Beta Binomial             package:rmutil             R Documentation

_B_e_t_a _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 beta binomial
     distribution with parameters 'm' and 's': density, cumulative
     distribution, quantiles, and random generation.

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

       p(y) = B(y+s m,n-y+s (1-m)) Choose(n,y) / B(s m,s (1-m))

     for y = 0, ..., n where B() is the beta function.

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

     dbetabinom(y, size, m, s, log=FALSE)
     pbetabinom(q, size, m, s)
     qbetabinom(p, size, m, s)
     rbetabinom(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 'dmultbinom' for the multiplicative binomial distribution.

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

     # compute P(45 < y < 55) for y beta binomial(100,0.5,1.1)
     sum(dbetabinom(46:54, 100, 0.5, 1.1))
     pbetabinom(54,100,0.5,1.1)-pbetabinom(45,100,0.5,1.1)
     pbetabinom(2,10,0.5,1.1)
     qbetabinom(0.33,10,0.5,1.1)
     rbetabinom(10,10,0.5,1.1)

