dnbinom(x, size, prob) pnbinom(q, size, prob) qnbinom(p, size, prob) rnbinom(n, size, prob)
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. |
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, ...dbinom
for the binomial, dpois
for the
Poisson and dgeom
for the geometric distribution, which
is a special case of the negative binomial.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))