dkagan                 package:ssEDA                 R Documentation

_K_a_g_a_n _D_i_s_t_r_i_b_u_t_i_o_n

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

     Density, cumulative probability, quantiles and random generation
     for the Kagan distribution.

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

     dkagan(M, alpha=1, beta=0, gamma=7, M0=4, mag=TRUE, theta=0.75, phi=2.4)
     pkagan(M, alpha=1, beta=0, gamma=7, M0=4, mag=TRUE, theta=0.75, phi=2.4)
     qkagan(p, alpha=1, beta=0, gamma=7, M0=4, mag=TRUE, theta=0.75, phi=2.4)
     rkagan(n, alpha=1, beta=0, gamma=7, M0=4, mag=TRUE, theta=0.75, phi=2.4)

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

       p: Vector of probabilities. 

       n: Non-negative sample size. If 'length(n)' is greater than 1,
          then 'length(n)' random variables are returned. 

       M: Vector of quantiles.  

   alpha: Parameter of Kagan distribution. Index of the power law. 

    beta: Parameter of Kagan distribution. Controls the lower end of
          the distribution. 

   gamma: Parameter of Kagan distribution. Controls the upper end of
          the distribution. 

      M0: Lowest magnitude under consideration. 

     mag: Flag indicating whether stress or magnitudes are to be used.
          Default is true where stresses are used. 

   theta: Parameter of 'magnitude.convert'. 

     phi: Parameter of 'magnitude.convert'. 

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

     Elements of 'p' or 'M' that are missing will cause the
     corresponding elements of the result to be missing.

     The variables in this basic form of the distribution correspond
     physically to moments (stress, benioff strain relief). The
     alternative form allows the parameters and variable to be
     specified in terms of magnitudes. Once the appropriate values are
     calculated, if need be, they can be transformed to magnitudes
     using the 'magnitude.convert' function.

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

     Density ('dkagan'), probability ('pkagan'), quantile ('qkagan') or
     random sample ('rkagan') for the Kagan distribution. The
     cumulative density function is given by:

          F(x) = 1-((1 + (x/beta))^(-alpha))*(exp(-x/delta))

     where 'x', 'beta' (beta) and 'delta' (delta) are to be interpreted
     as stresses according to the relation:

                     S(M) = 10^(phi + theta * M).

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

     The function 'qkagan' uses a approximate numerical method
     (Newton-Raphson) to evaluate the quantile.

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

     Vere-Jones, D.; Robinson, R. & Yang, W. (2001). Remarks on the
     accelerated moment release model: problems of model formulation,
     simulation and estimation. _Geophysical Journal International_
     *144*, 517-531.

     Kagan, Y.Y. (1997). Seismic moment-frequency relation for shallow
     earthquakes: Regional comparison. _Journal of Geophysical
     Research_ *102*, 2835-2852.

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

     'magnitude.convert'

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

     #  Examine the Gutenberg-Richter Law:
     #  Use default parameters

     x <- seq(0, 10, length=1000)
     plot(log(x), log(1-pkagan(x)), type="l")

