Distributions {RTMB}

Distributions and special functions for which AD is implemented

Description

The functions listed in this help page are all applicable for AD types. Method dispatching follows a simple rule: If at least one argument is an AD type then a special AD implementation is selected. In all other cases a default implementation is used (typically that of the stats package). Argument recycling follows the R standard (although wihout any warnings).

Usage

## S4 method for signature 'ad,ad.,logical.'
dexp(x, rate = 1, log = FALSE)

## S4 method for signature 'num,num.,logical.'
dexp(x, rate = 1, log = FALSE)

## S4 method for signature 'osa,ANY,ANY'
dexp(x, rate = 1, log = FALSE)

## S4 method for signature 'simref,ANY,ANY'
dexp(x, rate = 1, log = FALSE)

## S4 method for signature 'ad,ad,ad.,logical.'
dweibull(x, shape, scale = 1, log = FALSE)

## S4 method for signature 'num,num,num.,logical.'
dweibull(x, shape, scale = 1, log = FALSE)

## S4 method for signature 'osa,ANY,ANY,ANY'
dweibull(x, shape, scale = 1, log = FALSE)

## S4 method for signature 'simref,ANY,ANY,ANY'
dweibull(x, shape, scale = 1, log = FALSE)

## S4 method for signature 'ad,ad,ad,logical.'
dbinom(x, size, prob, log = FALSE)

## S4 method for signature 'num,num,num,logical.'
dbinom(x, size, prob, log = FALSE)

## S4 method for signature 'osa,ANY,ANY,ANY'
dbinom(x, size, prob, log = FALSE)

## S4 method for signature 'simref,ANY,ANY,ANY'
dbinom(x, size, prob, log = FALSE)

## S4 method for signature 'ad,ad,ad,missing,logical.'
dbeta(x, shape1, shape2, log)

## S4 method for signature 'num,num,num,missing,logical.'
dbeta(x, shape1, shape2, log)

## S4 method for signature 'osa,ANY,ANY,ANY,ANY'
dbeta(x, shape1, shape2, log)

## S4 method for signature 'simref,ANY,ANY,ANY,ANY'
dbeta(x, shape1, shape2, log)

## S4 method for signature 'ad,ad,ad,missing,logical.'
df(x, df1, df2, log)

## S4 method for signature 'num,num,num,missing,logical.'
df(x, df1, df2, log)

## S4 method for signature 'osa,ANY,ANY,ANY,ANY'
df(x, df1, df2, log)

## S4 method for signature 'simref,ANY,ANY,ANY,ANY'
df(x, df1, df2, log)

## S4 method for signature 'ad,ad.,ad.,logical.'
dlogis(x, location = 0, scale = 1, log = FALSE)

## S4 method for signature 'num,num.,num.,logical.'
dlogis(x, location = 0, scale = 1, log = FALSE)

## S4 method for signature 'osa,ANY,ANY,ANY'
dlogis(x, location = 0, scale = 1, log = FALSE)

## S4 method for signature 'simref,ANY,ANY,ANY'
dlogis(x, location = 0, scale = 1, log = FALSE)

## S4 method for signature 'ad,ad,missing,logical.'
dt(x, df, log)

## S4 method for signature 'num,num,missing,logical.'
dt(x, df, log)

## S4 method for signature 'osa,ANY,ANY,ANY'
dt(x, df, log)

## S4 method for signature 'simref,ANY,ANY,ANY'
dt(x, df, log)

## S4 method for signature 'ad,ad,ad,missing,logical.'
dnbinom(x, size, prob, log)

## S4 method for signature 'num,num,num,missing,logical.'
dnbinom(x, size, prob, log)

## S4 method for signature 'osa,ANY,ANY,ANY,ANY'
dnbinom(x, size, prob, log)

## S4 method for signature 'simref,ANY,ANY,ANY,ANY'
dnbinom(x, size, prob, log)

