Double Binomial            package:rmutil            R Documentation

_T_h_e _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

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

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

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

       y: vector of frequencies

       q: vector of quantiles

       n: vector of totals

       m: vector of probabilities

       s: vector of overdispersion parameters

_V_a_l_u_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 constant.

_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)

