Type:	Package
Title:	Distributions Compatible with Automatic Differentiation by 'RTMB'
Version:	0.1.0
Description:	Extends the functionality of the 'RTMB' https://kaskr.r-universe.dev/RTMB package by providing a collection of non-standard probability distributions compatible with automatic differentiation (AD). While 'RTMB' enables flexible and efficient modelling, including random effects, its built-in support is limited to standard distributions. The package adds additional AD-compatible distributions, broadening the range of models that can be implemented and estimated using 'RTMB'. Automatic differentiation and Laplace approximation are described in Kristensen et al. (2016) <doi:10.18637/jss.v070.i05>.
License:	MIT + file LICENSE
Encoding:	UTF-8
Imports:	stats, gamlss.dist, circular, sn, statmod, movMF
Depends:	R (≥ 3.5.0), RTMB (≥ 1.7.0)
RoxygenNote:	7.3.2
Suggests:	knitr, rmarkdown, testthat (≥ 3.0.0), LaMa (≥ 2.0.6), Matrix, TMB, gamlss.data, mvtnorm
Config/testthat/edition:	3
URL:	https://janoleko.github.io/RTMBdist/
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2025-10-01 08:06:59 UTC; jan-ole
Author:	Jan-Ole Koslik [aut, cre]
Maintainer:	Jan-Ole Koslik <jan-ole.koslik@uni-bielefeld.de>
Repository:	CRAN
Date/Publication:	2025-10-07 18:30:15 UTC

Box–Cox Cole and Green distribution (BCCG)

Description

Density, distribution function, quantile function, and random generation for the Box–Cox Cole and Green distribution.

Usage

dbccg(x, mu = 1, sigma = 0.1, nu = 1, log = FALSE)

pbccg(q, mu = 1, sigma = 0.1, nu = 1, lower.tail = TRUE, log.p = FALSE)

qbccg(p, mu = 1, sigma = 0.1, nu = 1, lower.tail = TRUE, log.p = FALSE)

rbccg(n, mu = 1, sigma = 0.1, nu = 1)

Arguments

Details

This implementation of dbccg and pbccg allows for automatic differentiation with RTMB while the other functions are imported from gamlss.dist package. See gamlss.dist::BCCG for more details.

Value

dbccg gives the density, pbccg gives the distribution function, qbccg gives the quantile function, and rbccg generates random deviates.

References

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Examples

x <- rbccg(5, mu = 10, sigma = 0.2, nu = 0.5)
d <- dbccg(x, mu = 10, sigma = 0.2, nu = 0.5)
p <- pbccg(x, mu = 10, sigma = 0.2, nu = 0.5)
q <- qbccg(p, mu = 10, sigma = 0.2, nu = 0.5)

Box-Cox Power Exponential distribution (BCPE)

Description

Density, distribution function, quantile function, and random generation for the Box-Cox Power Exponential distribution.

Usage

dbcpe(x, mu = 5, sigma = 0.1, nu = 1, tau = 2, log = FALSE)

pbcpe(q, mu = 5, sigma = 0.1, nu = 1, tau = 2, lower.tail = TRUE, log.p = FALSE)

qbcpe(p, mu = 5, sigma = 0.1, nu = 1, tau = 2, lower.tail = TRUE, log.p = FALSE)

rbcpe(n, mu = 5, sigma = 0.1, nu = 1, tau = 2)

Arguments

Details

This implementation of dbcpe and pbcpe allows for automatic differentiation with RTMB while the other functions are imported from gamlss.dist package. See gamlss.dist::BCPE for more details.

Value

dbcpe gives the density, pbcpe gives the distribution function, qbcpe gives the quantile function, and rbcpe generates random deviates.

References

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Examples

x <- rbcpe(1, mu = 5, sigma = 0.1, nu = 1, tau = 1)
d <- dbcpe(x, mu = 5, sigma = 0.1, nu = 1, tau = 1)
p <- pbcpe(x, mu = 5, sigma = 0.1, nu = 1, tau = 1)
q <- qbcpe(p, mu = 5, sigma = 0.1, nu = 1, tau = 1)

Box–Cox t distribution (BCT)

Description

Density, distribution function, quantile function, and random generation for the Box–Cox t distribution.

Usage

dbct(x, mu = 5, sigma = 0.1, nu = 1, tau = 2, log = FALSE)

pbct(q, mu = 5, sigma = 0.1, nu = 1, tau = 2, lower.tail = TRUE, log.p = FALSE)

qbct(p, mu = 5, sigma = 0.1, nu = 1, tau = 2, lower.tail = TRUE, log.p = FALSE)

rbct(n, mu = 5, sigma = 0.1, nu = 1, tau = 2)

Arguments

Details

This implementation of dbct and pbct allows for automatic differentiation with RTMB while the other functions are imported from gamlss.dist package. See gamlss.dist::BCT for more details.

Value

dbct gives the density, pbct gives the distribution function, qbct gives the quantile function, and rbct generates random deviates.

References

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Examples

x <- rbct(1, mu = 10, sigma = 0.2, nu = 0.5, tau = 4)
d <- dbct(x, mu = 10, sigma = 0.2, nu = 0.5, tau = 4)
p <- pbct(x, mu = 10, sigma = 0.2, nu = 0.5, tau = 4)
q <- qbct(p, mu = 10, sigma = 0.2, nu = 0.5, tau = 4)

Reparameterised beta distribution

Description

Density, distribution function, quantile function, and random generation for the beta distribution reparameterised in terms of mean and concentration.

Usage

dbeta(x, shape1, shape2, log = FALSE, eps = 0)

dbeta2(x, mu, phi, log = FALSE, eps = 0)

pbeta2(q, mu, phi, lower.tail = TRUE, log.p = FALSE)

qbeta2(p, mu, phi, lower.tail = TRUE, log.p = FALSE)

rbeta2(n, mu, phi)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Currently, dbeta masks RTMB::dbeta because the latter has a numerically unstable gradient.

Value

dbeta2 gives the density, pbeta2 gives the distribution function, qbeta2 gives the quantile function, and rbeta2 generates random deviates.

Examples

set.seed(123)
x <- rbeta2(1, 0.5, 1)
d <- dbeta2(x, 0.5, 1)
p <- pbeta2(x, 0.5, 1)
q <- qbeta2(p, 0.5, 1)

Beta-binomial distribution

Description

Density and random generation for the beta-binomial distribution.