## S4 method for signature 'ad,ad,logical.'
dpois(x, lambda, log = FALSE)

## S4 method for signature 'num,num,logical.'
dpois(x, lambda, log = FALSE)

## S4 method for signature 'osa,ANY,ANY'
dpois(x, lambda, log = FALSE)

## S4 method for signature 'simref,ANY,ANY'
dpois(x, lambda, log = FALSE)

## S4 method for signature 'ad,ad,missing,ad.,logical.'
dgamma(x, shape, scale, log)

## S4 method for signature 'num,num,missing,num.,logical.'
dgamma(x, shape, scale, log)

## S4 method for signature 'osa,ANY,ANY,ANY,ANY'
dgamma(x, shape, scale, log)

## S4 method for signature 'simref,ANY,ANY,ANY,ANY'
dgamma(x, shape, scale, log)

## S4 method for signature 'ad,ad.,ad.,missing,missing'
pnorm(q, mean, sd)

## S4 method for signature 'num,num.,num.,missing,missing'
pnorm(q, mean, sd)

## S4 method for signature 'ad,ad,missing,ad.,missing,missing'
pgamma(q, shape, scale)

## S4 method for signature 'num,num,missing,num.,missing,missing'
pgamma(q, shape, scale)

## S4 method for signature 'ad,ad,missing,missing'
ppois(q, lambda)

## S4 method for signature 'num,num,missing,missing'
ppois(q, lambda)

## S4 method for signature 'ad,ad.,missing,missing'
pexp(q, rate)

## S4 method for signature 'num,num.,missing,missing'
pexp(q, rate)

## S4 method for signature 'ad,ad,ad.,missing,missing'
pweibull(q, shape, scale)

## S4 method for signature 'num,num,num.,missing,missing'
pweibull(q, shape, scale)

## S4 method for signature 'ad,ad,ad,missing,missing,missing'
pbeta(q, shape1, shape2)

## S4 method for signature 'num,num,num,missing,missing,missing'
pbeta(q, shape1, shape2)

## S4 method for signature 'ad,ad.,ad.,missing,missing'
qnorm(p, mean, sd)

## S4 method for signature 'num,num.,num.,missing,missing'
qnorm(p, mean, sd)

## S4 method for signature 'ad,ad,missing,ad.,missing,missing'
qgamma(p, shape, scale)

## S4 method for signature 'num,num,missing,num.,missing,missing'
qgamma(p, shape, scale)

## S4 method for signature 'ad,ad.,missing,missing'
qexp(p, rate)

## S4 method for signature 'num,num.,missing,missing'
qexp(p, rate)

## S4 method for signature 'ad,ad,ad.,missing,missing'
qweibull(p, shape, scale)

## S4 method for signature 'num,num,num.,missing,missing'
qweibull(p, shape, scale)

## S4 method for signature 'ad,ad,ad,missing,missing,missing'
qbeta(p, shape1, shape2)

## S4 method for signature 'num,num,num,missing,missing,missing'
qbeta(p, shape1, shape2)

## S4 method for signature 'ad,ad,missing'
besselK(x, nu)

## S4 method for signature 'num,num,missing'
besselK(x, nu)

## S4 method for signature 'ad,ad,missing'
besselI(x, nu)

## S4 method for signature 'num,num,missing'
besselI(x, nu)

## S4 method for signature 'ad,ad'
besselJ(x, nu)

## S4 method for signature 'num,num'
besselJ(x, nu)

## S4 method for signature 'ad,ad'
besselY(x, nu)

## S4 method for signature 'num,num'
besselY(x, nu)

dbinom_robust(x, size, logit_p, log)

dsn(x, alpha, log)

dSHASHo(x, mu, sigma, nu, tau, log)

dtweedie(x, mu, phi, p, log)

dnbinom2(x, mu, var, log)

dnbinom_robust(x, log_mu, log_var_minus_mu, log)

dlgamma(x, shape, scale, log)

