

_T_h_e _N_e_g_a_t_i_v_e _B_i_n_o_m_i_a_l _D_i_s_t_r_i_b_u_t_i_o_n

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

_A_r_g_u_m_e_n_t_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_e_s_c_r_i_p_t_i_o_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_e_e _A_l_s_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_x_a_m_p_l_e_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))

