Zeta                  package:VGAM                  R Documentation

_T_h_e _Z_e_t_a _D_i_s_t_r_i_b_u_t_i_o_n

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

     Density for the zeta distribution.

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

     dzeta(x, p)

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

       x: Numerical vector/matrix to evaluate the density. 

       p: The parameter p. This must be greater than 1. 

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

     The density function of the zeta distribution is given by

                          y^(-p) /  zeta(p)

     where p>1, y=1,2,..., and zeta is Riemann's zeta function.

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

     Returns the density evaluated at 'x'.

_W_a_r_n_i_n_g:

     This function has not been fully tested.

_N_o_t_e:

     The 'VGAM' family function 'zetaff' estimates the parameter p.

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

     T. W. Yee

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

     Johnson N. L., Kotz S., and Balakrishnan N. (1993) _Univariate
     Discrete Distributions_, 2nd ed. New York: Wiley.

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

     'zeta', 'zetaff'.

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

     dzeta(1:20, p=2)
     ## Not run: 
     plot(1:6, dzeta(1:6, p=4), type="h", las=1, ylab="Probability",
          main="zeta probability function; black: p = 4; blue: p = 2")
     points(0.10+1:6, dzeta(1:6, p=2), type="h", col="blue")
     ## End(Not run)

