Negative Binomial Distribution

DESCRIPTION:

Functions for the density, cumulative distribution, quantiles and random generation of the Negative Binomial distribution. The distribution models the number of failures before size successes occur in a sequence of Bernoulli trials.

USAGE:

dnbinom(x, size, prob, log=F) 
pnbinom(q, size, prob) 
qnbinom(p, size, prob) 
rnbinom(n, size, prob, bigdata=F) 

REQUIRED ARGUMENTS:

x
vector or bdVector of (positive) quantiles. Missing values ( NAs) are allowed.
q
vector or bdVector of (positive) quantiles. Missing values ( NAs) are allowed.
p
vector or bdVector of probabilities. Missing values ( NAs) are allowed.
n
sample size.
size
vector or bdVector of positive integers; the Negative Binomial represents the number of failures (or tails in coin tossing) before size successes (or heads in coin tossing) are achieved where the probability of a success (or of a head) is prob.
prob
vector or bdVector of probabilities of a success. If length(n) is larger than 1, then length(n) random values are returned.

OPTIONAL ARGUMENTS:

bigdata
a logical value; if TRUE, an object of type bdVector is returned. Otherwise, a vector object is returned. This argument can be used only if the bigdata library section has been loaded.
log
a logical scalar; if TRUE, dnbinom will return the log of the density, not the density itself.

VALUE:

density ( dnbinom), probability ( pnbinom), quantile ( qnbinom), or random sample ( rnbinom) for the Negative Binomial distribution with parameters size and prob. The quantile is defined as the smallest value q such that Pr(Negative Binomial random variate <= x) >= p.

SIDE EFFECTS:

The function rbinom causes the creation of the dataset .Random.seed if it does not already exist, otherwise its value is updated.

Elements of q or p that are missing will cause the corresponding elements of the result to be missing.

DETAILS:

For details on the uniform random number generator implemented in S-PLUS, see the set.seed help file.

SEE ALSO:

, .

EXAMPLES:

rbinom(20,10,0.5)  # sample of size 20 with mean 10*0.5 = 5