---
title: "List of distributions"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{distlist}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

## Continuous distributions

* [`bccg(mu, sigma, nu)`](../reference/bccg.html): Box-Cox Cole and Green distribution parameterised by location `mu`, scale `sigma`, and skewness `nu`

* [`bcpe(mu, sigma, nu, tau)`](../reference/bcpe.html): Box-Cox power exponential distribution parameterised by location `mu`, scale `sigma`, `nu`, and `tau`

* [`bct(mu, sigma, nu, tau)`](../reference/bct.html): Box-Cox t-distribution parameterised by location `mu`, scale `sigma`, skewness `nu`, and degrees of freedom `tau`

* [`betaprime(shape1, shape2)`](../reference/betaprime.html): Beta prime distribution parameterised in terms of `shape1` and `shape2` of the corresponding Beta distribution

* [`beta2(mu, phi)`](../reference/beta2.html): Beta distribution reparameterised by mean `mu` and precision `phi`

* [`exgauss(mu, sigma, lambda)`](../reference/exgauss.html): Exponentially modified Gaussian distribution parameterised by location `mu`, scale `sigma`, and rate `lambda`

* [`foldnorm(mu, sigma)`](../reference/foldnorm.html): Folded normal distribution parameterised by location `mu` and scale `sigma`

* [`gamma2(mean, sd)`](../reference/gamma2.html): Gamma distribution reparameterised by mean and standard deviation

* [`gengamma(mu, sigma, nu)`](../reference/gengamma.html): Generalised gamma distribution parameterised by location `mu`, scale `sigma`, and skewness `nu`

* [`gompertz(eta, b)`](../reference/gompertz.html): Gompertz distribution parameterised by shape `eta` and rate `b`

* [`gumbel(location, scale)`](../reference/gumbel.html): Gumbel distribution parameterised by `location` and `scale`

* [`invchisq(df, scale)`](../reference/invchisq.html): Inverse Chi-squared distribution parameterised by degrees of freedom `df` and optional `scale`

* [`invgamma(shape, rate, scale)`](../reference/invgamma.html): Inverse gamma distribution parameterised by `shape`, `rate`, and `scale` of the corresponding gamma distribution

* [`invgauss(mean, shape)`](../reference/invgauss.html): Inverse Gaussian distribution parameterised by mean and shape

* [`kumar(a, b)`](../reference/kumar.html): Kumaraswamy distribution parameterised by shape parameters `a` and `b`

* [`laplace(mu, b)`](../reference/laplace.html): Laplace distribution parameterised by location `mu` and scale `b`

* [`llogis(alpha, beta)`](../reference/llogis.html): Log-logistic distribution parameterised by scale `alpha` (equal to the median) and shape `beta`

* [`oibeta(shape1, shape2, oneprob)`](../reference/oibeta.html): One-inflated beta distribution parameterised by shape parameters `shape1`, `shape2` and one-probability `oneprob`

* [`oibeta2(mu, phi, oneprob)`](../reference/oibeta2.html): One-inflated beta distribution reparameterised by mean `mu`, precision `phi`, and one-probability `oneprob`

* [`pareto(mu)`](../reference/pareto.html): Pareto distribution parameterised by `mu`

* [`powerexp(mu, sigma, nu)`](../reference/powerexp.html): Power exponential distribution parameterised by mean `mu`, standard deviation `sigma` and shape `nu`

* [`powerexp2(mu, sigma, nu)`](../reference/powerexp.html): Power exponential distribution reparameterised by location `mu`, scale `sigma` and shape `nu`

* [`pgweibull(scale, shape, powershape)`](../reference/pgweibull.html): Power generalised Weibull distribution parameterised by `scale`, `shape` and `powershape`

* [`skewnorm(xi, omega, alpha)`](../reference/skewnorm.html): Skew normal distribution parameterised by location `xi`, scale `omega` and skewness `alpha`

