---
title: "Case Studies"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Case Studies}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(MD2sample)
cases=MD2sample::case.studies(ReturnCaseNames=TRUE)
```

```{r}
multiple.graphs = function (px, py,xname=" ") {
  egg::ggarrange(px, py, ncol = 2, nrow = 1)
} 
```

This vignette lists the case studies included in the package:

## Dim=2, equal marginals

```{r}
for(i in seq_along(cases)) {
   if(!endsWith(cases[i], "D2")) next
   tmp=case.studies(i, 2000)
   print(cases[i])
   p=tmp$param_alt[2]
   if(startsWith(cases[i],"Dalitz")) p=10*p
   dta=tmp$f(p)
   dtax=data.frame(x=dta$x[,1], y=dta$x[,2])
   dtay=data.frame(x=dta$y[,1], y=dta$y[,2])
   px=ggplot2::ggplot(dtax, ggplot2::aes(x=x, y=y))+
     ggplot2::geom_point(color="blue", alpha=0.5, size=0.5)+
     ggplot2::labs(x=expression(x[1]), y=expression(x[2])) 
     
   py=ggplot2::ggplot(dtay, ggplot2::aes(x=x, y=y))+
     ggplot2::geom_point(color="red", alpha=0.5)+
     ggplot2::labs(x=expression(x[1]), y=expression(x[2])) 
  multiple.graphs(px, py, cases[i])
}
```

## Dim=2, unequal marginals

```{r}
for(i in seq_along(cases)) {
   if(!endsWith(cases[i], "M")) next
   tmp=case.studies(i, 2000)
   print(cases[i])
   p=tmp$param_alt[2]
   if(startsWith(cases[i],"Dalitz")) p=10*p
   dta=tmp$f(p)
   dtax=data.frame(x=dta$x[,1], y=dta$x[,2])
   dtay=data.frame(x=dta$y[,1], y=dta$y[,2])
   px=ggplot2::ggplot(dtax, ggplot2::aes(x=x, y=y))+
     ggplot2::geom_point(color="blue", alpha=0.5, size=0.5)+
     ggplot2::labs(x=expression(x[1]), y=expression(x[2])) 
     
   py=ggplot2::ggplot(dtay, ggplot2::aes(x=x, y=y))+
     ggplot2::geom_point(color="red", alpha=0.5)+
     ggplot2::labs(x=expression(x[1]), y=expression(x[2])) 
  multiple.graphs(px, py, cases[i])
}
```

## Dim=5, equal marginals


-   NormalD5:  multivariate normal distribution with equal marginals.  
-   tD5:  multivariate t distribution with 5 degrees of freedom and equal marginals.                 
- FrankD5: Frank cupola.  
- ClaytonD5: Clayton cupola.  
- GumbelD5: Gumbel copula.  
- JoeD5: Joe cupola.  
- UniformFrankD5: mixture of uniform and Frank cupola.  
- FrankClaytonD5: mixture of Frank and Clayton cupolas.  
- FrankJoeD5: mixture of Frank and Joe cupolas.           


## Dim=5, unequal marginals

- UniformExponentialM5: Exponential distributions.  
- FrankExponentialM5: Frank cupola with exponential marginals.  
- FrankLinearM5: Frank cupola with linear marginals.  
- FrankNormalM5: Frank cupola with linear marginals.  
- ClaytonExponentialM5: Clayton cupola with exponential marginals.  
- ClaytonLinearM5: Clayton cupola with linear marginals.  
- ClaytonNormalM5: Clayton cupola with linear marginals.