| NegBinomial {base} | R Documentation |
The Negative Binomial Distribution
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.
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, or alternately the probability distribution
of a compound Poisson process whose intensity is distributed
as a gamma ( |
x |
vector of (non-negative integer) quantiles. |
q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations to generate. |
size |
target for number of successful trials / |
prob |
probability of success in each trial / |
Details
The negative binomial distribution with size = n and
prob = p has density
p(x) = \frac{\Gamma(x+n)}{\Gamma(n) x!} p^n (1-p)^x
for x = 0, 1, 2, \ldots
If an element of x is not integer, the result of dnbinom
is zero, with a warning.
The quantile is left continuous: qnbinom(q, ...) is the
largest integer x such that P(X <= x) < q.
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))
x <- 0:15
size <- (1:20)/4
persp(x,size, dnb <- outer(x,size,function(x,s)dnbinom(x,s, pr= 0.4)))
title(tit <- "negative binomial density(x,s, pr = 0.4) vs. x & s")
## if persp() only could label axes ....
image (x,size, log10(dnb), main= paste("log [",tit,"]"))
contour(x,size, log10(dnb),add=TRUE)