Double Binomial            package:rmutil            R Documentation

_D_o_u_b_l_e _B_i_n_o_m_i_a_l _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 double binomial
     distribution with parameters 'm' and 's': density, cumulative
     distribution, quantiles, and random generation.

     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 constant.

_U_s_a_g_e:

     ddoublebinom(y, size, m, s, log=FALSE)
     pdoublebinom(q, size, m, s)
     qdoublebinom(p, size, m, s)
     rdoublebinom(n, size, m, s)

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

       y: vector of frequencies

       q: vector of quantiles

       p: vector of probabilities

       n: number of values to generate

    size: vector of totals

       m: vector of probabilities of success

       s: vector of overdispersion parameters

     log: if TRUE, log probabilities are supplied.

_A_u_t_h_o_r(_s):

     J.K. Lindsey

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

     'dbinom' for the binomial, 'dmultbinom' for the multiplicative
     binomial, and 'dbetabinom' for the beta binomial distribution.

_E_x_a_m_p_l_e_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)
     pdoublebinom(2,10,0.5,1.1)
     qdoublebinom(0.05,10,0.5,1.1)
     rdoublebinom(10,10,0.5,1.1)

