GevGlmFit             package:fExtremes             R Documentation

_M_o_d_e_l_l_i_n_g _t_h_e _G_E_V _D_i_s_t_r_i_b_u_t_i_o_n _i_n_c_l_u_d_i_n_g _G_L_M

_D_e_s_c_r_i_p_t_i_o_n:

     A collection and description of functions to model the 
     Generalized Extreme Value, GEV, distribution by maximum 
     likelihood approximation based on R's 'ismev' package. In 
     addition to the function gevFit the parameter estimation  allows
     to include generalized linear modelling, GLM, of  each parameter. 

     The functions are:

       'gevglmFit'         fits empirical or simulated data to the distribution,
       'print'             print method for a fitted GEV object of class ...,
       'plot'              plot method for a fitted GEV object,
       'summary'           summary method for a fitted GEV object,
       'gevglmprofPlot'    profile log-likelihoods for return levels,
       'gevglmprofxiPlot'  profile log-likelihoods for shape parameters.

_U_s_a_g_e:

     gevglmFit(x, y = NULL, gumbel = FALSE, mul = NULL, sigl = NULL, shl = NULL, 
         mulink = identity, siglink = identity, shlink = identity, show = FALSE, 
         method = "Nelder-Mead", maxit = 10000, ...)

     ## S3 method for class 'gevglmFit':
     print(x, ...)
     ## S3 method for class 'gevglmFit':
     plot(x, which = "ask", ...)
     ## S3 method for class 'gevglmFit':
     summary(object, doplot = TRUE, which = "all", ...)

     gevglmprofPlot(object, m, xlow, xup, conf = 0.95, nint = 100)
     gevglmprofxiPlot(object, xlow, xup, conf = 0.95, nint = 100)

_A_r_g_u_m_e_n_t_s:

    conf: [gevglmprof*Plot] - 
           the confidence coefficient of the plotted profile confidence
           interval. 

  doplot: a logical. Should the results be plotted? 

  gumbel: [gevglmFit] - 
           a logical, should a Gumbel fit be created? In this case the
          shape parameter equals zero, and the arguments 'shl' and and 
          'shlink' are omitted. 

       m: [gevglmprofPlot] - 
           the return level; i.e. the profile likelihood is for the
          value  that is exceeded with probability 1/'m'. 

   maxit: [gevglmFit] - 
           the maximum number of iterations. 

  method: [gevglmFit] - 
           the optimization method (see 'optim' for details). 

mul, sigl, shl: [gevglmFit] - 
           numeric vectors of integers, giving the columns of 'ydat'
          that contain covariates for generalized linear modelling of
          the location, scale and shape parameters repectively (or
          'NULL' (the default) if the corresponding parameter is
          stationary). 

mulink, siglink, shlink: [gevglmFit] - 
           inverse link functions for generalized linear modelling of
          the  location, scale and shape parameters repectively. 

    nint: [gevglmprof*Plot] - 
           the number of points at which the profile likelihood is
          evaluated. 

  object: [summary][grlevelPlot] - 
           a fitted object of class '"gevglmFit"'. 

    show: [gevglmFit] - 
           a logical; if 'TRUE' (the default), print details of the
          fit. 

       x: [gevglmFit] - 
           a numeric vector of data to be fitted. 
           [print][plot] - 
           a fitted object of class '"gevglmFit"'. 

xlow, xup: [gevglmprof*Plot] - 
           the least and greatest value at which to evaluate the
          profile  likelihood. 

       y: [gevglmFit] - 
           a matrix of covariates for generalized linear modelling of
          the parameters (or 'NULL' (the default) for stationary
          fitting). The number of rows should be the same as the length
          of 'xdat'. 

   which: [plot][summary] - 
           a vector of logicals, one for each plot, denoting which plot
           should be displayed. 

     ...: [gevglmFit] - 
           control parameters optionally passed to the  optimization
          function. Parameters for the optimization function are passed
          to components of the 'control' argument of 'optim'.  
           [plot][summary] - 
           arguments passed to the plot function. 

_D_e_t_a_i_l_s:

     *Simulation:* 

      To simulate a GEV series use the function 'gevSim'.  