Usage

dbetabinom(x, size, shape1, shape2, log = FALSE)

rbetabinom(n, size, shape1, shape2)

Arguments

Details

This implementation of dbetabinom allows for automatic differentiation with RTMB.

Value

dbetabinom gives the density and rbetabinom generates random samples.

Examples

set.seed(123)
x <- rbetabinom(1, 10, 2, 5)
d <- dbetabinom(x, 10, 2, 5)

Clayton copula constructor

Description

Returns a function that computes the log density of the bivariate Clayton copula, intended to be used with dcopula.

Usage

cclayton(theta)

Arguments

Details

The Clayton copula density is

c(u,v;\theta) = (1+\theta) (uv)^{-(1+\theta)} \left( u^{-\theta} + v^{-\theta} - 1 \right)^{-(2\theta+1)/\theta}, \quad \theta > 0.

Value

A function of two arguments (u,v) returning log copula density.

See Also

cgaussian(), cgumbel(), cfrank()

Examples

x <- c(0.5, 1); y <- c(0.2, 0.8)
d1 <- dnorm(x, 1, log = TRUE); d2 <- dbeta(y, 2, 1, log = TRUE)
p1 <- pnorm(x, 1); p2 <- pbeta(y, 2, 1)
dcopula(d1, d2, p1, p2, copula = cclayton(2), log = TRUE)

Frank copula constructor

Description

Returns a function computing the log density of the bivariate Frank copula, intended to be used with dcopula.

Usage

cfrank(theta)

Arguments

Details

The Frank copula density is

c(u,v;\theta) = \frac{\theta (1-e^{-\theta}) e^{-\theta(u+v)}} {\left[(e^{-\theta u}-1)(e^{-\theta v}-1) + (1 - e^{-\theta}) \right]^2}, \quad \theta \ne 0.

Value

Function of two arguments (u,v) returning log copula density.

See Also

cgaussian(), cclayton(), cgumbel()

Examples

x <- c(0.5, 1); y <- c(1, 2)
d1 <- dnorm(x, 1, log = TRUE); d2 <- dexp(y, 2, log = TRUE)
p1 <- pnorm(x, 1); p2 <- pexp(y, 2)
dcopula(d1, d2, p1, p2, copula = cfrank(2), log = TRUE)

Gaussian copula constructor

Description

Returns a function computing the log density of the bivariate Gaussian copula, intended to be used with dcopula.

Usage

cgaussian(rho = 0)

Arguments

Value

Function of two arguments (u,v) returning log copula density.

The Gaussian copula density is

c(u,v;\rho) = \frac{1}{\sqrt{1-\rho^2}} \exp\left\{-\frac{1}{2(1-\rho^2)} (z_1^2 - 2 \rho z_1 z_2 + z_2^2) + \frac{1}{2}(z_1^2 + z_2^2) \right\},

where z_1 = \Phi^{-1}(u), z_2 = \Phi^{-1}(v), and -1 < \rho < 1.

See Also

cclayton(), cgumbel(), cfrank()

Examples

x <- c(0.5, 1); y <- c(1, 2)
d1 <- dnorm(x, 1, log = TRUE); d2 <- dexp(y, 2, log = TRUE)
p1 <- pnorm(x, 1); p2 <- pexp(y, 2)
dcopula(d1  , d2, p1, p2, copula = cgaussian(0.5), log = TRUE)

Gumbel copula constructor

Description

Returns a function that computes the log density of the bivariate Gumbel copula, intended to be used with dcopula.

Usage

cgumbel(theta)

Arguments

Details

The Gumbel copula density

c(u,v;\theta) = \exp\Big[-\big((-\log u)^\theta + (-\log v)^\theta\big)^{1/\theta}\Big] \cdot h(u,v;\theta),

where h(u,v;\theta) contains the derivative terms ensuring the function is a density.

Value

A function of two arguments (u,v) returning log copula density.

See Also

cgaussian(), cclayton(), cfrank()

Examples

x <- c(0.5, 1); y <- c(0.2, 0.4)
d1 <- dnorm(x, 1, log = TRUE); d2 <- dbeta(y, 2, 1, log = TRUE)
p1 <- pnorm(x, 1); p2 <- pbeta(y, 2, 1)
dcopula(d1, d2, p1, p2, copula = cgumbel(1.5), log = TRUE)

Joint density under a bivariate copula

Description

Computes the joint density (or log-density) of a bivariate distribution constructed from two arbitrary margins combined with a specified copula.

Usage

dcopula(d1, d2, p1, p2, copula = cgaussian(0), log = FALSE)

Arguments

Details

The joint density is

f(x,y) = c(F_1(x), F_2(y)) \, f_1(x) f_2(y),

where F_i are the marginal CDFs, f_i are the marginal densities, and c is the copula density.

The marginal densities d1, d2 and CDFs p1, p2 must be differentiable for automatic differentiation (AD) to work.

Available copula constructors are:

• cgaussian (Gaussian copula)

• cclayton (Clayton copula)

• cgumbel (Gumbel copula)

• cfrank (Frank copula)

Value

Joint density (or log-density) under the bivariate copula.

Examples

# Normal + Exponential margins with Gaussian copula
x <- c(0.5, 1); y <- c(1, 2)
d1 <- dnorm(x, 1, log = TRUE); d2 <- dexp(y, 2, log = TRUE)
p1 <- pnorm(x, 1); p2 <- pexp(y, 2)
dcopula(d1, d2, p1, p2, copula = cgaussian(0.5), log = TRUE)

# Normal + Beta margins with Clayton copula
x <- c(0.5, 1); y <- c(0.2, 0.8)
d1 <- dnorm(x, 1, log = TRUE); d2 <- dbeta(y, 2, 1, log = TRUE)
p1 <- pnorm(x, 1); p2 <- pbeta(y, 2, 1)
dcopula(d1, d2, p1, p2, copula = cclayton(2), log = TRUE)

# Normal + Beta margins with Gumbel copula
x <- c(0.5, 1); y <- c(0.2, 0.4)
d1 <- dnorm(x, 1, log = TRUE); d2 <- dbeta(y, 2, 1, log = TRUE)
p1 <- pnorm(x, 1); p2 <- pbeta(y, 2, 1)
dcopula(d1, d2, p1, p2, copula = cgumbel(1.5), log = TRUE)

# Normal + Exponential margins with Frank copula
x <- c(0.5, 1); y <- c(1, 2)
d1 <- dnorm(x, 1, log = TRUE); d2 <- dexp(y, 2, log = TRUE)
p1 <- pnorm(x, 1); p2 <- pexp(y, 2)
dcopula(d1, d2, p1, p2, copula = cfrank(2), log = TRUE)

Dirichlet distribution

Description

Density and and random generation for the Dirichlet distribution.