* [`skewnorm2(mean, sd, alpha)`](../reference/skewnorm2.html): Skew normal distribution reparameterised by mean, standard deviation and skewness `alpha`

* [`skewt(mu, sigma, skew, df)`](../reference/skewt.html): Skew t-distribution parameterised by location `mu`, scale `sigma`, skewness `skew` and degrees of freedom `df`

* [`skewt2(mean, sd, skew, df)`](../reference/skewt2.html): Skew t-distribution reparameterised by mean, standard deviation, skewness `skew` and degrees of freedom `df`

* [`truncnorm(mean, sd, min, max)`](../reference/truncnorm.html): Truncated normal distribution parameterised by mean, standard deviation, lower bound `min` and upper bound `max`

* [`trunct(df, min, max)`](../reference/trunct.html): Truncated t-distribution parameterised by degrees of freedom `df`, lower bound `min` and upper bound `max`

* [`trunct2(df, mu, sigma, min, max)`](../reference/trunct.html): Truncated t-distribution parameterised location `mu`, scale `sigma`, degrees of freedom `df`, lower bound `min` and upper bound `max`

* [`t2(mu, sigma, df)`](../reference/t2.html): Non-central and scaled t-distribution parameterised by location `mu`, scale `sigma` and degrees of freedom `df`

* [`vm(mu, kappa)`](../reference/vm.html): Von Mises distribution parameterised by mean direction `mu` and concentration `kappa`

* [`wrpcauchy(mu, rho)`](../reference/wrpcauchy.html): Wrapped Cauchy distribution parameterised by mean direction `mu` and concentration `rho`

* [`zibeta(shape1, shape2, zeroprob)`](../reference/zibeta.html): Zero-inflated beta distribution parameterised by shape parameters `shape1`, `shape2` and zero-probability `zeroprob`

* [`zibeta2(mu, phi, zeroprob)`](../reference/zibeta2.html): Zero-inflated beta distribution reparameterised by mean `mu`, precision `phi`, and zero-probability `zeroprob`

* [`zigamma(shape, scale, zeroprob)`](../reference/zigamma.html): Zero-inflated gamma distribution parameterised by shape, scale, and zero-probability `zeroprob`

* [`zigamma2(mean, sd, zeroprob)`](../reference/zigamma2.html): Zero-inflated gamma distribution reparameterised by mean, standard deviation, and zero-probability `zeroprob`

* [`ziinvgauss(mean, shape, zeroprob)`](../reference/ziinvgauss.html): Zero-inflated inverse Gaussian distribution parameterised by mean, shape, and zero-probability `zeroprob`

* [`zilnorm(meanlog, sdlog, zeroprob)`](../reference/zilnorm.html): Zero-inflated log normal distribution parameterised by meanlog, sdlog, and zero-probability `zeroprob`

* [`ziweibull(shape, scale, zeroprob)`](../reference/ziweibull.html): Zero-inflated Weibull distribution parameterised by shape, scale, and zero-probability `zeroprob`

* [`zoibeta(shape1, shape2, zeroprob, oneprob)`](../reference/zoibeta.html): Zero- and one-inflated beta distribution parameterised by shape parameters `shape1`, `shape2`, zero-probability `zeroprob` and one-probability `oneprob`

* [`zoibeta2(mu, phi, zeroprob, oneprob)`](../reference/zoibeta2.html): Zero- and one-inflated beta distribution reparameterised by mean `mu`, precision `phi`, zero-probability `zeroprob` and one-probability `oneprob`


## Discrete distributions

* [`betabinom(size, shape1, shape2)`](../reference/betabinom.html): Beta-binomial distribution parameterised by size `size`, shape parameters `shape1` and `shape2`

* [`genpois(lambda, phi)`](../reference/genpois.html): Generalised Poisson distribution parameterised by mean `lambda` and dispersion `phi`

* [`nbinom2(mu, size)`](../reference/nbinom2.html): Negative binomial distribution reparameterised by mean `mu` and size `size`

