Multiplicative Binomial        package:rmutil        R Documentation

_M_u_l_t_i_p_l_i_c_a_t_i_v_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 multiplicative
     binomial distribution with parameters 'm' and 's': density,
     cumulative distribution, quantiles, and random generation.

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

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

     for y = 0, ..., n, where c(.) is a normalizing constant.

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

     dmultbinom(y, size, m, s, log=FALSE)
     pmultbinom(q, size, m, s)
     qmultbinom(p, size, m, s)
     rmultbinom(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, 'ddoublebinom' for the double binomial,
     and 'dbetabinom' for the beta binomial distribution.

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

     # compute P(45 < y < 55) for y multiplicative binomial(100,0.5,1.1)
     sum(dmultbinom(46:54, 100, 0.5, 1.1))
     pmultbinom(54, 100, 0.5, 1.1)-pmultbinom(45, 100, 0.5, 1.1)
     pmultbinom(2,10,0.5,1.1)
     qmultbinom(0.025,10,0.5,1.1)
     rmultbinom(10,10,0.5,1.1)

