---
title: "Neo-Normal Distributions Family for MCMC Models in JAGS"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Neo-Normal Distributions Family for MCMC Models in JAGS}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

```{r setup}
if (requireNamespace("neojags", quietly = TRUE)){
	  neojags::load.neojagsmodule()
} 
if (requireNamespace("neojags", quietly = TRUE)){
	  library(rjags)
} 
```

## Generate data

### Create model for JAGS
```{r}
mod <- "
model {
  # Likelihood
  for (i in 1:100) {
    x[i] ~ djskew.ep(2,1,0.8,1)
  }
}
"
```
### Compile the model
```{r}
modelv <- jags.model(textConnection(mod), n.chains=1, inits = list(".RNG.name" = "base::Wichmann-Hill",".RNG.seed" = 314159))
```
### Generate samples 
```{r}
samplesv <- coda.samples(modelv, variable.names = c("x"), n.iter = 1)
gen_datav <- (as.data.frame(as.matrix(samplesv)))
x <- as.numeric(gen_datav[1,])
```


## Parameter Estimation

### Create model for JAGS
```{r}
model_string <- "
model {
  # Likelihood
  for (i in 1:100) {
    x[i] ~ djskew.ep(mu, tau,nu1, nu2)
  }
  
  # Prior distributions
  mu ~ dnorm(2,10000)
  tau ~ dgamma(10,10)
  nu1 ~ dgamma(10,10)
  nu2 ~ dgamma(10,10)
}
"
```

### Compile the model
```{r}
model <- jags.model(textConnection(model_string), data = list(x=c(x)),n.chains=2)
```

### Generate samples from the posterior distribution
```{r}
samples<- coda.samples(model, variable.names = c("mu", "tau", "nu1", "nu2"), n.iter = 2000)
```

### Summary Samples
```{r}
summary(samples)
```

### Traceplot
```{r}
traceplot(samples)
```


## Probability Density Function (PDF), Cumulative Density Function (CDF), and Invers CDF (Quantile)
```{r}
model_string1 <- "
model {
    d <- djskew.ep(0.5,2,2,2,2)
		p <- pjskew.ep(0.5,2,2,2,2)
		q <- qjskew.ep(0.5,2,2,2,2)
}
"
```

### Compile the model
```{r}
model1 <- jags.model(textConnection(model_string1),  n.chains=2)
```

### Generate samples from the posterior distribution
```{r}
samples1<- coda.samples(model1, variable.names = c("d","p","q"), n.iter = 2)
```

### Summary samples
```{r}
summary(samples1)
```