Usage

ddirichlet(x, alpha, log = FALSE)

rdirichlet(n, alpha)

Arguments

Details

This implementation of ddirichlet allows for automatic differentiation with RTMB.

Value

ddirichlet gives the density, rdirichlet generates random deviates.

Examples

# single alpha
alpha <- c(1,2,3)
x <- rdirichlet(1, alpha)
d <- ddirichlet(x, alpha)
# vectorised over alpha
alpha <- rbind(alpha, 2*alpha)
x <- rdirichlet(2, alpha)

Dirichlet-multinomial distribution

Description

Density and and random generation for the Dirichlet-multinomial distribution.

Usage

ddirmult(x, size, alpha, log = FALSE)

rdirmult(n, size, alpha)

Arguments

Details

This implementation of ddirmult allows for automatic differentiation with RTMB.

Value

ddirmult gives the density and rdirmult generates random samples.

Examples

# single alpha
alpha <- c(1,2,3)
size <- 10
x <- rdirmult(1, size, alpha)
d <- ddirmult(x, size, alpha)
# vectorised over alpha and size
alpha <- rbind(alpha, 2*alpha)
size <- c(size, 3*size)
x <- rdirmult(2, size, alpha)

AD-compatible error function and complementary error function

Description

AD-compatible error function and complementary error function

Usage

erf(x)

erfc(x)

Arguments

Value

erf(x) returns the error function and erfc(x) returns the complementary error function.

Examples

erf(1)
erfc(1)

Exponentially modified Gaussian distribution

Description

Density, distribution function, quantile function, and random generation for the exponentially modified Gaussian distribution.

Usage

dexgauss(x, mu = 0, sigma = 1, lambda = 1, log = FALSE)

pexgauss(q, mu = 0, sigma = 1, lambda = 1, lower.tail = TRUE, log.p = FALSE)

qexgauss(p, mu = 0, sigma = 1, lambda = 1, lower.tail = TRUE, log.p = FALSE)

rexgauss(n, mu = 0, sigma = 1, lambda = 1)

Arguments

Details

This implementation of dexgauss and pexgauss allows for automatic differentiation with RTMB. qexgauss and rexgauss are reparameterised imports from gamlss.dist::exGAUS.

If X \sim N(\mu, \sigma^2) and Y \sim \text{Exp}(\lambda), then Z = X + Y follows the exponentially modified Gaussian distribution with parameters \mu, \sigma, and \lambda.

Value

dexgauss gives the density, pexgauss gives the distribution function, qexgauss gives the quantile function, and rexgauss generates random deviates.

References

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Examples

x <- rexgauss(1, 1, 2, 2)
d <- dexgauss(x, 1, 2, 2)
p <- pexgauss(x, 1, 2, 2)
q <- qexgauss(p, 1, 2, 2)

Folded normal distribution

Description

Density, distribution function, and random generation for the folded normal distribution.

Usage

dfoldnorm(x, mu = 0, sigma = 1, log = FALSE)

pfoldnorm(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

rfoldnorm(n, mu = 0, sigma = 1)

Arguments

Details

This implementation of dfoldnorm allows for automatic differentiation with RTMB.

Value

dfoldnorm gives the density, pfoldnorm gives the distribution function, and rfoldnorm generates random deviates.

Examples

x <- rfoldnorm(1, 1, 2)
d <- dfoldnorm(x, 1, 2)
p <- pfoldnorm(x, 1, 2)

Reparameterised gamma distribution

Description

Density, distribution function, quantile function, and random generation for the gamma distribution reparameterised in terms of mean and standard deviation.

Usage

dgamma2(x, mean = 1, sd = 1, log = FALSE)

pgamma2(q, mean = 1, sd = 1, lower.tail = TRUE, log.p = FALSE)

qgamma2(p, mean = 1, sd = 1, lower.tail = TRUE, log.p = FALSE)

rgamma2(n, mean = 1, sd = 1)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dgamma2 gives the density, pgamma2 gives the distribution function, qgamma2 gives the quantile function, and rgamma2 generates random deviates.

Examples

x <- rgamma2(1)
d <- dgamma2(x)
p <- pgamma2(x)
q <- qgamma2(p)

Generalised Poisson distribution

Description

Probability mass function, distribution function, and random generation for the generalised Poisson distribution.

Usage

dgenpois(x, lambda = 1, phi = 1, log = FALSE)

pgenpois(q, lambda = 1, phi = 1, lower.tail = TRUE, log.p = FALSE)

qgenpois(p, lambda = 1, phi = 1,
         lower.tail = TRUE, log.p = FALSE, max.value = 10000)

rgenpois(n, lambda = 1, phi = 1, max.value = 10000)

Arguments

Details

This implementation of dgenpois allows for automatic differentiation with RTMB. The other functions are imported from gamlss.dist::GPO.

The distribution has mean \lambda and variance \lambda(1 + \phi \lambda)^2. For \phi = 0 it reduces to the Poisson distribution, however \phi must be strictly positive here.

Value

dgenpois gives the probability mass function, pgenpois gives the distribution function, qgenpois gives the quantile function, and rgenpois generates random deviates.

Examples

set.seed(123)
x <- rgenpois(1, 2, 3)
d <- dgenpois(x, 2, 3)
p <- pgenpois(x, 2, 3)
q <- qgenpois(p, 2, 3)

Gumbel distribution

Description

Density, distribution function, quantile function, and random generation for the Gumbel distribution.

Usage

dgumbel(x, location = 0, scale = 1, log = FALSE)

pgumbel(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)

qgumbel(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)

rgumbel(n, location = 0, scale = 1)

Arguments

Details

This implementation of dgumbel allows for automatic differentiation with RTMB.

Value

dgumbel gives the density, pgumbel gives the distribution function, qgumbel gives the quantile function, and rgumbel generates random deviates.

