ParetoIV                package:VGAM                R Documentation

_T_h_e _P_a_r_e_t_o(_I_V/_I_I_I/_I_I) _D_i_s_t_r_i_b_u_t_i_o_n_s

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

     Density, distribution function, quantile function and random
     generation for the Pareto(IV/III/II) distributions.

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

     dparetoIV(x, location=0, scale=1, inequality=1, shape=1)
     pparetoIV(q, location=0, scale=1, inequality=1, shape=1)
     qparetoIV(p, location=0, scale=1, inequality=1, shape=1)
     rparetoIV(n, location=0, scale=1, inequality=1, shape=1)
     dparetoIII(x, location=0, scale=1, inequality=1)
     pparetoIII(q, location=0, scale=1, inequality=1)
     qparetoIII(p, location=0, scale=1, inequality=1)
     rparetoIII(n, location=0, scale=1, inequality=1)
     dparetoII(x, location=0, scale=1, shape=1)
     pparetoII(q, location=0, scale=1, shape=1)
     qparetoII(p, location=0, scale=1, shape=1)
     rparetoII(n, location=0, scale=1, shape=1)
     dparetoI(x, scale=1, shape=1)
     pparetoI(q, scale=1, shape=1)
     qparetoI(p, scale=1, shape=1)
     rparetoI(n, scale=1, shape=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 single positive integer. 

location: the location parameter. 

scale, shape, inequality: the (positive) scale, inequality and shape
          parameters. 

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

     For the formulas and other details  see 'paretoIV'.

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

     Functions beginning with the letter 'd' give the density,
     functions beginning with the letter 'p' give the distribution
     function, functions beginning with the letter 'q' give the
     quantile function, and functions beginning with the letter 'r'
     generates random deviates.

_N_o_t_e:

     The functions '[dpqr]paretoI' are the same as '[dpqr]pareto1'
     except for a slight change in notation: s=k and b=alpha; see
     'Pareto'.

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

     T. W. Yee

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

     Brazauskas, V. (2003) Information matrix for Pareto(IV), Burr, and
     related distributions. _Comm. Statist. Theory and Methods_ *32*,
     315-325.

     Arnold, B. C. (1983) _Pareto Distributions_. Fairland, Maryland:
     International Cooperative Publishing House.

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

     'paretoIV', 'Pareto'.

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

     ## Not run: 
     x = seq(-0.2, 4, by=0.01)
     loc = 0; Scale = 1; ineq = 1; shape = 1.0;
     plot(x, dparetoIV(x, loc, Scale, ineq, shape), type="l", col="blue",
          main="Blue is density, red is cumulative distribution function",
          sub="Purple are 5,10,...,95 percentiles", ylim=0:1, las=1, ylab="")
     abline(h=0, col="blue", lty=2)
     Q = qparetoIV(seq(0.05,0.95,by=0.05), loc, Scale, ineq, shape)
     lines(Q, dparetoIV(Q, loc, Scale, ineq, shape), col="purple", lty=3, type="h")
     lines(x, pparetoIV(x, loc, Scale, ineq, shape), col="red")
     abline(h=0, lty=2)
     ## End(Not run)

