Distributions: 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 ad,ad.,logical.
dexp(x, rate = 1, log = FALSE)
# S4 method for num,num.,logical.
dexp(x, rate = 1, log = FALSE)
# S4 method for osa,ANY,ANY
dexp(x, rate = 1, log = FALSE)
# S4 method for simref,ANY,ANY
dexp(x, rate = 1, log = FALSE)
# S4 method for ad,ad,ad.,logical.
dweibull(x, shape, scale = 1, log = FALSE)
# S4 method for num,num,num.,logical.
dweibull(x, shape, scale = 1, log = FALSE)
# S4 method for osa,ANY,ANY,ANY
dweibull(x, shape, scale = 1, log = FALSE)
# S4 method for simref,ANY,ANY,ANY
dweibull(x, shape, scale = 1, log = FALSE)
# S4 method for ad,ad,ad,logical.
dbinom(x, size, prob, log = FALSE)
# S4 method for num,num,num,logical.
dbinom(x, size, prob, log = FALSE)
# S4 method for osa,ANY,ANY,ANY
dbinom(x, size, prob, log = FALSE)
# S4 method for simref,ANY,ANY,ANY
dbinom(x, size, prob, log = FALSE)
# S4 method for ad,ad,ad,missing,logical.
dbeta(x, shape1, shape2, log)
# S4 method for num,num,num,missing,logical.
dbeta(x, shape1, shape2, log)
# S4 method for osa,ANY,ANY,ANY,ANY
dbeta(x, shape1, shape2, log)
# S4 method for simref,ANY,ANY,ANY,ANY
dbeta(x, shape1, shape2, log)
# S4 method for ad,ad,ad,missing,logical.
df(x, df1, df2, log)
# S4 method for num,num,num,missing,logical.
df(x, df1, df2, log)
# S4 method for osa,ANY,ANY,ANY,ANY
df(x, df1, df2, log)
# S4 method for simref,ANY,ANY,ANY,ANY
df(x, df1, df2, log)
# S4 method for ad,ad.,ad.,logical.
dlogis(x, location = 0, scale = 1, log = FALSE)
# S4 method for num,num.,num.,logical.
dlogis(x, location = 0, scale = 1, log = FALSE)
# S4 method for osa,ANY,ANY,ANY
dlogis(x, location = 0, scale = 1, log = FALSE)
# S4 method for simref,ANY,ANY,ANY
dlogis(x, location = 0, scale = 1, log = FALSE)
# S4 method for ad,ad,missing,logical.
dt(x, df, log)
# S4 method for num,num,missing,logical.
dt(x, df, log)
# S4 method for osa,ANY,ANY,ANY
dt(x, df, log)
# S4 method for simref,ANY,ANY,ANY
dt(x, df, log)
# S4 method for ad,ad,ad,missing,logical.
dnbinom(x, size, prob, log)
# S4 method for num,num,num,missing,logical.
dnbinom(x, size, prob, log)
# S4 method for osa,ANY,ANY,ANY,ANY
dnbinom(x, size, prob, log)
# S4 method for simref,ANY,ANY,ANY,ANY
dnbinom(x, size, prob, log)
# S4 method for ad,ad,logical.
dpois(x, lambda, log = FALSE)
# S4 method for num,num,logical.
dpois(x, lambda, log = FALSE)
# S4 method for osa,ANY,ANY
dpois(x, lambda, log = FALSE)
# S4 method for simref,ANY,ANY
dpois(x, lambda, log = FALSE)
# S4 method for ad,ad,missing,ad.,logical.
dgamma(x, shape, scale, log)
# S4 method for num,num,missing,num.,logical.
dgamma(x, shape, scale, log)
# S4 method for osa,ANY,ANY,ANY,ANY
dgamma(x, shape, scale, log)
# S4 method for simref,ANY,ANY,ANY,ANY
dgamma(x, shape, scale, log)
# S4 method for ad,ad.,ad.,missing,missing
pnorm(q, mean, sd)
# S4 method for num,num.,num.,missing,missing
pnorm(q, mean, sd)
# S4 method for ad,ad,missing,ad.,missing,missing
pgamma(q, shape, scale)
# S4 method for num,num,missing,num.,missing,missing
pgamma(q, shape, scale)
# S4 method for ad,ad,missing,missing
ppois(q, lambda)
