dhnbinom {distributions3} R Documentation

## The hurdle negative binomial distribution

### Description

Density, distribution function, quantile function, and random generation for the zero-hurdle negative binomial distribution with parameters mu, theta (or size), and pi.

### Usage

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)

### Arguments

 x vector of (non-negative integer) quantiles. mu vector of (non-negative) negative binomial location parameters. theta, size vector of (non-negative) negative binomial overdispersion parameters. Only theta or, equivalently, size may be specified. pi vector of zero-hurdle probabilities in the unit interval. log, log.p logical indicating whether probabilities p are given as log(p). q vector of quantiles. lower.tail logical indicating whether probabilities are P[X \le x] (lower tail) or P[X > x] (upper tail). p vector of probabilities. n number of random values to return.

### Details

All functions follow the usual conventions of d/p/q/r functions in base R. In particular, all four hnbinom functions for the hurdle negative binomial distribution call the corresponding nbinom functions for the negative binomial distribution from base R internally.

Note, however, that the precision of qhnbinom for very large probabilities (close to 1) is limited because the probabilities are internally handled in levels and not in logs (even if log.p = TRUE).

### Examples

## theoretical probabilities for a hurdle negative binomial distribution
x <- 0:8
p <- dhnbinom(x, mu = 2.5, theta = 1, pi = 0.75)
plot(x, p, type = "h", lwd = 2)

## corresponding empirical frequencies from a simulated sample
set.seed(0)
y <- rhnbinom(500, mu = 2.5, theta = 1, pi = 0.75)
hist(y, breaks = -1:max(y) + 0.5)

[Package distributions3 version 0.2.1 Index]