dcor0                 package:GeneTS                 R Documentation

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

     Density and distribution function and a random number generator of
     Pearson's correlation coefficient assuming that there is no
     correlation present (rho = 0).

     The degree of freedom kappa depends both on the sample size N and
     the number G of investigated variables,  i.e. whether simple or
     partial correlation coefficients are being considered. For G=2
     (simple correlation coefficient) the degree of freedom equals
     kappa = N-1, whereas for arbitrary G (with G-2 variables
     eliminated in the partial correlation coefficient) kappa = N-G+1
     (see also 'cor0.estimate.kappa').

     The incomplete beta function is needed to compute the distribution
     function. For z=1 the incomplete beta function reduces to the beta
     function ('ibeta'(1, a, b) = 'beta'(a, b)).

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

     dcor0(x, kappa, log=FALSE)
     pcor0(q, kappa, lower.tail=TRUE, log.p=FALSE)
     rcor0(n, kappa)
     ibeta(z, a, b)

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

     x,q: vector of sample correlations

   kappa: the degree of freedom of the distribution

       n: number of values to generate. If n is a vector, length(n)
          values will be generated

log, log.p: logical vector; if TRUE, probabilities p are given as
          log(p)

lower.tail: logical vector; if TRUE (default), probabilities are P[R <=
          r], otherwise, P[R > r]

   a,b,z: numeric vectors

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

     For density and distribution functions (as well as a corresponding
     random number generator) of the correlation coefficient for
     arbitrary values of rho please refer to the 'SuppDists' package by
      Bob Wheeler bwheeler@echip.com (available on CRAN). Note that the
     parameter N in the 'dPearson' function (and others in the 
     'SuppDists' package) corresponds to  N=kappa+1 (i.e. G=2).

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

     The output values conform to the output from other such functions 
     in R. 'dcor0' gives the density and 'pcor0'  the distribution
     function.

     The function 'ibeta' returns a numeric value.

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

     Juliane Schaefer (<URL:
     http://www.stat.uni-muenchen.de/~schaefer/>) and Korbinian
     Strimmer (<URL: http://www.stat.uni-muenchen.de/~strimmer/>).

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

     'cor', 'cor0.estimate.kappa', 'beta'.

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

     # load GeneTS library
     library(GeneTS)

     # distribution of r for various degrees of freedom
     x <- seq(-1,1,0.01)
     y1 <- dcor0(x, kappa=7)
     y2 <- dcor0(x, kappa=15)
     plot(x,y2,type="l", xlab="r", ylab="pdf",
       xlim=c(-1,1), ylim=c(0,2))
     lines(x,y1)

     # simulated data
     r <- rcor0(1000, kappa=7)
     hist(r, freq=FALSE, 
       xlim=c(-1,1), ylim=c(0,5))
     lines(x,y1,type="l")

     # distribution function
     pcor0(-0.2, kappa=15)

     # incomplete beta function
     ibeta(0.4, 1, 3)
     ibeta(1, 2, 3)
     beta(2, 3)

