Sinmad                 package:VGAM                 R Documentation

_T_h_e _S_i_n_g_h-_M_a_d_d_a_l_a _D_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Density, distribution function, quantile function and random
     generation for the Singh-Maddala distribution with shape
     parameters 'a' and 'q', and scale parameter 'scale'.

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

     dsinmad(x, a, scale, q.arg)
     psinmad(q, a, scale, q.arg)
     qsinmad(p, a, scale, q.arg)
     rsinmad(n, a, scale, q.arg)

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

    x, q: vector of quantiles.

       p: vector of probabilities.

       n: number of observations. If 'length(n) > 1', the length is
          taken to be the number required.

a, q.arg: shape parameters.

   scale: scale parameter.

_D_e_t_a_i_l_s:

     See 'sinmad', which is the 'VGAM' family function for estimating
     the parameters by maximum likelihood estimation.

_V_a_l_u_e:

     'dsinmad' gives the density, 'psinmad' gives the distribution
     function, 'qsinmad' gives the quantile function, and 'rsinmad'
     generates random deviates.

_N_o_t_e:

     The Singh-Maddala distribution is a special case of the
     4-parameter generalized beta II distribution.

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

     T. W. Yee

_R_e_f_e_r_e_n_c_e_s:

     Kleiber, C. and Kotz, S. (2003) _Statistical Size Distributions in
     Economics and Actuarial Sciences_, Hoboken, NJ:
     Wiley-Interscience.

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

     'sinmad', 'genbetaII'.

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

     y = rsinmad(n=3000, 4, 6, 2)
     fit = vglm(y ~ 1, sinmad(init.a=2.1), trace=TRUE, crit="c")
     coef(fit, mat=TRUE)
     Coef(fit)

