Pareto                 package:VGAM                 R Documentation

_T_h_e _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 Pareto(I) distribution with parameters
     'location' and 'shape'.

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

     dpareto(x, location, shape)
     ppareto(q, location, shape)
     qpareto(p, location, shape)
     rpareto(n, location, 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. 

location, shape: the alpha and k parameters.

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

     See 'pareto1', 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:

     'dpareto' gives the density, 'ppareto' gives the distribution
     function, 'qpareto' gives the quantile function, and 'rpareto'
     generates random deviates.

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

     T. W. Yee

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

     Evans, M., Hastings, N. and Peacock, B. (2000) _Statistical
     Distributions_, New York: Wiley-Interscience, Third edition.

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

     'pareto1', 'ParetoIV'.

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

     alpha = 3; k = exp(1); x = seq(2.8, 8, len=300)
     ## Not run: 
     plot(x, dpareto(x, location=alpha, shape=k), type="l",
          main="Pareto density split into 10 equal areas")
     abline(h=0, col="blue", lty=2)
     qq = qpareto(seq(0.1,0.9,by=0.1),location=alpha,shape=k)
     lines(qq, dpareto(qq, loc=alpha, shape=k), col="purple", lty=3, type="h")
     ## End(Not run)
     pp = seq(0.1,0.9,by=0.1)
     qq = qpareto(pp, location=alpha, shape=k)
     ppareto(qq, location=alpha, shape=k)
     qpareto(ppareto(qq,loc=alpha,shape=k),loc=alpha,shape=k) - qq # Should be 0

