

   TThhee DDoouubbllee BBiinnoommiiaall DDiissttrriibbuuttiioonn

        ddoublebinom(y, n, m, s)
        pdoublebinom(q, n, m, s)

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

          y: vector of frequencies

          q: vector of quantiles

          n: vector of totals

          m: vector of probabilities

          s: vector of overdispersion parameters

   VVaalluuee::

        These functions provide information about the double
        binomial distribution with parameters `m' and `s'.
        `ddoublebinom' gives the density and `pdoublebinom'
        gives the distribution function.

        The double binomial distribution with total = n and
        `prob' = m has density

        p(y) = c(n,m,s) Choose(n,y) n^(n log(s)) (m/y)^(y log(s))
        ((1-m)/(n-y))^(s(n-y)) y^y (n-y)^(n-y)

        for y = 0, ..., n, where c(.) is a normalizing con-
        stant.

   AAuutthhoorr((ss))::

        J.K. Lindsey

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

        `dbinom' for the binomial, `dmultbinom' for the multi-
        plicative binomial, and `dbetabinom' for the beta bino-
        mial distribution.

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

        # Compute P(45 < y < 55) for y double binomial(100,0.5,1.1)
        sum(ddoublebinom(46:54, 100, 0.5, 1.1))
        pdoublebinom(54, 100, 0.5, 1.1)-pdoublebinom(45, 100, 0.5, 1.1)