Examples

x <- rgumbel(1, 0.5, 2)
d <- dgumbel(x, 0.5, 2)
p <- pgumbel(x, 0.5, 2)
q <- qgumbel(p, 0.5, 2)

Inverse Gaussian distribution

Description

Density, distribution function, and random generation for the inverse Gaussian distribution.

Usage

dinvgauss(x, mean = 1, shape = 1, log = FALSE)

pinvgauss(q, mean = 1, shape = 1, lower.tail = TRUE, log.p = FALSE)

qinvgauss(p, mean = 1, shape = 1, lower.tail = TRUE, log.p = FALSE, ...)

rinvgauss(n, mean = 1, shape = 1)

Arguments

Details

This implementation of dinvgauss allows for automatic differentiation with RTMB. qinvgauss and rinvgauss are imported from the statmod package.

Value

dinvgauss gives the density, pinvgauss gives the distribution function, qinvgauss gives the quantile function, and rinvgauss generates random deviates.

Examples

x <- rinvgauss(1, 1, 0.5)
d <- dinvgauss(x, 1, 0.5)
p <- pinvgauss(x, 1, 0.5)
q <- qinvgauss(p, 1, 0.5)

Laplace distribution

Description

Density, distribution function, quantile function, and random generation for the Laplace distribution.

Usage

dlaplace(x, mu = 0, b = 1, log = FALSE)

plaplace(q, mu = 0, b = 1, lower.tail = TRUE, log.p = FALSE)

qlaplace(p, mu = 0, b = 1, lower.tail = TRUE, log.p = FALSE)

rlaplace(n, mu = 0, b = 1)

Arguments

Details

This implementation of dlaplace allows for automatic differentiation with RTMB.

Value

dlaplace gives the density, plaplace gives the distribution function, qlaplace gives the quantile function, and rlaplace generates random deviates.

Examples

x <- rlaplace(1, 1, 1)
d <- dlaplace(x, 1, 1)
p <- plaplace(x, 1, 1)
q <- qlaplace(p, 1, 1)

Multivariate t distribution

Description

Density and and random generation for the multivariate t distribution

Usage

dmvt(x, mu, Sigma, df, log = FALSE)

rmvt(n, mu, Sigma, df)

Arguments

Details

This implementation of dmvt allows for automatic differentiation with RTMB.

Note: for df \le 1 the mean is undefined, and for df \le 2 the covariance is infinite. For df > 2, the covariance is df/(df-2) * Sigma.

Value

dmvt gives the density, rmvt generates random deviates.

Examples

# single mu
mu <- c(1,2,3)
Sigma <- diag(c(1,1,1))
df <- 5
x <- rmvt(2, mu, Sigma, df)
d <- dmvt(x, mu, Sigma, df)
# vectorised over mu
mu <- rbind(c(1,2,3), c(0, 0.5, 1))
x <- rmvt(2, mu, Sigma, df)
d <- dmvt(x, mu, Sigma, df)

Reparameterised negative binomial distribution

Description

Probability mass function, distribution function, quantile function, and random generation for the negative binomial distribution reparameterised in terms of mean and size.

Usage

dnbinom2(x, mu, size, log = FALSE)

pnbinom2(q, mu, size, lower.tail = TRUE, log.p = FALSE)

qnbinom2(p, mu, size, lower.tail = TRUE, log.p = FALSE)

rnbinom2(n, mu, size)

pnbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

pnbinom is an AD-compatible implementation of the standard parameterisation of the CDF, missing from RTMB.

Value

dnbinom2 gives the density, pnbinom2 gives the distribution function, qnbinom2 gives the quantile function, and rnbinom2 generates random deviates.

Examples

set.seed(123)
x <- rnbinom2(1, 1, 2)
d <- dnbinom2(x, 1, 2)
p <- pnbinom2(x, 1, 2)
q <- qnbinom2(p, 1, 2)

One-inflated beta distribution

Description

Density, distribution function, and random generation for the one-inflated beta distribution.

Usage

doibeta(x, shape1, shape2, oneprob = 0, log = FALSE)

poibeta(q, shape1, shape2, oneprob = 0, lower.tail = TRUE, log.p = FALSE)

roibeta(n, shape1, shape2, oneprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

doibeta gives the density, poibeta gives the distribution function, and roibeta generates random deviates.

Examples

set.seed(123)
x <- roibeta(1, 2, 2, 0.5)
d <- doibeta(x, 2, 2, 0.5)
p <- poibeta(x, 2, 2, 0.5)

Reparameterised one-inflated beta distribution

Description

Density, distribution function, and random generation for the one-inflated beta distribution reparameterised in terms of mean and concentration.

Usage

doibeta2(x, mu, phi, oneprob = 0, log = FALSE)

poibeta2(q, mu, phi, oneprob = 0, lower.tail = TRUE, log.p = FALSE)

roibeta2(n, mu, phi, oneprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

doibeta2 gives the density, poibeta2 gives the distribution function, and roibeta2 generates random deviates.

Examples

set.seed(123)
x <- roibeta2(1, 0.6, 2, 0.5)
d <- doibeta2(x, 0.6, 2, 0.5)
p <- poibeta2(x, 0.6, 2, 0.5)

Pareto distribution

Description

Density, distribution function, quantile function, and random generation for the pareto distribution.

Usage

dpareto(x, mu = 1, log = FALSE)

ppareto(q, mu = 1, lower.tail = TRUE, log.p = FALSE)

qpareto(p, mu = 1, lower.tail = TRUE, log.p = FALSE)

rpareto(n, mu = 1)

Arguments

Details

This implementation of dpareto and ppareto allows for automatic differentiation with RTMB while the other functions are imported from gamlss.dist package. See gamlss.dist::PARETO for more details.

Value

dpareto gives the density, ppareto gives the distribution function, qpareto gives the quantile function, and rpareto generates random deviates.

References

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Examples

set.seed(123)
x <- rpareto(1, mu = 5)
d <- dpareto(x, mu = 5)
p <- ppareto(x, mu = 5)
q <- qpareto(p, mu = 5)

Power Exponential distribution (PE and PE2)

Description

Density, distribution function, quantile function, and random generation for the Power Exponential distribution (two versions).

