Lino                  package:VGAM                  R Documentation

_T_h_e _G_e_n_e_r_a_l_i_z_e_d _B_e_t_a _D_i_s_t_r_i_b_u_t_i_o_n (_L_i_b_b_y _a_n_d _N_o_v_i_c_k, _1_9_8_2)

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

     Density, distribution function, quantile function and random
     generation for the generalized beta distribution, as proposed by
     Libby and Novick (1982).

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

     dlino(x, shape1, shape2, lambda=1)
     plino(q, shape1, shape2, lambda=1)
     qlino(p, shape1, shape2, lambda=1)
     rlino(n, shape1, shape2, lambda=1)

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

    x, q: vector of quantiles.

       p: vector of probabilities.

       n: number of observations. Must be a positive integer of length
          1.

shape1, shape2, lambda: see 'lino'. 

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

     See 'lino', the 'VGAM' family function for estimating the
     parameters,  for the formula of the probability density function
     and other details.

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

     'dlino' gives the density, 'plino' gives the distribution
     function, 'qlino' gives the quantile function, and 'rlino'
     generates random deviates.

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

     T. W. Yee

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

     'lino'.

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

     ## Not run: 
     lambda = 0.4
     shape1 = exp(1.3)
     shape2 = exp(1.3)
     x = seq(0.0, 1.0, len=101)
     plot(x, dlino(x, shape1=shape1, shape2=shape2, lambda=lambda),
          type="l", col="blue", las=1, ylab="",
          main="Blue is density, red is cumulative distribution function",
          sub="Purple lines are the 10,20,...,90 percentiles")
     abline(h=0, col="blue", lty=2)
     lines(x, plino(x, shape1=shape1, shape2=shape2, l=lambda), col="red")
     probs = seq(0.1, 0.9, by=0.1)
     Q = qlino(probs, shape1=shape1, shape2=shape2, lambda=lambda)
     lines(Q, dlino(Q, shape1=shape1, shape2=shape2, lambda=lambda),
           col="purple", lty=3, type="h")
     plino(Q, shape1=shape1, shape2=shape2, l=lambda) - probs # Should be all 0
     ## End(Not run)

