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, or alternately the probability distribution
of a heterogeneous Poisson process whose intensity is distributed
as a gamma distribution with scale parameter prob/(1-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 / shape parameter of gamma distribution. |
prob
|
probability of success in each trial / determines scale of gamma distribution ( prob = scale/(1+scale)).
|
size and prob. dnbinom
gives the density, pnbinom gives the distribution function,
qnbinom gives the quantile function and rnbinom
generates random deviates.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.
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)))
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)