Usage

dpowerexp(x, mu = 0, sigma = 1, nu = 2, log = FALSE)

ppowerexp(q, mu = 0, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)

qpowerexp(p, mu = 0, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)

rpowerexp(n, mu = 0, sigma = 1, nu = 2)

dpowerexp2(x, mu = 0, sigma = 1, nu = 2, log = FALSE)

ppowerexp2(q, mu = 0, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)

qpowerexp2(p, mu = 0, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)

rpowerexp2(n, mu = 0, sigma = 1, nu = 2)

Arguments

Details

This implementation of the densities and distribution functions allow for automatic differentiation with RTMB while the other functions are imported from gamlss.dist package.

For powerexp, mu is the mean and sigma is the standard deviation while this does not hold for powerexp2.

See gamlss.dist::PE for more details.

Value

dpowerexp gives the density, ppowerexp gives the distribution function, qpowerexp gives the quantile function, and rpowerexp generates random deviates.

References

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Examples

# PE
x <- rpowerexp(1, mu = 0, sigma = 1, nu = 2)
d <- dpowerexp(x, mu = 0, sigma = 1, nu = 2)
p <- ppowerexp(x, mu = 0, sigma = 1, nu = 2)
q <- qpowerexp(p, mu = 0, sigma = 1, nu = 2)

# PE2
x <- rpowerexp2(1, mu = 0, sigma = 1, nu = 2)
d <- dpowerexp2(x, mu = 0, sigma = 1, nu = 2)
p <- ppowerexp2(x, mu = 0, sigma = 1, nu = 2)
q <- qpowerexp2(p, mu = 0, sigma = 1, nu = 2)

Skew normal distribution

Description

Density, distribution function, quantile function, and random generation for the skew normal distribution.

Usage

dskewnorm(x, xi = 0, omega = 1, alpha = 0, log = FALSE)

pskewnorm(q, xi = 0, omega = 1, alpha = 0, ...)

qskewnorm(p, xi = 0, omega = 1, alpha = 0, ...)

rskewnorm(n, xi = 0, omega = 1, alpha = 0)

Arguments

Details

This implementation of dskewnorm allows for automatic differentiation with RTMB while the other functions are imported from the sn package. See sn::dsn for more details.

Value

dskewnorm gives the density, pskewnorm gives the distribution function, qskewnorm gives the quantile function, and rskewnorm generates random deviates.

Examples

# alpha is skew parameter
x <- rskewnorm(1, alpha = 1)
d <- dskewnorm(x, alpha = 1)
p <- pskewnorm(x, alpha = 1)
q <- qskewnorm(p, alpha = 1)

Reparameterised skew normal distribution

Description

Density, distribution function, quantile function and random generation for the skew normal distribution reparameterised in terms of mean, standard deviation and skew magnitude

Usage

dskewnorm2(x, mean = 0, sd = 1, alpha = 0, log = FALSE)

pskewnorm2(q, mean = 0, sd = 1, alpha = 0, ...)

qskewnorm2(p, mean = 0, sd = 1, alpha = 0, ...)

rskewnorm2(n, mean = 0, sd = 1, alpha = 0)

Arguments

Details

This implementation of dskewnorm2 allows for automatic differentiation with RTMB while the other functions are imported from the sn package.

Value

dskewnorm2 gives the density, pskewnorm2 gives the distribution function, qskewnorm2 gives the quantile function, and rskewnorm2 generates random deviates.

Examples

# alpha is skew parameter
x <- rskewnorm2(1, alpha = 1)
d <- dskewnorm2(x, alpha = 1)
p <- pskewnorm2(x, alpha = 1)
q <- qskewnorm2(p, alpha = 1)

Skewed students t distribution

Description

Density, distribution function, quantile function, and random generation for the skew t distribution (type 2).

Usage

dskewt(x, mu = 0, sigma = 1, skew = 0, df = 1000, log = FALSE)

pskewt(q, mu = 0, sigma = 1, skew = 0, df = 1000,
       method = 0, lower.tail = TRUE, log.p = FALSE)

qskewt(p, mu = 0, sigma = 1, skew = 0, df = 1000,
       tol = 1e-8, method = 0)

rskewt(n, mu = 0, sigma = 1, skew = 0, df = 1000)

Arguments

Details

This corresponds to the skew t type 2 distribution in GAMLSS (ST2), see pp. 411-412 of Rigby et al. (2019) and the version implemented in the sn package. This implementation of dskewt allows for automatic differentiation with RTMB while the other functions are imported from the sn package. See sn::dst for more details.

Caution: In a numerial optimisation, the skew parameter should NEVER be initialised with exactly zero. This will cause the initial and all subsequent derivatives to be exactly zero and hence the parameter will remain at its initial value.

Value

dskewt gives the density, pskewt gives the distribution function, qskewt gives the quantile function, and rskewt generates random deviates.

Examples

x <- rskewt(1, 1, 2, 5, 2)
d <- dskewt(x, 1, 2, 5, 2)
p <- pskewt(x, 1, 2, 5, 2)
q <- qskewt(p, 1, 2, 5, 2)

Student t distribution with location and scale

Description

Density, distribution function, quantile function, and random generation for the t distribution with location and scale parameters.

Usage

dt2(x, mu, sigma, df, log = FALSE)

pt2(q, mu, sigma, df)

rt2(n, mu, sigma, df)

qt2(p, mu, sigma, df)

pt(q, df)

Arguments

Details

This implementation of dt2 allows for automatic differentiation with RTMB.

Value

dt2 gives the density, pt2 gives the distribution function, qt2 gives the quantile function, and rt2 generates random deviates.

Examples

x <- rt2(1, 1, 2, 5)
d <- dt2(x, 1, 2, 5)
p <- pt2(x, 1, 2, 5)
q <- qt2(p, 1, 2, 5)

Truncated normal distribution

Description

Density, distribution function, quantile function, and random generation for the truncated normal distribution.

Usage

dtruncnorm(x, mean = 0, sd = 1, min = -Inf, max = Inf, log = FALSE)

ptruncnorm(q, mean = 0, sd = 1, min = -Inf, max = Inf,
           lower.tail = TRUE, log.p = FALSE)

qtruncnorm(p, mean = 0, sd = 1, min = -Inf, max = Inf,
           lower.tail = TRUE, log.p = FALSE)

rtruncnorm(n, mean = 0, sd = 1, min = -Inf, max = Inf)

Arguments

Details

This implementation of dtruncnorm allows for automatic differentiation with RTMB.

Value

dtruncnorm gives the density, ptruncnorm gives the distribution function, qtruncnorm gives the quantile function, and rtruncnorm generates random deviates.

