Benini                 package:VGAM                 R Documentation

_T_h_e _B_e_n_i_n_i _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 Benini distribution with parameter 'shape'.

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

     dbenini(x, shape, y0)
     pbenini(q, shape, y0)
     qbenini(p, shape, y0)
     rbenini(n, shape, y0)

_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.

   shape: the shape parameter b.

      y0: the scale parameter y0.

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

     See 'benini', the 'VGAM' family function for estimating the
     parameter b by maximum likelihood estimation, for the formula of
     the probability density function and other details.

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

     'dbenini' gives the density, 'pbenini' gives the distribution
     function, 'qbenini' gives the quantile function, and 'rbenini'
     generates random deviates.

_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:

     'benini'.

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

     ## Not run: 
     y0 = 1
     shape = exp(1)
     x = seq(-0.0, 4, len=101)
     plot(x, dbenini(x, y0=y0,shape=shape), type="l", col="blue", las=1,
          main="Blue is density, red is cumulative distribution function",
          sub="Purple lines are the 10,20,...,90 percentiles", ylim=0:1,
          ylab="")
     abline(h=0, col="blue", lty=2)
     lines(x, pbenini(x, y0=y0,shape=shape), col="red")
     probs = seq(0.1, 0.9, by=0.1)
     Q = qbenini(probs, y0=y0,shape=shape)
     lines(Q, dbenini(Q, y0=y0,shape=shape), col="purple", lty=3, type="h")
     pbenini(Q, y0=y0,shape=shape) - probs    # Should be all zero
     ## End(Not run)

