NegBinomial {base} | R Documentation |
Density, distribution function, quantile function and random
generation for the negative binomial distribution with parameters
size
and prob
.
dnbinom(x, size, prob, log = FALSE) pnbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE) qnbinom(p, size, prob, lower.tail = TRUE, log.p = FALSE) 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, or alternately the probability distribution
of a compound Poisson process whose intensity is distributed as a
gamma (pgamma ) distribution with scale parameter
(1-prob)/prob and shape parameter size (this
definition allows non-integer values of size ). |
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, or shape parameter of gamma distribution. |
prob |
probability of success in each trial, or scale of gamma
distribution (prob = scale/(1+scale) ). |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]. |
The negative binomial distribution with size
= n and
prob
= p has density
p(x) = Gamma(x+n)/(Gamma(n) x!) p^n (1-p)^x
for x = 0, 1, 2, ...
If an element of x
is not integer, the result of dnbinom
is zero, with a warning.
The quantile is defined as the smallest value x such that F(x) >= p, where F is the distribution function.
dnbinom
gives the density,
pnbinom
gives the distribution function,
qnbinom
gives the quantile function, and
rnbinom
generates random deviates.
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)) x <- 0:15 size <- (1:20)/4 persp(x,size, dnb <- outer(x,size,function(x,s)dnbinom(x,s, pr= 0.4)), xlab = "x", ylab = "s", zlab="density", theta = 150) title(tit <- "negative binomial density(x,s, pr = 0.4) vs. x & s") image (x,size, log10(dnb), main= paste("log [",tit,"]")) contour(x,size, log10(dnb),add=TRUE)