Examples

x <- rtruncnorm(1, mean = 2, sd = 2, min = -1, max = 5)
d <- dtruncnorm(x, mean = 2, sd = 2, min = -1, max = 5)
p <- ptruncnorm(x, mean = 2, sd = 2, min = -1, max = 5)
q <- qtruncnorm(p, mean = 2, sd = 2, min = -1, max = 5)

Truncated t distribution

Description

Density, distribution function, quantile function, and random generation for the truncated t distribution.

Usage

dtrunct(x, df, min = -Inf, max = Inf, log = FALSE)

ptrunct(q, df, min = -Inf, max = Inf, lower.tail = TRUE, log.p = FALSE)

qtrunct(p, df, min = -Inf, max = Inf, lower.tail = TRUE, log.p = FALSE)

rtrunct(n, df, min = -Inf, max = Inf)

Arguments

Details

This implementation of dtrunct allows for automatic differentiation with RTMB.

Value

dtrunct gives the density, ptrunct gives the distribution function, qtrunct gives the quantile function, and rtrunct generates random deviates.

Examples

x <- rtrunct(1, df = 5, min = -1, max = 5)
d <- dtrunct(x, df = 5, min = -1, max = 5)
p <- ptrunct(x, df = 5, min = -1, max = 5)
q <- qtrunct(p, df = 5, min = -1, max = 5)

Truncated t distribution with location and scale

Description

Density, distribution function, quantile function, and random generation for the truncated t distribution with location mu and scale sigma.

Usage

dtrunct2(x, df, mu = 0, sigma = 1, min = -Inf, max = Inf, log = FALSE)

ptrunct2(q, df, mu = 0, sigma = 1, min = -Inf, max = Inf,
         lower.tail = TRUE, log.p = FALSE)

qtrunct2(p, df, mu = 0, sigma = 1, min = -Inf, max = Inf,
         lower.tail = TRUE, log.p = FALSE)

rtrunct2(n, df, mu = 0, sigma = 1, min = -Inf, max = Inf)

Arguments

Details

This implementation of dtrunct2 allows for automatic differentiation with RTMB.

Value

dtrunct2 gives the density, ptrunct2 gives the distribution function, qtrunct2 gives the quantile function, and rtrunct2 generates random deviates.

Examples

x <- rtrunct2(1, df = 5, mu = 2, sigma = 3, min = -1, max = 5)
d <- dtrunct2(x, df = 5, mu = 2, sigma = 3, min = -1, max = 5)
p <- ptrunct2(x, df = 5, mu = 2, sigma = 3, min = -1, max = 5)
q <- qtrunct2(p, df = 5, mu = 2, sigma = 3, min = -1, max = 5)

von Mises distribution

Description

Density, distribution function, and random generation for the von Mises distribution.

Usage

dvm(x, mu = 0, kappa = 1, log = FALSE)

pvm(q, mu = 0, kappa = 1, from = NULL, tol = 1e-20)

rvm(n, mu = 0, kappa = 1, wrap = TRUE)

Arguments

Details

This implementation of dvm allows for automatic differentiation with RTMB. rvm and pvm are simply wrappers of the corresponding functions from circular.

Value

dvm gives the density, pvm gives the distribution function, and rvm generates random deviates.

Examples

set.seed(1)
x <- rvm(10, 0, 1)
d <- dvm(x, 0, 1)
p <- pvm(x, 0, 1)

von Mises-Fisher distribution

Description

Density, distribution function, and random generation for the von Mises-Fisher distribution.

Usage

dvmf(x, mu, kappa, log = FALSE)

rvmf(n, mu, kappa)

Arguments

Details

This implementation of dvmf allows for automatic differentiation with RTMB. rvmf is a reparameterised import from movMF::rmovMF.

Value

dvmf gives the density and rvm generates random deviates.

Examples

set.seed(123)
# single parameter set
mu <- rep(1, 3) / sqrt(3)
kappa <- 4
x <- rvmf(1, mu, kappa)
d <- dvmf(x, mu, kappa)

# vectorised over parameters
mu <- matrix(mu, nrow = 1)
mu <- mu[rep(1,10), ]
kappa <- rep(kappa, 10)
x <- rvmf(10, mu, kappa)
d <- dvmf(x, mu, kappa)

Reparameterised von Mises-Fisher distribution

Description

Density, distribution function, and random generation for the von Mises-Fisher distribution.

Usage

dvmf2(x, theta, log = FALSE)

rvmf2(n, theta)

Arguments

Details

In this parameterisation, \theta = \kappa \mu, where \mu is a unit vector and \kappa is the concentration parameter.

dvmf2 allows for automatic differentiation with RTMB. rvmf2 is imported from movMF::rmovMF.

Value

dvmf gives the density and rvm generates random deviates.

Examples

set.seed(123)
# single parameter set
theta <- c(1,2,3)
x <- rvmf2(1, theta)
d <- dvmf2(x, theta)

# vectorised over parameters
theta <- matrix(theta, nrow = 1)
theta <- theta[rep(1,10), ]
x <- rvmf2(10, theta)
d <- dvmf2(x, theta)

wrapped Cauchy distribution

Description

Density and random generation for the wrapped Cauchy distribution.

Usage

dwrpcauchy(x, mu = 0, rho, log = FALSE)

rwrpcauchy(n, mu = 0, rho, wrap = TRUE)

Arguments

Details

This implementation of dwrpcauchy allows for automatic differentiation with RTMB. rwrpcauchy is simply a wrapper for rwrappedcauchyimported from circular.

Value

dwrpcauchy gives the density and rwrpcauchy generates random deviates.

Examples

set.seed(1)
x <- rwrpcauchy(10, 0, 0.5)
d <- dwrpcauchy(x, 0, 0.5)

Zero-inflated density constructer

Description

Constructs a zero-inflated density function from a given probability density function

Usage

zero_inflate(dist, discrete = NULL)

Arguments

Details

The definition of zero-inflation is different for discrete and continuous distributions. For discrete distributions with p.m.f. f and zero-inflation probability p, we have

\Pr(X = 0) = p + (1 - p) \cdot f(0),

and

\Pr(X = x) = (1 - p) \cdot f(x), \quad x > 0.

For continuous distributions with p.d.f. f, we have

f_{\text{zinfl}}(x) = p \cdot \delta_0(x) + (1 - p) \cdot f(x),

where \delta_0 is the Dirac delta function at zero.

