List of distributions
In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

knitr::opts_chunk$set(
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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
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
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)