     *Parameter Estimation:* 

      'gevglmFit' fits by the Maximum-likelihood approach the
     generalized  extreme value distribution, including generalized
     linear modelling  of each parameter.  

     *Methods:* 

      'print.gevglm', 'plot.gevglm' and 'summary.gevglm'  are print,
     plot, and summary methods for a fitted object of class 
     'gevglmFit'. 

     *Profile Likelihood:* 

      'gevglmprofPlot' and 'gevglmprofxiPlot' produce profile 
     log-likelihoods for shape parameters and 'm' year/block return 
     levels for stationary GEV models using the output of the function 
     'gevFit'. 

     *Nonstationary Models:* 

      For non-stationary fitting it is recommended that the covariates
     within the generalized linear models are (at least approximately)
     centered and scaled (i.e. the columns of 'ydat' should be
     approximately centered and scaled).

_V_a_l_u_e:

     'gevglmFit' 
      returns a list containing the following components. A subset of
     these components are printed after the fit. If 'show'  is 'TRUE',
     then assuming that successful convergence is indicated, the
     components 'nllh', 'mle' and 'se' are always printed.

   trans: an logical indicator for a non-stationary fit. 

   model: a list with components 'mul', 'sigl' and 'shl'. 

    link: a character vector giving inverse link functions. 

    conv: the convergence code, taken from the list returned by
          'optim'. A zero indicates successful convergence. 

    nllh: the negative logarithm of the likelihood evaluated at the
          maximum likelihood estimates. 

    data: the data that has been fitted. For non-stationary models, the
          data is standardized. 

     mle: a vector containing the maximum likelihood estimates. 

     cov: the covariance matrix. 

      se: a vector containing the standard errors. 

    vals: a matrix with three columns containing the maximum likelihood
          estimates of the location, scale and shape parameters at each
          data point. 


     For stationary models four plots are produced; a probability plot,
     a quantile plot, a return level plot and a histogram of data with
     fitted density. For non-stationary models two plots  are produced;
     a residual probability plot and a residual quantile  plot. 

     'gevglmprofPlot'
      'gevglmprofxiPlot'
      a plot of the profile likelihood is produced, with a horizontal
     line  representing a profile confidence interval with confidence
     coefficient  'conf'.

_A_u_t_h_o_r(_s):

     Alec Stephenson for the code implemented from R's ismev package, 
      Stuart Scott for the original code, and Diethelm Wuertz for this
     R-port.

_R_e_f_e_r_e_n_c_e_s:

     Coles S. (2001); _Introduction to Statistical Modelling of Extreme
     Values_, Springer.

_E_x_a_m_p_l_e_s:

     ## SOURCE("fExtremes.54A-ExtremesGlm")

     ## Simulated GEV Data:
        xmpExtremes("\nStart: Simulte GEV Sample >")
        x = gevSim(model = list(shape = 0.25, location = 0, scale = 1), n = 1000)
        par(mfrow = c(2, 2))
        plot(x, main = "Simulated GEV Data")
        # Fit GEV Data:
        fit = gevglmFit(x) 
        print(fit)
        # Summarize Results:
        summary(fit, which = c(TRUE, TRUE, TRUE, FALSE))
        
     ## Simulated GEV Data:
        xmpExtremes("\nNext: Estimate Parameters >")
        ##> x = gevSim(model = list(shape = 0, location = 0, scale = 1), n = 1000)
        ##> par(mfrow = c(2, 2))
        ##> plot(x, main = "Simulated Gumbel Data")
        # Fit GEV Data:
        ##> fit = gevglmFit(x, gumbel = TRUE) 
        ##> print(fit)
        # Summarize Results:
        ##> summary(fit, which = c(TRUE, TRUE, TRUE, FALSE))
        
     ## Portpirie Data:
        xmpExtremes("\nNext: Fit Portpirie Data >")
        par(mfrow = c(2, 1))
        data(portpirie)
        fit = gevglmFit(portpirie[, 2])
        gevglmprofPlot(fit, m = 10, 4.1, 5)
        title(main = "Portpirie")
        gevglmprofxiPlot(fit, -0.3, 0.3)
        title(main = "Portpirie")
        
     ## Interactive Plot:
        ##> par(mfrow = c(2, 2))
        ##> plot(fit)

