

   TThhee NNeeggaattiivvee BBiinnoommiiaall DDiissttrriibbuuttiioonn

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

   AArrgguummeennttss::

        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.

          p: vector of probabilities.

          n: number of observations to generate.

       size: target for number of successful trials.

       prob: probability of success in each trial.

   DDeessccrriippttiioonn::

        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.

        The negative binomial distribution with `size' = n and
        `prob' = p has density

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

        for x = 0, 1, 2, ...

   SSeeee AAllssoo::

        `dbinom' for the binomial, `dpois' for the Poisson and
        `dgeom' for the geometric distribution, which is a spe-
        cial case of the negative binomial.

   EExxaammpplleess::

        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))

