hnbinom {countreg} | R Documentation |
Density, distribution function, quantile function, random
generation, score function, hessian, mean, and, variance
for the (zero-)hurdle negative binomial
distribution with parameters mu
(= mean of the
underlying negative binomial distribution), dispersion parameter theta
(or equivalently size
), and hurdle crossing probability
pi
(i.e., 1 - pi
is the probability for observed zeros).
dhnbinom(x, mu, theta, size, pi, log = FALSE) phnbinom(q, mu, theta, size, pi, lower.tail = TRUE, log.p = FALSE) qhnbinom(p, mu, theta, size, pi, lower.tail = TRUE, log.p = FALSE) rhnbinom(n, mu, theta, size, pi) shnbinom(x, mu, theta, size, pi, parameter = c("mu", "theta", "pi"), drop = TRUE) hhnbinom(x, mu, theta, size, pi, parameter = c("mu", "theta", "pi"), drop = TRUE) mean_hnbinom(mu, theta, size, pi, drop = TRUE) var_hnbinom(mu, theta, size, pi, drop = TRUE)
x |
vector of (positive integer) quantiles. |
q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of random values to return. |
mu |
vector of non-negative means of the underlying negative binomial distribution. |
theta, size |
vector of strictly positive dispersion
parameters (shape parameter of the gamma mixing distribution).
Only one of |
pi |
vector of hurdle crossing probabilities (i.e., |
log, log.p |
logical. If |
lower.tail |
logical. If |
parameter |
character. Should the derivative with respect to
|
drop |
logical. Should the result be a matrix ( |
The underlying negative binomial distribution has density
Γ(x + θ)/(Γ(θ) x!) (μ^y θ^θ)/((μ + θ)^(y + θ)
for x = 0, 1, 2, …. The hurdle density is then simply obtained as
g(x) = π f(x)/(1 - f(0))
for x = 1, 2, … and g(0) = 1 - π, respectively.
dhnbinom
gives the (log) density,
phnbinom
gives the (log) distribution function,
qhnbinom
gives the quantile function,
rhnbinom
generates random deviates, and
shnbinom
gives the score function (= derivative of
the log-density with respect to mu and/or theta and/or pi).
hhnbinom
gives the hessian (= 2nd derivative of
the log-density with respect to mu and/or theta and/or pi).
mean_hnbinom
and var_hnbinom
give the mean
and the variance, respectively.