* [`skellam(mu1, mu2)`](../reference/skellam.html): Skellam distribution parameterised by Poisson means `mu1` and `mu2`

* [`zibinom(size, prob, zeroprob)`](../reference/zibinom.html): Zero-inflated binomial distribution parameterised by size `size`, success probability `prob` and zero-probability `zeroprob`

* [`zinbinom(size, prob, zeroprob)`](../reference/zinbinom.html): Zero-inflated negative binomial distribution parameterised by size `size`, success probability `prob` and zero-probability `zeroprob`

* [`zinbinom2(mu, size, zeroprob)`](../reference/zinbinom2.html): Zero-inflated negative binomial distribution reparameterised by mean `mu`, size `size` and zero-probability `zeroprob`

* [`zipois(lambda, zeroprob)`](../reference/zipois.html): Zero-inflated Poisson distribution parameterised by rate `lambda` and zero-probability `zeroprob`

* [`ztbinom(size, prob)`](../reference/ztbinom.html): Zero-truncated binomial distribution parameterised by size `size` and success probability `prob`

* [`ztnbinom(size, prob)`](../reference/ztnbinom.html): Zero-truncated negative binomial distribution parameterised by size `size` and success probability `prob`

* [`ztnbinom2(mu, size)`](../reference/ztnbinom2.html): Zero-truncated negative binomial distribution reparameterised by mean `mu` and size `size`

* [`ztpois(lambda)`](../reference/ztpois.html): Zero-truncated Poisson distribution parameterised by rate `lambda`


## Multivariate distributions

* [`dirichlet(alpha)`](../reference/dirichlet.html): Dirichlet distribution parameterised by concentration parameter vector `alpha`

* [`dirmult(size, alpha)`](../reference/dirmult.html): Dirichlet-multinomial distribution parameterised by `size` and concentration parameters `alpha`

* [`mvt(mu, Sigma, df)`](../reference/mvt.html): Multivariate t-distribution parameterised by location `mu`, scale matrix `Sigma` and degrees of freedom `df`

* [`vmf(mu, kappa)`](../reference/vmf.html): Multivariate von Mises-Fisher distribution parameterised by unit mean vector `mu` and concentration `kappa`

* [`vmf2(theta)`](../reference/vmf2.html): Multivariate von Mises-Fisher distribution parameterised by parameter `theta` equal to unit mean vector `mu` times concentration scalar `kappa`

* [`wishart(nu, Sigma)`](../reference/wishart.html): Wishart distribution parameterised by degrees of freedom `nu` and scale matrix `Sigma`


## Copulas

Bivariate copulas can be implemented in a modular way using the [`dcopula`](../reference/dcopula.html) function together with one of the copula constructors below. Available copula constructors are:

* [`cgaussian(rho)`](../reference/cgaussian.html) (Gaussian copula)
* [`cclayton(theta)`](../reference/cclayton.html) (Clayton copula)
* [`cgumbel(theta)`](../reference/cgumbel.html) (Gumbel copula)
* [`cfrank(theta)`](../reference/cfrank.html) (Frank copula)

For bivariate copulas with *discrete* margins, use the [`ddcopula`](../reference/ddcopula.html) function instead. In this case, instead of copula *densities*, copula *CDFs* are needed. The available constructors for this are:

* [`Cclayton`](../reference/Cclayton.html) (Clayton copula CDF)
* [`Cgumbel`](../reference/Cgumbel.html) (Gumbel copula CDF)
* [`Cfrank`](../reference/Cfrank.html) (Frank copula CDF)

Multivariate copulas are also possible using the [`dmvcopula`](../reference/dmvcopula.html) function together with one of the multivariate copula constructors below. Currently, only the multivariate Gaussian copula is implemented in two ways:

* [`cmvgauss(R)`](../reference/cmvgauss.html) (multivariate Gaussian copula parameterised by a correlation matrix)
* [`cgmrf(Q)`](../reference/cgmrf.html) (multivariate Gaussian copula parameterised by an inverse correlation matrix)




