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The Negative Binomial Distribution

Syntax

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

Description

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

The negative binomial distribution has density

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

((Equations will(?) come with HTML 3.x ))
for x = 0, 1, 2, ...

See Also

dbinom for the binomial and dpoisson for the Poisson distribution.

Examples

x <- 0:11 dnbinom(x, n = 1, p = 1/2) * 2^(1 + x) # == 1 126 / dnbinom(0:8, n = 2, p = 1/2) #- theoretically integer ## Cumulative ('p') = Sum of discrete prob.s ('d'); Relative error summary(1 - cumsum(dnbinom(x, n=2, p= 1/2)) / pnbinom(x, n=2, p= 1/2))