Paralogistic              package:VGAM              R Documentation

_T_h_e _P_a_r_a_l_o_g_i_s_t_i_c _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 paralogistic distribution with shape parameter
     'a' and scale parameter 'scale'.

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

     dparalogistic(x, a, scale)
     pparalogistic(q, a, scale)
     qparalogistic(p, a, scale)
     rparalogistic(n, a, scale)

_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: shape parameter.

   scale: scale parameter.

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

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

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

     'dparalogistic' gives the density, 'pparalogistic' gives the
     distribution function, 'qparalogistic' gives the quantile
     function, and 'rparalogistic' generates random deviates.

_N_o_t_e:

     The paralogistic 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:

     'paralogistic', 'genbetaII'.

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

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