## S4 method for signature 'ad,ad.,ad.,logical.'
dnorm(x, mean = 0, sd = 1, log = FALSE)

## S4 method for signature 'num,num.,num.,logical.'
dnorm(x, mean = 0, sd = 1, log = FALSE)

## S4 method for signature 'osa,ANY,ANY,ANY'
dnorm(x, mean = 0, sd = 1, log = FALSE)

## S4 method for signature 'simref,ANY,ANY,ANY'
dnorm(x, mean = 0, sd = 1, log = FALSE)

## S4 method for signature 'ANY,ANY,ANY,ANY'
dlnorm(x, meanlog = 0, sdlog = 1, log = FALSE)

## S4 method for signature 'osa,ANY,ANY,ANY'
dlnorm(x, meanlog = 0, sdlog = 1, log = FALSE)

## S4 method for signature 'num,num.,num.,logical.'
dlnorm(x, meanlog = 0, sdlog = 1, log = FALSE)

## S4 method for signature 'advector,missing,missing,missing,missing'
plogis(q)

## S4 method for signature 'advector,missing,missing,missing,missing'
qlogis(p)

dcompois(x, mode, nu, log = FALSE)

dcompois2(x, mean, nu, log = FALSE)

## S4 method for signature 'ad,ad,ad,missing,missing'
pbinom(q, size, prob)

## S4 method for signature 'num,num,num,missing,missing'
pbinom(q, size, prob)

## S4 method for signature 'ad,ad.,ad,logical.'
dmultinom(x, size = NULL, prob, log = FALSE)

## S4 method for signature 'num,num.,num,logical.'
dmultinom(x, size = NULL, prob, log = FALSE)

## S4 method for signature 'osa,ANY,ANY,ANY'
dmultinom(x, size = NULL, prob, log = FALSE)

## S4 method for signature 'simref,ANY,ANY,ANY'
dmultinom(x, size = NULL, prob, log = FALSE)

## S4 method for signature 'ANY,ANY,ANY,ANY'
dmultinom(x, size = NULL, prob, log = FALSE)

Arguments

x

observation vector

rate

parameter

log

Logical; Return log density/probability?

shape

parameter

scale

parameter

size

parameter

prob

parameter

shape1

parameter

shape2

parameter

df1

parameter

df2

parameter

location

parameter

df

parameter

lambda

parameter

q

vector of quantiles

mean

parameter

sd

parameter

p

parameter

nu

parameter

logit_p

parameter

alpha

parameter

mu

parameter

sigma

parameter

tau

parameter

phi

parameter

var

parameter

log_mu

parameter

log_var_minus_mu

parameter

meanlog

Parameter; Mean on log scale.

sdlog

Parameter; SD on log scale.

mode

parameter

Details

Specific documentation of the functions and arguments should be looked up elsewhere:

• All S4 methods behave as the corresponding functions in the stats package. However, some arguements may not be implemented in the AD case (e.g. lower-tail).

• Other funtions behave as the corresponding TMB versions for which documentation should be looked up online.

Value

In autodiff contexts an object of class "advector" is returned; Otherwise a standard numeric vector.

Functions

• dexp(x = ad, rate = ad., log = logical.): AD implementation of dexp

• dexp(x = num, rate = num., log = logical.): Default method

• dexp(x = osa, rate = ANY, log = ANY): OSA implementation

• dexp(x = simref, rate = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• dweibull(x = ad, shape = ad, scale = ad., log = logical.): AD implementation of dweibull

• dweibull(x = num, shape = num, scale = num., log = logical.): Default method

• dweibull(x = osa, shape = ANY, scale = ANY, log = ANY): OSA implementation

• dweibull(x = simref, shape = ANY, scale = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• dbinom(x = ad, size = ad, prob = ad, log = logical.): AD implementation of dbinom

• dbinom(x = num, size = num, prob = num, log = logical.): Default method

• dbinom(x = osa, size = ANY, prob = ANY, log = ANY): OSA implementation

• dbinom(x = simref, size = ANY, prob = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• dbeta(x = ad, shape1 = ad, shape2 = ad, ncp = missing, log = logical.): AD implementation of dbeta

