Tpareto                 package:VGAM                 R Documentation

_T_h_e _T_r_u_n_c_a_t_e_d _P_a_r_e_t_o _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 upper truncated Pareto(I) distribution with
     parameters 'lower', 'upper' and 'shape'.

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

     dtpareto(x, lower, upper, shape)
     ptpareto(q, lower, upper, shape)
     qtpareto(p, lower, upper, shape)
     rtpareto(n, lower, upper, shape)

_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 single positive integer. 

lower, upper, shape: the lower, upper and shape (k) parameters. If
          necessary, values are recycled. 

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

     See 'tpareto1', the 'VGAM' family function for estimating the
     parameter k by maximum likelihood estimation, for the formula of
     the probability density function and the range restrictions
     imposed on the parameters.

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

     'dtpareto' gives the density, 'ptpareto' gives the distribution
     function, 'qtpareto' gives the quantile function, and 'rtpareto'
     generates random deviates.

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

     T. W. Yee

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

     Aban, I. B., Meerschaert, M. M. and Panorska, A. K. (2006)
     Parameter estimation for the truncated Pareto distribution,
     _Journal of the American Statistical Association_, *101*(473),
     270-277.

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

     'tpareto1'.

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

     lower = 3; upper = 8; k = exp(0.5)
     ## Not run: 
     x = seq(lower, upper, len=200)
     plot(x, dtpareto(x, lo=lower, up=upper, shape=k), type="l",
          main="Truncated Pareto density split into 10 equal areas")
     abline(h=0, col="blue", lty=2)
     qq = qtpareto(seq(0.1,0.9,by=0.1),lo=lower, up=upper,shape=k)
     lines(qq, dtpareto(qq, lo=lower, up=upper, shape=k),
           col="purple", lty=3, type="h")
     ## End(Not run)
     pp = seq(0.1,0.9,by=0.1)
     qq = qtpareto(pp, lo=lower, up=upper, shape=k)
     ptpareto(qq, lo=lower, up=upper, shape=k)
     qtpareto(ptpareto(qq, lo=lower, up=upper, shape=k),
              lo=lower, up=upper, shape=k) - qq # Should be all 0

