exponential               package:VGAM               R Documentation

_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 for the exponential distribution.

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

     exponential(link = "loge", location = 0, expected = TRUE, earg = NULL)

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

    link: Parameter link function applied to the positive parameter
          rate. See 'Links' for more choices.

location: Numeric of length 1, the known location parameter, A, say.

expected: Logical. If 'TRUE' Fisher scoring is used, otherwise
          Newton-Raphson. The latter is usually faster.

    earg: Extra argument for the 'VGAM' link function. See 'Links' for
          more details.

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

     The family function assumes the response Y has density

                   f(y) = rate * exp(-rate * (y-A))

     for y > A, where A is the known location parameter. By default,
     A=0. Then E(Y) = A + 1/rate and Var(Y) = 1/rate^2.

_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:

     Suppose A=0. For a fixed time interval, the number of events is 
     Poisson with mean rate if the time between events has a geometric
     distribution with mean 1/rate. The argument 'rate' in
     'exponential' is the same as 'rexp' etc. The argument 'lambda' in
     'rpois' is somewhat the same as 'rate' here.

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

     T. W. Yee

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

     Evans, M., Hastings, N. and Peacock, B. (2000) _Statistical
     Distributions_, New York: Wiley-Interscience, Third edition.

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

     'cexpon', 'poissonff', 'freund61'.

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

     nn = 100
     x1 = runif(nn) - 0.5
     x2 = runif(nn) - 0.5
     eta = 0.2 - 0.7 * x1 + 1.9 * x2
     rate = exp(eta)
     y = rexp(nn, rate=rate)
     stem(y)
     fit = vglm(y ~ x1 + x2, exponential, trace=TRUE, crit="c") # slower
     fit = vglm(y ~ x1 + x2, exponential(exp=FALSE), trace=TRUE, crit="c") # faster
     coef(fit)
     coef(fit, mat=TRUE)
     Coef(fit)
     summary(fit)

