kumar                  package:VGAM                  R Documentation

_K_u_m_a_r_a_s_w_a_m_y _D_i_s_t_r_i_b_u_t_i_o_n _F_a_m_i_l_y _F_u_n_c_t_i_o_n

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

     Estimates the two parameters of the Kumaraswamy distribution by
     maximum likelihood estimation.

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

     kumar(lshape1="loge", lshape2="loge",
           eshape1=list(), eshape2=list(),
           ishape1=NULL, ishape2=NULL, nsimEIM=500, zero=NULL)

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

lshape1, lshape2: Link function for the two positive shape parameters.
          See 'Links' for more choices.

eshape1, eshape2: List. Extra argument for each of the links. See
          'earg' in 'Links' for general information.

ishape1, ishape2: Numeric. Optional initial values for the two positive
          shape parameters.

nsimEIM, zero: See 'CommonVGAMffArguments'.

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

     The Kumaraswamy distribution has density function

                      a*b*y^(a-1)*(1-y^a)^(b-1)

     where 0 < y < 1 and the two shape parameters, a and b, are
     positive. The mean is b Beta(1+1/a,b) (returned as the fitted
     values) and the variance is b Beta(1+2/a,b) - (b Beta(1+1/a,b))^2.
     Applications of the Kumaraswamy distribution include the storage
     volume of a water reservoir.

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

     An object of class '"vglmff"' (see 'vglmff-class'). The object is
     used by modelling functions such as 'vglm' and 'vgam'.

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

     T. W. Yee

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

     Kumaraswamy, P. (1980). A generalized probability density function
     for double-bounded random processes. _Journal of Hydrology_, *46*,
     79-88.

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

     'dkumar', 'betaff'.

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

     shape1 = exp(1); shape2 = exp(2);
     y = rkumar(n <- 1000, shape1, shape2)
     fit = vglm(y ~ 1, kumar, trace =TRUE)
     c(mean(y), fitted(fit)[1])
     coef(fit, matrix=TRUE)
     Coef(fit)
     summary(fit)

