expexp1                 package:VGAM                 R Documentation

_E_x_p_o_n_e_n_t_i_a_t_e_d _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:

     Estimates the two parameters of the exponentiated exponential
     distribution by maximizing a profile (concentrated) likelihood.

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

     expexp1(lscale = "loge", escale=list(), iscale = NULL, ishape = 1)

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

  lscale: Parameter link function for the (positive) scale parameter.
          See 'Links' for more choices.

  escale: List. Extra argument for the link. See 'earg' in 'Links' for
          general information.

  iscale: Initial value for the scale parameter. By default, an initial
          value is chosen internally using 'ishape'.

  ishape: Initial value for the shape parameter. If convergence fails
          try setting a different value for this argument.

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

     See 'expexp' for details about the exponentiated exponential
     distribution. This family function uses a different algorithm for
     fitting the model. Given scale, the MLE of shape can easily be
     solved in terms of scale. This family function maximizes a profile
     (concentrated) likelihood with respect to scale. Newton-Raphson is
     used, which compares with Fisher scoring with 'expexp'.

_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'.

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

     The standard errors produced by a 'summary' of the model may be
     wrong.

_N_o_t_e:

     This family function works only for intercept-only models, i.e.,
     'y ~ 1' where 'y' is the response.

     The estimate of  shape is attached to the 'misc' slot of the
     object, which is a list and contains the component 'shape'.

     As Newton-Raphson is used, the working weights are sometimes
     negative, and some adjustment is made to these to make them
     positive.

     Like 'expexp', good initial values are needed. Convergence may be
     slow.

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

     T. W. Yee

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

     Gupta, R. D. and Kundu, D. (2001) Exponentiated exponential
     family: an alternative to gamma and Weibull distributions,
     _Biometrical Journal_, *43*, 117-130.

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

     'expexp'.

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

     # Ball bearings data (number of million revolutions before failure)
     bbearings = c(17.88, 28.92, 33.00, 41.52, 42.12, 45.60,
     48.80, 51.84, 51.96, 54.12, 55.56, 67.80, 68.64, 68.64,
     68.88, 84.12, 93.12, 98.64, 105.12, 105.84, 127.92,
     128.04, 173.40)
     fit = vglm(bbearings ~ 1, expexp1(ishape=4), trace=TRUE,
                maxit=50, checkwz=FALSE)
     coef(fit, matrix=TRUE)
     Coef(fit) # Authors get c(0.0314, 5.2589) with log-lik -112.9763
     fit@misc$shape    # Estimate of shape
     logLik(fit)

     # Failure times of the airconditioning system of an airplane
     acplane = c(23, 261, 87, 7, 120, 14, 62, 47,
     225, 71, 246, 21, 42, 20, 5, 12, 120, 11, 3, 14,
     71, 11, 14, 11, 16, 90, 1, 16, 52, 95)
     fit = vglm(acplane ~ 1, expexp1(ishape=0.8), trace=TRUE,
                maxit=50, checkwz=FALSE)
     coef(fit, matrix=TRUE)
     Coef(fit) # Authors get c(0.0145, 0.8130) with log-lik -152.264
     fit@misc$shape    # Estimate of shape
     logLik(fit)