# S4 method for num,num,missing,missing
ppois(q, lambda)
# S4 method for ad,ad.,missing,missing
pexp(q, rate)
# S4 method for num,num.,missing,missing
pexp(q, rate)
# S4 method for ad,ad,ad.,missing,missing
pweibull(q, shape, scale)
# S4 method for num,num,num.,missing,missing
pweibull(q, shape, scale)
# S4 method for ad,ad,ad,missing,missing,missing
pbeta(q, shape1, shape2)
# S4 method for num,num,num,missing,missing,missing
pbeta(q, shape1, shape2)
# S4 method for ad,ad.,ad.,missing,missing
qnorm(p, mean, sd)
# S4 method for num,num.,num.,missing,missing
qnorm(p, mean, sd)
# S4 method for ad,ad,missing,ad.,missing,missing
qgamma(p, shape, scale)
# S4 method for num,num,missing,num.,missing,missing
qgamma(p, shape, scale)
# S4 method for ad,ad.,missing,missing
qexp(p, rate)
# S4 method for num,num.,missing,missing
qexp(p, rate)
# S4 method for ad,ad,ad.,missing,missing
qweibull(p, shape, scale)
# S4 method for num,num,num.,missing,missing
qweibull(p, shape, scale)
# S4 method for ad,ad,ad,missing,missing,missing
qbeta(p, shape1, shape2)
# S4 method for num,num,num,missing,missing,missing
qbeta(p, shape1, shape2)
# S4 method for ad,ad,missing
besselK(x, nu)
# S4 method for num,num,missing
besselK(x, nu)
# S4 method for ad,ad,missing
besselI(x, nu)
# S4 method for num,num,missing
besselI(x, nu)
# S4 method for ad,ad
besselJ(x, nu)
# S4 method for num,num
besselJ(x, nu)
# S4 method for ad,ad
besselY(x, nu)
# S4 method for 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 ad,ad.,ad.,logical.
dnorm(x, mean = 0, sd = 1, log = FALSE)
# S4 method for num,num.,num.,logical.
dnorm(x, mean = 0, sd = 1, log = FALSE)
# S4 method for osa,ANY,ANY,ANY
dnorm(x, mean = 0, sd = 1, log = FALSE)
# S4 method for simref,ANY,ANY,ANY
dnorm(x, mean = 0, sd = 1, log = FALSE)
# S4 method for ANY,ANY,ANY,ANY
dlnorm(x, meanlog = 0, sdlog = 1, log = FALSE)
# S4 method for osa,ANY,ANY,ANY
dlnorm(x, meanlog = 0, sdlog = 1, log = FALSE)
# S4 method for num,num.,num.,logical.
dlnorm(x, meanlog = 0, sdlog = 1, log = FALSE)
# S4 method for advector,missing,missing,missing,missing
plogis(q)
# S4 method for advector,missing,missing,missing,missing
qlogis(p)
dcompois(x, mode, nu, log = FALSE)
dcompois2(x, mean, nu, log = FALSE)
# S4 method for ad,ad,ad,missing,missing
pbinom(q, size, prob)
# S4 method for num,num,num,missing,missing
pbinom(q, size, prob)
# S4 method for ad,ad.,ad,logical.
dmultinom(x, size = NULL, prob, log = FALSE)
# S4 method for num,num.,num,logical.
dmultinom(x, size = NULL, prob, log = FALSE)
# S4 method for osa,ANY,ANY,ANY
dmultinom(x, size = NULL, prob, log = FALSE)
# S4 method for simref,ANY,ANY,ANY
dmultinom(x, size = NULL, prob, log = FALSE)
# S4 method for ANY,ANY,ANY,ANY
dmultinom(x, size = NULL, prob, log = FALSE)

Value

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

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

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.

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.

Examples

Run this code

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

Run the code above in your browser using DataLab