• dbeta(x = num, shape1 = num, shape2 = num, ncp = missing, log = logical.): Default method

• dbeta(x = osa, shape1 = ANY, shape2 = ANY, ncp = ANY, log = ANY): OSA implementation

• dbeta(x = simref, shape1 = ANY, shape2 = ANY, ncp = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• df(x = ad, df1 = ad, df2 = ad, ncp = missing, log = logical.): AD implementation of df

• df(x = num, df1 = num, df2 = num, ncp = missing, log = logical.): Default method

• df(x = osa, df1 = ANY, df2 = ANY, ncp = ANY, log = ANY): OSA implementation

• df(x = simref, df1 = ANY, df2 = ANY, ncp = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• dlogis(x = ad, location = ad., scale = ad., log = logical.): AD implementation of dlogis

• dlogis(x = num, location = num., scale = num., log = logical.): Default method

• dlogis(x = osa, location = ANY, scale = ANY, log = ANY): OSA implementation

• dlogis(x = simref, location = ANY, scale = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• dt(x = ad, df = ad, ncp = missing, log = logical.): AD implementation of dt

• dt(x = num, df = num, ncp = missing, log = logical.): Default method

• dt(x = osa, df = ANY, ncp = ANY, log = ANY): OSA implementation

• dt(x = simref, df = ANY, ncp = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• dnbinom(x = ad, size = ad, prob = ad, mu = missing, log = logical.): AD implementation of dnbinom

• dnbinom(x = num, size = num, prob = num, mu = missing, log = logical.): Default method

• dnbinom(x = osa, size = ANY, prob = ANY, mu = ANY, log = ANY): OSA implementation

• dnbinom(x = simref, size = ANY, prob = ANY, mu = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• dpois(x = ad, lambda = ad, log = logical.): AD implementation of dpois

• dpois(x = num, lambda = num, log = logical.): Default method

• dpois(x = osa, lambda = ANY, log = ANY): OSA implementation

• dpois(x = simref, lambda = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• dgamma(x = ad, shape = ad, rate = missing, scale = ad., log = logical.): AD implementation of dgamma

• dgamma(x = num, shape = num, rate = missing, scale = num., log = logical.): Default method

• dgamma(x = osa, shape = ANY, rate = ANY, scale = ANY, log = ANY): OSA implementation

• dgamma(x = simref, shape = ANY, rate = ANY, scale = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• pnorm(q = ad, mean = ad., sd = ad., lower.tail = missing, log.p = missing): AD implementation of pnorm

• pnorm(q = num, mean = num., sd = num., lower.tail = missing, log.p = missing): Default method

• pgamma( q = ad, shape = ad, rate = missing, scale = ad., lower.tail = missing, log.p = missing ): AD implementation of pgamma

• pgamma( q = num, shape = num, rate = missing, scale = num., lower.tail = missing, log.p = missing ): Default method

• ppois(q = ad, lambda = ad, lower.tail = missing, log.p = missing): AD implementation of ppois

• ppois(q = num, lambda = num, lower.tail = missing, log.p = missing): Default method

• pexp(q = ad, rate = ad., lower.tail = missing, log.p = missing): AD implementation of pexp

• pexp(q = num, rate = num., lower.tail = missing, log.p = missing): Default method

• pweibull( q = ad, shape = ad, scale = ad., lower.tail = missing, log.p = missing ): AD implementation of pweibull

• pweibull( q = num, shape = num, scale = num., lower.tail = missing, log.p = missing ): Default method

• pbeta( q = ad, shape1 = ad, shape2 = ad, ncp = missing, lower.tail = missing, log.p = missing ): AD implementation of pbeta

• pbeta( q = num, shape1 = num, shape2 = num, ncp = missing, lower.tail = missing, log.p = missing ): Default method

