The Negative Binomial Distribution

Usage

dnbinom(x, size, prob)
pnbinom(q, size, prob)
qnbinom(p, size, prob)
rnbinom(n, size, prob)

Arguments

x,q vector of quantiles representing the number of failures which occur in a sequence of Bernoulli trials before a target number of successes is reached.
p vector of probabilities.
n number of observations to generate.
size target for number of successful trials.
prob probability of success in each trial.

Description

These functions provide information about the negative binomial distribution with parameters size and prob. dnbinom gives the density, pnbinom gives the distribution function, qnbinom gives the quantile function and rnbinom generates random deviates.

The negative binomial distribution with size = n and prob = p has density

p(x) = Choose(x+n-1,x) p^n (1-p)^x

for x = 0, 1, 2, ...

See Also

dbinom for the binomial, dpois for the Poisson and dgeom for the geometric distribution, which is a special case of the negative binomial.

Examples

x <- 0:11
dnbinom(x, size = 1, prob = 1/2) * 2^(1 + x) # == 1
126 /  dnbinom(0:8, size  = 2, prob  = 1/2) #- theoretically integer

## Cumulative ('p') = Sum of discrete prob.s ('d');  Relative error :
summary(1 - cumsum(dnbinom(x, size = 2, prob = 1/2)) /
	          pnbinom(x, size  = 2, prob = 1/2))


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