slash                  package:VGAM                  R Documentation

_S_l_a_s_h _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 slash distribution by maximum
     likelihood estimation.

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

     slash (lmu="identity", lsigma="loge", emu=list(), esigma=list(),
            imu=NULL, isigma=NULL, iprobs = c(0.1, 0.9), nsimEIM=250,
            zero=NULL, smallno = .Machine$double.eps*1000)

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

lmu, lsigma: Parameter link functions applied to the mu and sigma
          parameters, respectively. See 'Links' for more choices.

emu, esigma: List. Extra argument for each of the link functions. See
          'earg' in 'Links' for general information.

imu, isigma: Initial values. A 'NULL' means an initial value is chosen
          internally. See 'CommonVGAMffArguments' for more information.

  iprobs: Used to compute the initial values for 'mu'. This argument is
          fed into the 'probs' argument of 'quantile', and then a grid
          between these two points is used to evaluate the
          log-likelihood. This argument must be of length two and have
          values between 0 and 1.

nsimEIM, zero: See 'CommonVGAMffArguments' for more information.

 smallno: Small positive number, used to test for the singularity.

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

     The standard slash distribution is the distribution of the ratio
     of  a standard normal variable to an independent standard
     uniform(0,1) variable.  It is mainly of use in simulation studies.
     One of its properties is that it has heavy tails, similar to those
     of the Cauchy.

     The general slash distribution can be obtained by replacing  the
     univariate normal variable by a general normal  N(mu,sigma) random
     variable. It has a density that can be written as

 f(y) = 1/(2*sigma*sqrt(2*pi)) if y=mu = 1-exp(-(((x-mu)/sigma)^2)/2))/(sqrt(2*pi)*sigma*((x-mu)/sigma)^2) if y!=mu

     where mu and sigma are  the mean and standard deviation of  the
     univariate normal distribution respectively.

_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:

     Fisher scoring using simulation is used. Convergence is often
     quite slow. Numerical problems may occur.

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

     T. W. Yee and C. S. Chee

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

     Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994) 
     _Continuous Univariate Distributions_, 2nd edition, Volume 1, New
     York: Wiley.

     Kafadar, K. (1982) A Biweight Approach to the One-Sample Problem
     _Journal of the American Statistical Association_, *77*, 416-424.

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

     'rslash'.

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

     y = rslash(n=1000, mu=4, sigma=exp(2))
     fit = vglm(y ~ 1, slash, trace=TRUE) 
     coef(fit, matrix=TRUE)
     Coef(fit)
     summary(fit)

