recexp1                 package:VGAM                 R Documentation

_U_p_p_e_r _R_e_c_o_r_d _V_a_l_u_e_s _f_r_o_m _a _1-_p_a_r_a_m_e_t_e_r _E_x_p_o_n_e_n_t_i_a_l _D_i_s_t_r_i_b_u_t_i_o_n

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

     Maximum likelihood estimation of the rate parameter of a
     1-parameter exponential distribution when the observations are
     upper  record values.

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

     recexp1(lrate="loge", irate=NULL, method.init=1)

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

   lrate: Link function applied to the rate parameter. See 'Links' for
          more choices.

   irate: Numeric. Optional initial values for the rate. The default
          value 'NULL' means they are computed internally, with the
          help of 'method.init'.

method.init: Integer, either 1 or 2 or 3. Initial method, three
          algorithms are implemented. Choose the another value if
          convergence fails, or use 'irate'.

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

     The response must be a vector or one-column matrix with strictly
     increasing values.

_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'.

_N_o_t_e:

     By default, this family function has the intercept-only MLE as the
     initial value, therefore convergence may only take one iteration.
     Fisher scoring is used.

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

     T. W. Yee

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

     Arnold, B. C. and Balakrishnan, N. and Nagaraja, H. N. (1998)
     _Records_, New York: John Wiley & Sons.

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

     'exponential'.

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

     rawy = rexp(n <- 10000, rate=exp(1))

     # Keep only the records
     delete = c(FALSE, rep(TRUE, len=n-1))
     for(i in 2:length(rawy))
         if(rawy[i] > max(rawy[1:(i-1)])) delete[i] = FALSE
     (y = rawy[!delete])

     length(y) / y[length(y)]   # MLE of rate

     fit = vglm(y ~ 1, recexp1, trace=TRUE)
     coef(fit, matrix=TRUE)
     Coef(fit)

