BivariateTools           package:fMultivar           R Documentation

_H_a_n_d_l_i_n_g _M_i_s_s_i_n_g _V_a_l_u_e_s

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

     A collection and description of functions  for managing bivariate
     data sets. The functions include a grid generator, a kernel
     density  estimator, a histogram counter, and a suite of bivariate
     elliptical distribution functions. 

     The functions are: 

       'grid2d'         Creates from two vectors x-y grid coordinates,
       'density2d'      returns 2D Kernel Density Estimates,
       'hist2d'         returns 2D Histogram Counts,
       'integrate2d'    integrates over a two dimensional unit square,
       'pnorm2d'        computes bivariate normal distribution function,
       'dnorm2d'        computes bivariate normal density function,
       'rnorm2d'        generates bivariate normal random deviates,
       'pcauchy2d'      computes bivariate Cauchy distribution function,
       'dcauchy2d'      computes bivariate Cauchy density function,
       'rcauchy2d'      generates bivariate Cauchy random deviates,
       'pt2d'           computes bivariate Student-t distribution function,
       'dt2d'           computes bivariate Student-t density function,
       'rt2d'           generates bivariate Student-t random deviates,
       'delliptical2d'  computes  bivariate density for elliptical distributions.

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

     grid2d(x = (0:10)/10, y = x)
     density2d(x, y = NULL, n = 20, h = NULL, limits = c(range(x), range(y))) 
     hist2d(x, y = NULL, n = c(20, 20))
     integrate2d(fun, error = 1.0e-5, ...)

     pnorm2d(x, y = x, rho = 0)
     dnorm2d(x, y = x, rho = 0)
     rnorm2d(n, rho = 0)

     pcauchy2d(x, y = x, rho = 0)
     dcauchy2d(x, y = x, rho = 0)
     rcauchy2d(n, rho = 0)

     pt2d(x, y = x, rho = 0, nu = 4)
     dt2d(x, y = x, rho = 0, nu = 4)
     rt2d(n, rho = 0, nu = 4)

     delliptical2d(x, y = x, rho = 0, param = NULL, type = c("norm", "cauchy", "t", 
         "logistic", "laplace", "kotz", "epower"), output = c("vector", "list"))

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

   error: [integrate2d] - 
           the error bound to be achieved by the integration formula. A
          numeric value. 

     fun: [integrate2d] - 
           the function to be integrated. The first argument requests
          the x values, the second the y values, and the remaining are
          reserved for additional parameters. The integration is  over
          the unit square "[0,1]\^2". 

       h: [density2d] - 
           a vector of bandwidths for 'x' and 'y' directions.  Defaults
          to normal reference bandwidth.  

  limits: [hist2d] - 
           the limits of the rectangle covered by the grid.    

       n: [density2d] - 
           n - an integer specifying the number of grid points in each 
          direction. The default value is 20.
           [hist2D] - 
           In this case 'n' may be a scalar or a two element vector. 
          The default value is 20.
           [rnorm2d] - 
           the number of random deviates to be generated, an integer
          value. 

      nu: [*t2d] - 
           the number of degrees of freedom, a numeric value ranging
          between  two and infinity, by default four.       

  output: [*elliptical2d] - 
           output - a character string specifying how the output should
          be  formatted. By default a vector of the same length as 'u' 
          and 'v'. If specified as '"list"' then 'u' and  'v' are
          expected to span a two-dimensional grid as outputted  by the
          function 'grid2d' and the function returns a list with
          elements '$x', 'y', and 'z' which can be directly  used for
          example by 2D plotting functions. 

   param: [delliptical2d] - 
           additional parameters to specify the bivariate density
          function. Only effective for the Kotz and Exponential Power
          distribution. For the Kotz distribution we can specify a
          numeric value, by default defined as 'param=c(r=sqrt(2))',
          and for the Exponential Power distribution a numeric vector,
          by default defined as 'param=c(r=sqrt(2)),s=1/2'. 

     rho: [*norm2d][*cauchy2d][*t2d][*elliptical2d] - 
           the correlation parameter, a numeric value ranging between 
          minus one and one, by default zero.      

    type: [*elliptical2d] - 
           the type of the elliptical copula. A character string
          selected  from: '"norm"', '"cauchy"', '"t"', '"laplace"', 
          '"kotz"', or '"epower"'. 

    x, y: [grid2d][*norm2d][*t2d] - 
           two numeric vectors defining the x and y coordinates. 
           [density2D][hist2D] - 
           two vectors of coordinates of data. If 'y' is NULL then 'x'
          is assumed to be a two column matrix, where the first  column
          contains the 'x' data, and the second column the  'y' data.  

     ...: [integrate2d] - 
           parameters passed to the function to be integrated.      

_V_a_l_u_e:

     'grid2d'  
      returns a list with two vectors named '$x' and '$y' spanning  the
     grid defined by the coordinate vectors 'x' and 'y'.

     'density2d'
      'hist2d' 
      returns a list with three elements '$x', '$y', and  '$z'. 'x' and
     'y' are vectors spanning the two  dimensional grid and 'z' the
     corresponding matrix. The  output can directly serve as input to
     the plotting functions  'image', 'contour' and 'persp'.

     'integrate2d' 
      returns a list with the '$value' of the integral over the unit
     square [0,1]\^2, an '$error' estimate and the number  of grid
     '$points' used by the integration function. 

     'pnorm2d' 
      returns a vector of probabilities for the normal distribution 
     function.  'pnorm2d' 
      returns a two column matrix of random deviates generated from the
     bivariate normal distribution function.

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

     W.N. Venables and B.D. Ripley for the underlying kde2d function, 
      Adelchi Azzalini for the underlying pnorm2d function, 
      Gregory R. Warnes for the underlying hist2d function, 
      Diethelm Wuertz for the Rmetrics R-port.

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

     Azzalini A., (2004); _The sn Package_; R Reference Guide available
     from www.r-project.org.

     Venables W.N., Ripley B.D., (2002);  _Modern Applied Statistics
     with S_, Fourth Edition, Springer.

     Warnes G.R., (2004); _The gregmisc Package_; R Reference Guide
     available from www.r-project.org.

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

     ## SOURCE("fMultivar.7A-BivariateTools")

     ## -

