# List of distributions

## Continuous distributions

- `bccg(mu, sigma, nu)`: Box-Cox Cole and Green distribution parameterised by location `mu`, scale `sigma`, and skewness `nu`

- `bcpe(mu, sigma, nu, tau)`: Box-Cox power exponential distribution parameterised by location `mu`, scale `sigma`, `nu`, and `tau`

- `bct(mu, sigma, nu, tau)`: Box-Cox t-distribution parameterised by location `mu`, scale `sigma`, skewness `nu`, and degrees of freedom `tau`

- `betaprime(shape1, shape2)`: Beta prime distribution parameterised in terms of `shape1` and `shape2` of the corresponding Beta distribution

- `beta2(mu, phi)`: Beta distribution reparameterised by mean `mu` and precision `phi`

- `exgauss(mu, sigma, lambda)`: Exponentially modified Gaussian distribution parameterised by location `mu`, scale `sigma`, and rate `lambda`

- `foldnorm(mu, sigma)`: Folded normal distribution parameterised by location `mu` and scale `sigma`

- `gamma2(mean, sd)`: Gamma distribution reparameterised by mean and standard deviation

- `gengamma(mu, sigma, nu)`: Generalised gamma distribution parameterised by location `mu`, scale `sigma`, and skewness `nu`

- `gompertz(eta, b)`: Gompertz distribution parameterised by shape `eta` and rate `b`

- `gumbel(location, scale)`: Gumbel distribution parameterised by `location` and `scale`

- `invchisq(df, scale)`: Inverse Chi-squared distribution parameterised by degrees of freedom `df` and optional `scale`

- `invgamma(shape, rate, scale)`: Inverse gamma distribution parameterised by `shape`, `rate`, and `scale` of the corresponding gamma distribution

- `invgauss(mean, shape)`: Inverse Gaussian distribution parameterised by mean and shape

- `kumar(a, b)`: Kumaraswamy distribution parameterised by shape parameters `a` and `b`

- `laplace(mu, b)`: Laplace distribution parameterised by location `mu` and scale `b`

- `llogis(alpha, beta)`: Log-logistic distribution parameterised by scale `alpha` (equal to the median) and shape `beta`

- `oibeta(shape1, shape2, oneprob)`: One-inflated beta distribution parameterised by shape parameters `shape1`, `shape2` and one-probability `oneprob`

- `oibeta2(mu, phi, oneprob)`: One-inflated beta distribution reparameterised by mean `mu`, precision `phi`, and one-probability `oneprob`

- `pareto(mu)`: Pareto distribution parameterised by `mu`

- `powerexp(mu, sigma, nu)`: Power exponential distribution parameterised by mean `mu`, standard deviation `sigma` and shape `nu`

- `powerexp2(mu, sigma, nu)`: Power exponential distribution reparameterised by location `mu`, scale `sigma` and shape `nu`

- `pgweibull(scale, shape, powershape)`: Power generalised Weibull distribution parameterised by `scale`, `shape` and `powershape`

- `skewnorm(xi, omega, alpha)`: Skew normal distribution parameterised by location `xi`, scale `omega` and skewness `alpha`

- `skewnorm2(mean, sd, alpha)`: Skew normal distribution reparameterised by mean, standard deviation and skewness `alpha`

- `skewt(mu, sigma, skew, df)`: Skew t-distribution parameterised by location `mu`, scale `sigma`, skewness `skew` and degrees of freedom `df`

- `skewt2(mean, sd, skew, df)`: Skew t-distribution reparameterised by mean, standard deviation, skewness `skew` and degrees of freedom `df`

- `truncnorm(mean, sd, min, max)`: Truncated normal distribution parameterised by mean, standard deviation, lower bound `min` and upper bound `max`

- `trunct(df, min, max)`: Truncated t-distribution parameterised by degrees of freedom `df`, lower bound `min` and upper bound `max`

- `trunct2(df, mu, sigma, min, max)`: Truncated t-distribution parameterised location `mu`, scale `sigma`, degrees of freedom `df`, lower bound `min` and upper bound `max`

- `t2(mu, sigma, df)`: Non-central and scaled t-distribution parameterised by location `mu`, scale `sigma` and degrees of freedom `df`

- `vm(mu, kappa)`: Von Mises distribution parameterised by mean direction `mu` and concentration `kappa`

- `wrpcauchy(mu, rho)`: Wrapped Cauchy distribution parameterised by mean direction `mu` and concentration `rho`

