Raport.Rmd

---
title: "Raport Proiect"
runtime: shiny_prerendered
output: html_document
---

# Ilustrarea repartitiilor

Acest proiect ilustreaza 15 repartitii si modul in care pot fi utilizate in calcul, alaturi de grafice pentru densitate (functie de masa) si functia de repartitie.

Repartitii ilustrate:

- Normal
- Beta
- Chi-squared
- Exponential
- F
- Cauchy
- Logistic
- StudentT
- Uniform
- Gamma
- Lognormal
- Weibull
- Binomial
- Poisson
- Geometric

## UI

Utilizatorul poate alege ce fel de repartitie vrea sa ilustreze folosind un meniu drop-down.

```{r , context="render"}
selectInput("dist","Choose the probability distribution: ", choices =
                    list(Continuous = list("Normal"),
                         Discrete = list()))
```

Fiecare repartitie are la dispozitie propriile casete de input pentru parametrii lor reprezentativi.
```{r , context="render"}
conditionalPanel(
             condition = "input.dist == 'Normal'",
             numericInput("mean", "Mean: ", value = 0),
             numericInput("sd", "Standard deviation: ", value = 1, min=0)
           )
```

Graficele vor fi afisate in propriile lor containere din client.


Dupa alegerea repartitiei, utilizatorul poate efectua si 3 tipuri de probabilitati.
```{r , context="render"}
 fluidRow(
    column(2,
         selectInput("probType", "Choose type of probability", 
                     choices = list("P(X<=a)", "P(X>=a)", "P(a<=X<=b)"))
    ),
    column(2,
         conditionalPanel(
           condition = "input.probType == 'P(X<=a)'",
           numericInput("a", "a:", value=0)
         ),
         conditionalPanel(
           condition = "input.probType == 'P(X>=a)'",
           numericInput("b", "a:", value=0)
         ),
         conditionalPanel(
           condition = "input.probType == 'P(a<=X<=b)'",
           numericInput("aa", "a:", value=0),
           numericInput("bb", "b:", value=0)
         )           
    )
 )
```

## Server

Mai intai am preluat toate datele de la client folosind reactive expressions pentru a avea cele mai noi valori din client.
```{r ,echo=TRUE, context="server"}
# Distribution specific vars
  # Normal
  nMean<-reactive(input$mean)
  sd<-reactive(input$sd)
  dist<-reactive(input$dist) 
```

Dupa preluarea datelor, am calculat diferite proprietati ale repartitiilor.
Pentru inceput, am stabilit limitele graficului in functie de repartitie si am definit multimea de valori.
```{r ,echo=TRUE, context="server"}
inf<-reactive({
    switch(input$dist,
           "Normal"=input$mean-3*input$sd)
})
sup<-reactive({
    switch(input$dist,
           "Normal"=input$mean+3*input$sd)
})
points<-reactive({
    switch(input$dist,
           "Normal"=seq(from=inf(),to=sup(),length.out=1000))
})
```

Avand multimea de puncte, am calculat densitatea/functia de masa, functia de repartitie si media.
```{r ,echo=TRUE, context="server"}
density<-reactive({
    switch(input$dist,
           "Normal"=dnorm(points(),input$mean,input$sd))
  })
cdf<-reactive({
    switch(input$dist,
           "Normal"=pnorm(points(),input$mean,input$sd))
  })
mean<-reactive({
    switch(input$dist,
           "Normal"=input$mean)
  })
```

In final, am pregatit cateva helper functions pentru calculul probabilitatilor.
```{r ,echo=TRUE, context="server"}
cdfHelper<-function(x) {
  reactive({
      switch(input$dist,
             "Normal"=pnorm(x,input$mean,input$sd))
  })
}
pdfHelper<-function(x) {
  reactive({
      switch(input$dist,
             "Normal"=dnorm(x,input$mean,input$sd))
    
  })
}
```

Graficele au fost create cu ajutorul functiei plot(). Unele repartitii au valori ce tind la infinit in densitate. Pentru a rezolva, am facut o verificare inainte de a folosi valoarea si am setat o valoare arbitrara in caz de infinit.

Acest yl este calculat pentru a seta limita maxima a graficului pe axa OY.
Am folosit abline() pentru a vizualiza unde se situeaza media pe grafic.
```{r, echo=FALSE}
plotOutput("densityPlot")
```

```{r ,echo=TRUE, context="server"}
output$densityPlot<-renderPlot({
    currDensity <- density()
    if (is.infinite(max(currDensity))) {
      yl<-c(0,4*5/3)
    } else {
      yl<-c(0,4*max(currDensity)/3)
    }
    plot(points(),currDensity,
         type="l",
         col = "cyan3",
         lwd=2.5,
         xlab="Values",
         ylab="PDF",
         main=input$dist,
         ylim=yl)
    abline(v = mean(), col="cyan2",lwd = 2, lty = 2)
})
```

```{r, echo=FALSE}
plotOutput("cdfPlot")
```
```{r ,echo=TRUE, context="server"}
output$cdfPlot<-renderPlot({
    currCdf <- cdf()
    plot(points(),currCdf,
         type="l",
         col = "cyan3",
         lwd=2.5,
         xlab="Values",
         ylab="CDF",
         main=dist(),
         ylim = c(0,1))
  })
```

Calculul probabilitatilor se foloseste de acele helper functions generate mai sus.
```{r ,echo=TRUE, context="server"}
output$result<-renderText({
    switch(input$probType,
           'P(X<=a)' = cdfHelper(input$a)(),
           'P(X>=a)' = 1 - cdfHelper(input$b)(),
           'P(a<=X<=b)' = cdfHelper(input$bb)() - cdfHelper(input$aa)()
           )
  })
```
```{r,echo=FALSE}
textOutput("result")
```
Pentru a hasura suprafata corespunzatoare calculului, am folosit functia polygon() pentru a genera un poligon peste grafic in plot.
```{r ,echo=TRUE, context="server"}
output$resultPlot<-renderPlot({
    switch(input$probType,
           'P(X<=a)' = {
               plot(points(),density(),
                    type="l",
                    col = "cyan3",
                    lwd=2.5,
                    xlab="Values",
                    ylab="CDF",
                    main=input$dist,
                    ylim = c(0,1))
               polygon(c(points()[points()<=input$a], input$a),
                       c(density()[points()<=input$a], density()[points()==min(points())]),
                       col="cyan",
                       density=10,
                       angle=90)
             })
  })
```
```{r, echo=FALSE}
plotOutput("resultPlot")
```