Distribuições de probabilidade |
require(shiny)
densityView <- function(m, s, sample){
curve(dnorm(x, mean=m, sd=s),
from=m-4*s, to=m+4*s)
abline(v=m, lty=1, col=2)
lines(density(sample), col=2)
}
ecdfView <- function(m, s, sample){
curve(pnorm(x, mean=m, sd=s),
from=m-4*s, to=m+4*s)
abline(v=m, lty=1, col=2)
lines(ecdf(sample), col=2)
}
qqView <- function(sample){
qqnorm(sample)
qqline(sample)
}
## Quantidade de amostras de y.
N <- 500
## Carrega template das aplicações elaboradas pelo projeto iguiR2
source("../template.R")
shinyServer(
function(input, output){
## Cabeçalho IGUIR2
output$header <- renderPrint({
template("TEMA")
})
output$ui <- renderUI({
if (is.null(input$dist)){
return(NULL)
}
switch(input$dist,
"poisson"={
output$plot <- renderPlot({
x <- 0:30
px <- dpois(x, lambda=input$poissonLambda)
plot(x, px, type="h", xlab="x", ylab="Pr(x)")
})
SAMPLER <- reactive({
popMean <- input$poissonLambda
popSd <- sqrt(input$poissonLambda)
meanSd <- popSd/sqrt(input$n)
sampleMean <-
replicate(
N,
mean(rpois(
input$n,
lambda=input$poissonLambda)))
return(list(
m=popMean,
s=meanSd,
sample=sampleMean))
})
output$density <- renderPlot({
with(SAMPLER(),
densityView(m=m, s=s, sample=sample))
})
output$ecdf <- renderPlot({
with(SAMPLER(),
ecdfView(m=m, s=s, sample=sample))
})
output$qqnorm <- renderPlot({
qqView(sample=SAMPLER()$sample)
})
wellPanel(
sliderInput(inputId="poissonLambda",
label="Média da Poisson",
min=0.1, max=20, value=10)
)
},
"binomial"={
output$plot <- renderPlot({
x <- 0:input$binomialSize
px <- dbinom(x, size=input$binomialSize,
prob=input$binomialProb)
plot(x, px, type="h",
xlab="x", ylab="Pr(x)")
})
SAMPLER <- reactive({
popMean <-
input$binomialSize*input$binomialProb
popSd <-
sqrt(popMean*(1-input$binomialProb))
meanSd <- popSd/sqrt(input$n)
sampleMean <-
replicate(
N,
mean(rbinom(
input$n,
size=input$binomialSize,
prob=input$binomialProb)))
return(list(
m=popMean,
s=meanSd,
sample=sampleMean))
})
output$density <- renderPlot({
with(SAMPLER(),
densityView(m=m, s=s, sample=sample))
})
output$ecdf <- renderPlot({
with(SAMPLER(),
ecdfView(m=m, s=s, sample=sample))
})
output$qqnorm <- renderPlot({
qqView(sample=SAMPLER()$sample)
})
wellPanel(
sliderInput(inputId="binomialSize",
"Número de ensaios",
min=0, max=30, value=10, step=1),
sliderInput(inputId="binomialProb",
label="Probabilidade de sucesso",
min=0.02, max=0.98,
value=0.5, step=0.02)
)
},
"beta"={
output$plot <- renderPlot({
curve(dbeta(x,
shape1=input$betaShape1,
shape2=input$betaShape2),
from=0, to=1,
xlab="x", ylab="f(x)")
})
SAMPLER <- reactive({
popMean <-
input$betaShape1/
(input$betaShape1+input$betaShape2)
popSd <- sqrt(
input$betaShape1*input$betaShape2/(
(input$betaShape1+
input$betaShape2+1)*
(input$betaShape1+
input$betaShape2)**2
)
)
meanSd <- popSd/sqrt(input$n)
sampleMean <-
replicate(
N,
mean(rbeta(
input$n,
shape1=input$betaShape1,
shape2=input$betaShape2)))
return(list(
m=popMean,
s=meanSd,
sample=sampleMean))
})
output$density <- renderPlot({
with(SAMPLER(),
densityView(m=m, s=s, sample=sample))
})
output$ecdf <- renderPlot({
with(SAMPLER(),
ecdfView(m=m, s=s, sample=sample))
})
output$qqnorm <- renderPlot({
qqView(sample=SAMPLER()$sample)