- `zibeta(shape1, shape2, zeroprob)`: Zero-inflated beta distribution parameterised by shape parameters `shape1`, `shape2` and zero-probability `zeroprob`

- `zibeta2(mu, phi, zeroprob)`: Zero-inflated beta distribution reparameterised by mean `mu`, precision `phi`, and zero-probability `zeroprob`

- `zigamma(shape, scale, zeroprob)`: Zero-inflated gamma distribution parameterised by shape, scale, and zero-probability `zeroprob`

- `zigamma2(mean, sd, zeroprob)`: Zero-inflated gamma distribution reparameterised by mean, standard deviation, and zero-probability `zeroprob`

- `ziinvgauss(mean, shape, zeroprob)`: Zero-inflated inverse Gaussian distribution parameterised by mean, shape, and zero-probability `zeroprob`

- `zilnorm(meanlog, sdlog, zeroprob)`: Zero-inflated log normal distribution parameterised by meanlog, sdlog, and zero-probability `zeroprob`

- `ziweibull(shape, scale, zeroprob)`: Zero-inflated Weibull distribution parameterised by shape, scale, and zero-probability `zeroprob`

- `zoibeta(shape1, shape2, zeroprob, oneprob)`: Zero- and one-inflated beta distribution parameterised by shape parameters `shape1`, `shape2`, zero-probability `zeroprob` and one-probability `oneprob`

- `zoibeta2(mu, phi, zeroprob, oneprob)`: 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)`: Beta-binomial distribution parameterised by size `size`, shape parameters `shape1` and `shape2`

- `genpois(lambda, phi)`: Generalised Poisson distribution parameterised by mean `lambda` and dispersion `phi`

- `nbinom2(mu, size)`: Negative binomial distribution reparameterised by mean `mu` and size `size`

- `skellam(mu1, mu2)`: Skellam distribution parameterised by Poisson means `mu1` and `mu2`

- `zibinom(size, prob, zeroprob)`: Zero-inflated binomial distribution parameterised by size `size`, success probability `prob` and zero-probability `zeroprob`

- `zinbinom(size, prob, zeroprob)`: Zero-inflated negative binomial distribution parameterised by size `size`, success probability `prob` and zero-probability `zeroprob`

- `zinbinom2(mu, size, zeroprob)`: Zero-inflated negative binomial distribution reparameterised by mean `mu`, size `size` and zero-probability `zeroprob`

- `zipois(lambda, zeroprob)`: Zero-inflated Poisson distribution parameterised by rate `lambda` and zero-probability `zeroprob`

- `ztbinom(size, prob)`: Zero-truncated binomial distribution parameterised by size `size` and success probability `prob`

- `ztnbinom(size, prob)`: Zero-truncated negative binomial distribution parameterised by size `size` and success probability `prob`

- `ztnbinom2(mu, size)`: Zero-truncated negative binomial distribution reparameterised by mean `mu` and size `size`

- `ztpois(lambda)`: Zero-truncated Poisson distribution parameterised by rate `lambda`

## Multivariate distributions

- `dirichlet(alpha)`: Dirichlet distribution parameterised by concentration parameter vector `alpha`

- `dirmult(size, alpha)`: Dirichlet-multinomial distribution parameterised by `size` and concentration parameters `alpha`

- `mvt(mu, Sigma, df)`: Multivariate t-distribution parameterised by location `mu`, scale matrix `Sigma` and degrees of freedom `df`

- `vmf(mu, kappa)`: Multivariate von Mises-Fisher distribution parameterised by unit mean vector `mu` and concentration `kappa`

- `vmf2(theta)`: Multivariate von Mises-Fisher distribution parameterised by parameter `theta` equal to unit mean vector `mu` times concentration scalar `kappa`

- `wishart(nu, Sigma)`: 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` function together with one of the copula constructors below. Available copula constructors are:

- `cgaussian(rho)` (Gaussian copula)
- `cclayton(theta)` (Clayton copula)
- `cgumbel(theta)` (Gumbel copula)
- `cfrank(theta)` (Frank copula)

For bivariate copulas with discrete margins, use the `ddcopula` function instead. In this case, instead of copula densities, copula CDFs are needed. The available constructors for this are:

- `Cclayton` (Clayton copula CDF)
- `Cgumbel` (Gumbel copula CDF)
- `Cfrank` (Frank copula CDF)

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

- `cmvgauss(R)` (multivariate Gaussian copula parameterised by a correlation matrix)
- `cgmrf(Q)` (multivariate Gaussian copula parameterised by an inverse correlation matrix)