size,
prob = input$nbinom.prob), from = 0, to = 20,
type = "h", xlab = "x", ylab = "y",
main = "Probability Function")
curve(pnbinom(x, size = input$nbinom.size,
prob = input$nbinom.prob), from = 0, to = 20,
xlab = "x", ylab = "y", main = "Distribution")},
"Lindley" = {
lindley <- function(x, theta) {
fx <- (((theta)^2) / (theta + 1)) * (1 + x) *
exp(-theta * x)}
lindley_cum <- function(x, theta) {
Fx <- sapply(x, function(k) integrate(lindley, 0, k,
theta = theta)$value)
}
curve(lindley(x, theta = input$theta.lindley), from = 0,
to = 10, xlab = "x", ylab = "y", main = "Density")
curve(lindley_cum(x, theta = input$theta.lindley), from = 0,
to = 5, xlab = "x", ylab = "y", main = "Distribution")
},
"Discrete Lindley" = {
plindley <- function(x, lambda) {
px <- ((lambda^x) / (1 - log(lambda))) *
(lambda * log(lambda) + (1 - lambda) *
(1 - log(lambda^(x + 1))))
return(px)
}
dlindley <- function(x, lambda) {
Fx <- ((1 - lambda^(x + 1)) + ((2 + x) * lambda^(x + 1) - 1) * log(lambda)) /
(1 - log(lambda))
return(Fx)
}
hlindley <- function(lambda, x) {
Hx <- (lambda * log(lambda) + (lambda - 1) * (log(lambda^(x + 1)) - 1)) /
(1 - (1 + x) * log(lambda))
return(Hx)
}
par(mfrow = c(1, 3))
plot(plindley(x = 1:30, lambda = input$discrete.lindley.lambda), xlab = "x", ylab = "y", main = "Probability")
plot(dlindley(x = 1:30, lambda = input$discrete.lindley.lambda), xlab = "x", ylab = "y", main = "Distribution")
plot(hlindley(x = 1:60, lambda = input$discrete.lindley.lambda), xlab = "x", ylab = "y", main = "Hazard")
},
"ZIP" = {
x <- 0:30
plot(gamlss.dist::dZIP(x, mu = input$zip.lambda,
sigma = input$zip.pi), type = "h",
xlab = "x", ylab = "y", main = "Probability Function")
if (input$MEAN) {
abline(v = input$zip.lambda * (1 - input$zip.pi),
col = "red")
}
curve(gamlss.dist::pZIP(x, mu = input$zip.lambda,
sigma = input$zip.pi), from = 0, to = 30,
xlab = "x", ylab = "y", main = "Distribution")
})
})
output$distPlot <- renderPlot({
funcInput()
})
observeEvent(input$exit, {stopApp()})
}
shinyApp(ui, server)