RlargFit              package:fExtremes              R Documentation

_M_o_d_e_l_l_i_n_g _t_h_e _O_r_d_e_r _S_t_a_t_i_s_t_i_c _M_o_d_e_l

_D_e_s_c_r_i_p_t_i_o_n:

     A collection and description of functions to model  the Order
     Statistic Model by maximum likelihood  approximation based on R's
     'ismev' package. The  parameter estimation allows to include
     generalized  linear modelling of each parameter. 

     The functions are:

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

_U_s_a_g_e:

     rlargFit(x, r = dim(x)[2], y = NULL, mul = NULL, sigl = NULL,
         shl = NULL, mulink = identity, siglink = identity, shlink = identity,
         method = "Nelder-Mead", maxit = 10000, ...)

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

_A_r_g_u_m_e_n_t_s:

  doplot: a logical. Should the results be plotted? 

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

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

mul, sigl, shl: [rlargFit] - 
           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: [rlargFit] - 
           inverse link functions for generalized linear modelling of
          the  location, scale and shape parameters repectively. 

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

       r: [rlargFit] - 
           the largest 'r' order statistics are used for the fitted
          model. 

       x: [rlargFit] - 
           a numeric matrix of data to be fitted. Each row should be a
          vector  of decreasing order, containing the largest order
          statistics for  each year (or time period). The first column
          therefore contains annual  (or period) maxima. Only the first
          'r' columns are used for the fitted model. By  default, all
          columns are used. If one year (or time period) contains fewer
          order statistics than  another, missing values can be
          appended to the end of the  corresponding row. 
           [print][plot] - 
           a fitted object of class '"rlargFit"'. 

       y: [rlargFit] - 
           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
          number of rows of  'x'. 

   which: [print][plot][summary] - 
           a logical for each plot, denoting which plots should be
          created. 

     ...: [rlargFit][plot] - 
           control parameters and plot parameters optionally passed to
          the  optimization and/or plot function. Parameters for the
          optimization function are passed to components of the
          'control' argument of 'optim'. 

_D_e_t_a_i_l_s:

     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:

     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. 

       r: The number of order statistics used. 


     For stationary models four plots are initially produced; a
     probability plot, a quantile plot, a return level plot and a
     histogram of data with fitted density. Then probability and
     quantile plots are produced for the largest 'n' order statistics.
     For non-stationary models  residual probability plots and residual
     quantile plots are  produced for the largest 'n' order statistics.

_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.54D-RlargFit")

     ## Use Venice Data:
        data(venice)
        
     ## Fit for the order statistic model:
        xmpExtremes("Start: Parameter Fit for Order Statistics Model > ")
        fit = rlargFit(venice[, 2:4], r = 3)
        fit
        
     ## Summarize Results:
        xmpExtremes("Next: Diagnostic Analysis > ")
        summary(fit) 