Value

zero-inflated density function with first argument x, second argument zeroprob, and additional arguments ... that will be passed to dist.

Examples

# Zero-inflated normal distribution
dzinorm <- zero_inflate(dnorm)
dzinorm(c(NA, 0, 2), 0.5, mean = 1, sd = 1)

# Zero-inflated Poisson distribution
zipois <- zero_inflate(dpois)
zipois(c(NA, 0, 1), 0.5, 1)

# Non-standard case: Zero-inflated reparametrised beta distribution
dzibeta2 <- zero_inflate(dbeta2, discrete = FALSE)

Zero-inflated beta distribution

Description

Density, distribution function, and random generation for the zero-inflated beta distribution.

Usage

dzibeta(x, shape1, shape2, zeroprob = 0, log = FALSE)

pzibeta(q, shape1, shape2, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzibeta(n, shape1, shape2, zeroprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzibeta gives the density, pzibeta gives the distribution function, and rzibeta generates random deviates.

Examples

set.seed(123)
x <- rzibeta(1, 2, 2, 0.5)
d <- dzibeta(x, 2, 2, 0.5)
p <- pzibeta(x, 2, 2, 0.5)

Reparameterised zero-inflated beta distribution

Description

Density, distribution function, and random generation for the zero-inflated beta distribution reparameterised in terms of mean and concentration.

Usage

dzibeta2(x, mu, phi, zeroprob = 0, log = FALSE)

pzibeta2(q, mu, phi, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzibeta2(n, mu, phi, zeroprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzibeta2 gives the density, pzibeta2 gives the distribution function, and rzibeta2 generates random deviates.

Examples

set.seed(123)
x <- rzibeta2(1, 0.5, 1, 0.5)
d <- dzibeta2(x, 0.5, 1, 0.5)
p <- pzibeta2(x, 0.5, 1, 0.5)

Zero-inflated binomial distribution

Description

Probability mass function, distribution function, and random generation for the zero-inflated binomial distribution.

Usage

dzibinom(x, size, prob, zeroprob = 0, log = FALSE)

pzibinom(q, size, prob, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzibinom(n, size, prob, zeroprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzibinom gives the probability mass function, pzibinom gives the distribution function, and rzibinom generates random deviates.

Examples

set.seed(123)
x <- rzibinom(1, size = 10, prob = 0.5, zeroprob = 0.5)
d <- dzibinom(x, size = 10, prob = 0.5, zeroprob = 0.5)
p <- pzibinom(x, size = 10, prob = 0.5, zeroprob = 0.5)

Zero-inflated gamma distribution

Description

Density, distribution function, and random generation for the zero-inflated gamma distribution.

Usage

dzigamma(x, shape, scale, zeroprob = 0, log = FALSE)

pzigamma(q, shape, scale, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzigamma(n, shape, scale, zeroprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzigamma gives the density, pzigamma gives the distribution function, and rzigamma generates random deviates.

Examples

x <- rzigamma(1, 1, 1, 0.5)
d <- dzigamma(x, 1, 1, 0.5)
p <- pzigamma(x, 1, 1, 0.5)

Zero-inflated and reparameterised gamma distribution

Description

Density, distribution function, and random generation for the zero-inflated gamma distribution reparameterised in terms of mean and standard deviation.

Usage

dzigamma2(x, mean = 1, sd = 1, zeroprob = 0, log = FALSE)

pzigamma2(q, mean = 1, sd = 1, zeroprob = 0)

rzigamma2(n, mean = 1, sd = 1, zeroprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzigamma2 gives the density, pzigamma2 gives the distribution function, and rzigamma generates random deviates.

Examples

x <- rzigamma2(1, 2, 1, 0.5)
d <- dzigamma2(x, 2, 1, 0.5)
p <- pzigamma2(x, 2, 1, 0.5)

Zero-inflated inverse Gaussian distribution

Description

Density, distribution function, and random generation for the zero-inflated inverse Gaussian distribution.

Usage

dziinvgauss(x, mean = 1, shape = 1, zeroprob = 0, log = FALSE)

pziinvgauss(q, mean = 1, shape = 1, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rziinvgauss(n, mean = 1, shape = 1, zeroprob = 0)

Arguments

Details

This implementation of zidinvgauss allows for automatic differentiation with RTMB.

Value

dziinvgauss gives the density, pziinvgauss gives the distribution function, and rziinvgauss generates random deviates.

Examples

x <- rziinvgauss(1, 1, 2, 0.5)
d <- dziinvgauss(x, 1, 2, 0.5)
p <- pziinvgauss(x, 1, 2, 0.5)

Zero-inflated log normal distribution

Description

Density, distribution function, and random generation for the zero-inflated log normal distribution.

Usage

dzilnorm(x, meanlog = 0, sdlog = 1, zeroprob = 0, log = FALSE)

pzilnorm(q, meanlog = 0, sdlog = 1, zeroprob = 0,
         lower.tail = TRUE, log.p = FALSE)

rzilnorm(n, meanlog = 0, sdlog = 1, zeroprob = 0)

plnorm(q, meanlog = 0, sdlog = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzilnorm gives the density, pzilnorm gives the distribution function, and rzilnorm generates random deviates.

Examples

x <- rzilnorm(1, 1, 1, 0.5)
d <- dzilnorm(x, 1, 1, 0.5)
p <- pzilnorm(x, 1, 1, 0.5)

Zero-inflated negative binomial distribution

Description

Probability mass function, distribution function, quantile function, and random generation for the zero-inflated negative binomial distribution.

Usage

dzinbinom(x, size, prob, zeroprob = 0, log = FALSE)

pzinbinom(q, size, prob, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzinbinom(n, size, prob, zeroprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzinbinom gives the density, pzinbinom gives the distribution function, and rzinbinom generates random deviates.

Examples

set.seed(123)
x <- rzinbinom(1, size = 2, prob = 0.5, zeroprob = 0.5)
d <- dzinbinom(x, size = 2, prob = 0.5, zeroprob = 0.5)
p <- pzinbinom(x, size = 2, prob = 0.5, zeroprob = 0.5)

Zero-inflated and reparameterised negative binomial distribution

Description

Probability mass function, distribution function, quantile function and random generation for the zero-inflated negative binomial distribution reparameterised in terms of mean and size.

