

   TThhee PPooiissssoonn DDiissttrriibbuuttiioonn

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

   AArrgguummeennttss::

          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.

   DDeessccrriippttiioonn::

        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.

   DDeettaaiillss::

        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.

   SSeeee AAllssoo::

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

   EExxaammpplleess::

        -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")

        -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")