})
wellPanel(
sliderInput(inputId="betaShape1",
label="Parâmetro de forma 1",
min=0.01, max=7, value=1,
step=0.1),
sliderInput(inputId="betaShape2",
label="Parâmetro de forma 2",
min=0.01, max=7, value=1,
step=0.1)
)
},
"gamma"={
output$plot <- renderPlot({
curve(dgamma(x,
shape=input$gammaShape,
rate=input$gammaRate),
from=0, to=20,
xlab="x", ylab="f(x)")
})
SAMPLER <- reactive({
popMean <- input$gammaShape/input$gammaRate
popSd <- sqrt(
input$gammaShape/(input$gammaRate**2))
meanSd <- popSd/sqrt(input$n)
sampleMean <-
replicate(
N,
mean(rgamma(
input$n,
shape=input$gammaShape,
rate=input$gammaRate)))
return(list(
m=popMean,
s=meanSd,
sample=sampleMean))
})
output$density <- renderPlot({
with(SAMPLER(),
densityView(m=m, s=s, sample=sample))
})
output$ecdf <- renderPlot({
with(SAMPLER(),
ecdfView(m=m, s=s, sample=sample))
})
output$qqnorm <- renderPlot({
qqView(sample=SAMPLER()$sample)
})
wellPanel(
sliderInput(inputId="gammaShape",
label="Parâmetro de forma",
min=0.01, max=7, value=1,
step=0.1),
sliderInput(inputId="gammaRate",
label="Parâmetro de taxa",
min=0.01, max=7, value=1,
step=0.1)
)
},
"normal"={
output$plot <- renderPlot({
curve(dnorm(x,
mean=input$normalMean,
sd=input$normalSd),
from=-3, to=3,
xlab="x", ylab="f(x)")
})
SAMPLER <- reactive({
popMean <- input$normalMean
popSd <- input$normalSd
meanSd <- popSd/sqrt(input$n)
sampleMean <-
replicate(
N,
mean(rnorm(
input$n,
mean=input$normalMean,
sd=input$normalSd)))
return(list(
m=popMean,
s=meanSd,
sample=sampleMean))
})
output$density <- renderPlot({
with(SAMPLER(),
densityView(m=m, s=s, sample=sample))
})
output$ecdf <- renderPlot({
with(SAMPLER(),
ecdfView(m=m, s=s, sample=sample))
})
output$qqnorm <- renderPlot({
qqView(sample=SAMPLER()$sample)
})
wellPanel(
sliderInput(inputId="normalMean",
label="Média da normal",
min=-3, max=3, value=0,
step=0.05),
sliderInput(inputId="normalSd",
label="Desvio-padrão da normal",
min=0.1, max=3, value=1,
step=0.05)
)
}
) ## switch()
}) ## renderUI
## Opções para média amostral
output$OptsMedia <- renderUI({
if (input$tab == "Distribuição") {
return(NULL)
} else {
wellPanel(
numericInput(
inputId="n",
label="Tamanho da amostra:",
min = 2, max = 1000, value=10),
HTML("<label>Tipo de gráfico: </label>"),
tabsetPanel(
id = "graf",
type = "pills",
tabPanel("Density"),
tabPanel("ECDF"),
tabPanel("Q-QNorm")
),
helpText("Baseados em 500 amostras")
)
}
})
## Gráficos para a distribuição média amostral
output$grafsMedia <- renderUI({
if (is.null(input$graf)) {
return(NULL)
} else {
switch(
input$graf,
"Density" = plotOutput("density"),
"ECDF" = plotOutput("ecdf"),
"Q-QNorm" = plotOutput("qqnorm")
)
}
})
}) ## shinyServer()require(shiny)
choi <- c("Poisson"="poisson",
"Binomial"="binomial",
"Beta"="beta",
"Gamma"="gamma",
"Normal"="normal")
shinyUI(
fluidPage(
## Cabeçalho IGUIR2
htmlOutput("header"),
titlePanel("Distribuições de probabilidade"),
sidebarPanel(
selectInput(inputId="dist",
label="Distribuição",
choices=choi),
uiOutput("ui"),
uiOutput("OptsMedia")
),
mainPanel(
tabsetPanel(
id = "tab",
tabPanel("Distribuição",
plotOutput("plot")),
tabPanel("Distribuição Amostral da Média",
uiOutput("grafsMedia")
)
)
)
)
)