---
title: "Supported Distributions"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{supported-distributions}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

```{r setup}
library(samplr)
```

The current distributions in the samplr package are those supported by [Rcpp](https://www.rcpp.org/) and [RcppDist](https://github.com/duckmayr/RcppDist).

## Univariate Distributions
The parameters these distributions take can be provided in a vector, e.g. a vector `c(0,1)` for the standard normal distribution.

### Continuous Distributions

```{r echo=FALSE}
abbrev_cont <- c("unif", "norm","lnorm", "gamma", "beta", "nbeta", "chisq", "nchisq", "t", "nt", "f", "nf", "cauchy", "exp", "logis", "weibull",
                "4beta", "lst", "truncnorm", "trunct", "trunclst", "triangular")

for (i in 1:length(abbrev_cont)){abbrev_cont[i] <- paste("*", abbrev_cont[i],"*", sep="")}
name_cont <- c("Uniform", "Normal","Lognormal", "Gamma", "Beta", "Non-central Beta", "Chi-squared", "Non-central Chi-squared", "t", "Non-central t", "F", "Non-central F", "Cauchy", "Exponential", "Logistic", "Weibull",
                           "4-parameter Beta", "Location-scale t", "Truncated Normal", "Truncated t", "Truncated Location-scale t", "Triangular")

for (i in 1:length(name_cont)){name_cont[i] <- paste(name_cont[i],"Distribution")}

parameters <- c(
  "`min`, `max`", # "unif",
  "`mean`, `sd`",# "norm",
  "`log_mean`, `log_sd`", # "lnorm",
  "`shape`, `scale`", # "gamma",
  "`shape1`,`shape2`", # "beta",
  "`shape1`,`shape2`, `ncp`", # "nbeta",
  "`df`", # "chisq",
  "`df`, `ncp`", # "nchisq",
  "`df`", # "t",
  "`df`, `ncp`", # "nt",
  "`df1`, `df2`", # "f",
  "`df1`, `df2`, `ncp`", # "nf",
  "`location`, `scale`, ", # "cauchy",
  "`rate`", # "exp",
  "`location`, `scale`", # "logis",
  "`shape`, `scale`",# "weibull",
  "`shape1`,`shape2`, `minumum`, `maximum`", # "4beta",
  "`df`, `location`, `scale`, ", # "lst",
  "`mean`, `sd`, `low_bound`, `high_bound`", # "truncnorm",
  "`df`, `low_bound`, `high_bound`", # "trunct",
  "`df`, `location`, `scale`, `low_bound`, `high_bound`", # "trunclst",
  "`lower_limit`, `upper_limit`, `mode`"# "triangular"
)

X <- data.frame(abbrev_cont, name_cont, parameters)
names(X) <- c("Abbreviation", "Distribution Name", "Parameters")
knitr::kable(X)
```

### Discrete Distributions

```{r echo=FALSE}
abbr_discr <- c("binom", "nbinom", "nbinom_mu", "pois", "geom", "hyper", "wilcox", "signrank")
for (i in 1:length(abbr_discr)){abbr_discr[i] <- paste("*", abbr_discr[i],"*", sep="")}


name_discr <- c("Binomial", "Negative Binomial", "Negative Binomial", "Poisson", "Geometric", "Hypergeometric", "Wilcoxon rank-sum test statistic", "Wilcoxon signed-rank test statistic")

for (i in 1:length(name_discr)){
  if ((name_discr[i] != "Wilcoxon rank-sum test statistic") && (name_discr[i] != "Wilcoxon signed-rank test statistic")){
    name_discr[i] <- paste(name_discr[i],"Distribution")
  } else{
    name_discr[i] <- paste("Distribution of", name_discr[i])
  }
  if (i == 2){
    name_discr[i] <- paste(name_discr[i],"(with success probability as parameter)")
  }
  else if (i == 3){
    name_discr[i] <- paste(name_discr[i],"(with mean as parameter)")
  }
}

parameters_discr <-c(
  "`size`, `success_prob`", # Binomial", 
  "`size`, `success_prob`", # Non-central Binomial", 
  "`size`, `mean`", # Negative binomial", 
  "`lambda`", # Poisson", 
  "`success_prob`", # Geometric", 
  "`number_successes`, `number_failures`, `number_samples`", # Hypergeometric", 
  "`number_samples1`, `number_samples2`", # Wilcoxon rank-sum test statistic", 
  "`number_samples`" # Wilcoxon signed-rank test statistic"
  )

X <- data.frame(abbr_discr, name_discr, parameters_discr)
names(X) <- c("Abbreviation", "Distribution Name", "Parameters")
knitr::kable(X)
```
## Multivariate Distributions
For multivariate distributions, distribution parameters are provided in a list, not a vector. 

### Continuous Distributions
```{r echo=FALSE}
abbrev_cont_mv <- c("mvnorm", "mvt")

for (i in 1:length(abbrev_cont_mv)){abbrev_cont_mv[i] <- paste("*", abbrev_cont_mv[i],"*", sep="")}

name_cont_mv <- c("Multivariate Normal", "Multivariate t")

for (i in 1:length(name_cont)){name_cont[i] <- paste(name_cont[i],"Distribution")}

parameters_cont_mv <- c(
  "`mean` (vector); `covariance_matrix` (matrix)", # Multivariate Normal", 
  "`location` (vector); `scale_matrix` (matrix), `df` (number)" # Multivariate t"
  )

X <- data.frame(abbrev_cont_mv, name_cont_mv, parameters_cont_mv)
names(X) <- c("Abbreviation", "Distribution Name", "Parameters")
knitr::kable(X)
```

## Examples
### Univariate distribution
```{r}
X <- sampler_mh(
  start = 0, # starting point for the sampler
  distr_name = "truncnorm", # Use abbreviation in distr_name
  distr_params = c(0,1,-5,0), # provide distribution parameters as a vector for univariate distributions
  sigma_prop = 1, # variance of the proposal distribution
)
hist(X[[1]])
```

### Multivariate distribution
```{r}
X <- sampler_hmc(
  start = c(0,0), 
  distr_name = "mvnorm", # as before
  list(c(0,0), diag(2)), # provide distribution parameters as a list for multivariate distributions
)

x <- X[[1]][,1]
y <- X[[1]][,2]
plot(x,y)
```