• qnorm(p = ad, mean = ad., sd = ad., lower.tail = missing, log.p = missing): AD implementation of qnorm

• qnorm(p = num, mean = num., sd = num., lower.tail = missing, log.p = missing): Default method

• qgamma( p = ad, shape = ad, rate = missing, scale = ad., lower.tail = missing, log.p = missing ): AD implementation of qgamma

• qgamma( p = num, shape = num, rate = missing, scale = num., lower.tail = missing, log.p = missing ): Default method

• qexp(p = ad, rate = ad., lower.tail = missing, log.p = missing): AD implementation of qexp

• qexp(p = num, rate = num., lower.tail = missing, log.p = missing): Default method

• qweibull( p = ad, shape = ad, scale = ad., lower.tail = missing, log.p = missing ): AD implementation of qweibull

• qweibull( p = num, shape = num, scale = num., lower.tail = missing, log.p = missing ): Default method

• qbeta( p = ad, shape1 = ad, shape2 = ad, ncp = missing, lower.tail = missing, log.p = missing ): AD implementation of qbeta

• qbeta( p = num, shape1 = num, shape2 = num, ncp = missing, lower.tail = missing, log.p = missing ): Default method

• besselK(x = ad, nu = ad, expon.scaled = missing): AD implementation of besselK

• besselK(x = num, nu = num, expon.scaled = missing): Default method

• besselI(x = ad, nu = ad, expon.scaled = missing): AD implementation of besselI

• besselI(x = num, nu = num, expon.scaled = missing): Default method

• besselJ(x = ad, nu = ad): AD implementation of besselJ

• besselJ(x = num, nu = num): Default method

• besselY(x = ad, nu = ad): AD implementation of besselY

• besselY(x = num, nu = num): Default method

• dbinom_robust(): AD implementation

• dsn(): AD implementation

• dSHASHo(): AD implementation

• dtweedie(): AD implementation

• dnbinom2(): AD implementation

• dnbinom_robust(): AD implementation

• dlgamma(): AD implementation

• dnorm(x = ad, mean = ad., sd = ad., log = logical.): AD implementation of dnorm

• dnorm(x = num, mean = num., sd = num., log = logical.): Default method

• dnorm(x = osa, mean = ANY, sd = ANY, log = ANY): OSA implementation

• dnorm(x = simref, mean = ANY, sd = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• dlnorm(x = ANY, meanlog = ANY, sdlog = ANY, log = ANY): AD implementation of dlnorm.

• dlnorm(x = osa, meanlog = ANY, sdlog = ANY, log = ANY): OSA implementation.

• dlnorm(x = num, meanlog = num., sdlog = num., log = logical.): Default method.

• plogis( q = advector, location = missing, scale = missing, lower.tail = missing, log.p = missing ): Minimal AD implementation of plogis

• qlogis( p = advector, location = missing, scale = missing, lower.tail = missing, log.p = missing ): Minimal AD implementation of qlogis

• dcompois(): Conway-Maxwell-Poisson. Calculate density.

• dcompois2(): Conway-Maxwell-Poisson. Calculate density parameterized via the mean.

• pbinom(q = ad, size = ad, prob = ad, lower.tail = missing, log.p = missing): AD implementation of pbinom

• pbinom(q = num, size = num, prob = num, lower.tail = missing, log.p = missing): Default method

• dmultinom(x = ad, size = ad., prob = ad, log = logical.): AD implementation of dmultinom

• dmultinom(x = num, size = num., prob = num, log = logical.): Default method

• dmultinom(x = osa, size = ANY, prob = ANY, log = ANY): OSA implementation

• dmultinom(x = simref, size = ANY, prob = ANY, log = ANY): Simulation implementation. Modifies x and returns zero.

• dmultinom(x = ANY, size = ANY, prob = ANY, log = ANY): Default implementation that checks for invalid usage.

Examples

MakeTape( function(x) pnorm(x), x=numeric(5))$jacobian(1:5)