

Poisson {base}                               R Documentation

_T_h_e _P_o_i_s_s_o_n _D_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n_:

     These functions provide information about the Poisson
     distribution with parameter `lambda'.  `dpois' gives
     the density, `ppois' gives the distribution function
     `qpois' gives the quantile function and `rpois' gener-
     ates random deviates.

_U_s_a_g_e_:

     dpois(x, lambda)
     ppois(q, lambda)
     qpois(p, lambda)
     rpois(n, lambda)

_A_r_g_u_m_e_n_t_s_:

       x: vector of (non-negative integer) quantiles.

       q: vector of quantiles.

       p: vector of probabilities.

       n: number of random values to return.

  lambda: vector of positive means.

_D_e_t_a_i_l_s_:

     The Poisson distribution has density

                 p(x) = lambda^x exp(-lambda)/x!

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

     If an element of `x' is not integer, the result of
     `dpois' is zero, with a warning.

     The quantile is left continuous: `qpois(q, lambda)' is
     the largest integer x such that P(X <= x) < q.

_S_e_e _A_l_s_o_:

     `dbinom' for the binomial and `dnbinom' for the nega-
     tive binomial distribution.

_E_x_a_m_p_l_e_s_:

     -log(dpois(0:7, lambda=1) * gamma(1+ 0:7))
     Ni <- rpois(50, lam= 4); table(factor(Ni, 0:max(Ni)))

     par(mfrow = c(2, 1))
     x <- seq(-0.01, 5, 0.01)
     plot(x, ppois(x, 1), type="s", ylab="F(x)", main="Poisson(1) CDF")
     plot(x, pbinom(x, 100, 0.01),type="s", ylab="F(x)",
          main="Binomial(100, 0.01) CDF")