Usage

dzinbinom2(x, mu, size, zeroprob = 0, log = FALSE)

pzinbinom2(q, mu, size, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzinbinom2(n, mu, size, zeroprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzinbinom2 gives the density, pzinbinom2 gives the distribution function, and rzinbinom2 generates random deviates.

Examples

set.seed(123)
x <- rzinbinom2(1, 2, 1, zeroprob = 0.5)
d <- dzinbinom2(x, 2, 1, zeroprob = 0.5)
p <- pzinbinom2(x, 2, 1, zeroprob = 0.5)

Zero-inflated Poisson distribution

Description

Probability mass function, distribution function, and random generation for the zero-inflated Poisson distribution.

Usage

dzipois(x, lambda, zeroprob = 0, log = FALSE)

pzipois(q, lambda, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzipois(n, lambda, zeroprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzipois gives the probability mass function, pzipois gives the distribution function, and rzipois generates random deviates.

Examples

set.seed(123)
x <- rzipois(1, 0.5, 1)
d <- dzipois(x, 0.5, 1)
p <- pzipois(x, 0.5, 1)

Zero- and one-inflated beta distribution

Description

Density, distribution function, and random generation for the zero-one-inflated beta distribution.

Usage

dzoibeta(x, shape1, shape2, zeroprob = 0, oneprob = 0, log = FALSE)

pzoibeta(q, shape1, shape2, zeroprob = 0, oneprob = 0,
         lower.tail = TRUE, log.p = FALSE)

rzoibeta(n, shape1, shape2, zeroprob = 0, oneprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzoibeta gives the density, pzoibeta gives the distribution function, and rzoibeta generates random deviates.

Examples

set.seed(123)
x <- rzoibeta(1, 2, 2, 0.2, 0.3)
d <- dzoibeta(x, 2, 2, 0.2, 0.3)
p <- pzoibeta(x, 2, 2, 0.2, 0.3)

Reparameterised zero- and one-inflated beta distribution

Description

Density, distribution function, and random generation for the zero-one-inflated beta distribution reparameterised in terms of mean and concentration.

Usage

dzoibeta2(x, mu, phi, zeroprob = 0, oneprob = 0, log = FALSE)

pzoibeta2(q, mu, phi, zeroprob = 0, oneprob = 0,
         lower.tail = TRUE, log.p = FALSE)

rzoibeta2(n, mu, phi, zeroprob = 0, oneprob = 0)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

Value

dzoibeta2 gives the density, pzoibeta2 gives the distribution function, and rzoibeta2 generates random deviates.

Examples

set.seed(123)
x <- rzoibeta2(1, 0.6, 2, 0.2, 0.3)
d <- dzoibeta2(x, 0.6, 2, 0.2, 0.3)
p <- pzoibeta2(x, 0.6, 2, 0.2, 0.3)

Zero-truncated Binomial distribution

Description

Probability mass function, distribution function, and random generation for the zero-truncated Binomial distribution.

Usage

dztbinom(x, size, prob, log = FALSE)

pztbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE)

rztbinom(n, size, prob)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

By definition, this distribution only has support on the positive integers (1, ..., size). Any zero-truncated distribution is defined as

P(X=x | X>0) = P(X=x) / (1 - P(X=0)),

where P(X=x) is the probability mass function of the corresponding untruncated distribution.

Value

dztbinom gives the probability mass function, pztbinom gives the distribution function, and rztbinom generates random deviates.

Examples

set.seed(123)
x <- rztbinom(1, size = 10, prob = 0.3)
d <- dztbinom(x, size = 10, prob = 0.3)
p <- pztbinom(x, size = 10, prob = 0.3)

Zero-truncated Negative Binomial distribution

Description

Probability mass function, distribution function, and random generation for the zero-truncated Negative Binomial distribution.

Usage

dztnbinom(x, size, prob, log = FALSE)

pztnbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE)

rztnbinom(n, size, prob)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

By definition, this distribution only has support on the positive integers (1, 2, ...). Any zero-truncated distribution is defined as

P(X=x | X>0) = P(X=x) / (1 - P(X=0)),

where P(X=x) is the probability mass function of the corresponding untruncated distribution.

Value

dztnbinom gives the probability mass function, pztnbinom gives the distribution function, and rztnbinom generates random deviates.

Examples

set.seed(123)
x <- rztnbinom(1, size = 2, prob = 0.5)
d <- dztnbinom(x, size = 2, prob = 0.5)
p <- pztnbinom(x, size = 2, prob = 0.5)

Reparameterised zero-truncated negative binomial distribution

Description

Probability mass function, distribution function, quantile function, and random generation for the zero-truncated negative binomial distribution reparameterised in terms of mean and size.

Usage

dztnbinom2(x, mu, size, log = FALSE)

pztnbinom2(q, mu, size, lower.tail = TRUE, log.p = FALSE)

rztnbinom2(n, mu, size)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

By definition, this distribution only has support on the positive integers (1, 2, ...). Any zero-truncated distribution is defined as

P(X=x | X>0) = P(X=x) / (1 - P(X=0)),

where P(X=x) is the probability mass function of the corresponding untruncated distribution.

Value

dztnbinom2 gives the probability mass function, pztnbinom2 gives the distribution function, and rztnbinom2 generates random deviates.

Examples

set.seed(123)
x <- rztnbinom2(1, mu = 2, size = 1)
d <- dztnbinom2(x, mu = 2, size = 1)
p <- pztnbinom2(x, mu = 2, size = 1)

Zero-truncated Poisson distribution

Description

Probability mass function, distribution function, and random generation for the zero-truncated Poisson distribution.

Usage

dztpois(x, lambda, log = FALSE)

pztpois(q, lambda, lower.tail = TRUE, log.p = FALSE)

rztpois(n, lambda)

Arguments

Details

This implementation allows for automatic differentiation with RTMB.

By definition, this distribution only has support on the positive integers (1, 2, ...). Any zero-truncated distribution is defined as

P(X=x | X>0) = P(X=x) / (1 - P(X=0)),

where P(X=x) is the probability mass function of the corresponding untruncated distribution.

Value

dztpois gives the probability mass function, pztpois gives the distribution function, and rztpois generates random deviates.

Examples

set.seed(123)
x <- rztpois(1, 0.5)
d <- dztpois(x, 0.5)
p <- pztpois(x, 0.5)