rlargFit              package:fExtremes              R Documentation

_M_a_x_i_m_u_m-_l_i_k_e_l_i_h_o_o_d _F_i_t_t_i_n_g _o_f _O_r_d_e_r _S_t_a_t_i_s_t_i_c_s _M_o_d_e_l

_D_e_s_c_r_i_p_t_i_o_n:

     This is a collection 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:

       1  'gpdglmFit'         fits empirical or simulated data to the distribution,
       2  'print'             print method for a fitted GPD object of class ...,
       3  'plot'              plot method for a fitted GPD object,
       4  'summary'           summary method for a fitted GPD object,
       5  'gevglmprofPlot'    profile log-likelihoods for return levels,
       6  '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.

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

     'ppFit', 'potFit'.

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

     ## 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) 

