qmvnorm               package:mvtnorm               R Documentation

_Q_u_a_n_t_i_l_e_s _o_f _t_h_e _M_u_l_t_v_a_r_i_a_t_e _N_o_r_m_a_l _D_i_s_t_r_i_b_u_t_i_o_n

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

     Computes the equicoordinate quantile function of the multivariate
     normal distribution for arbitrary correlation matrices based on an
     inversion of the algorithms by Genz and Bretz.

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

     qmvnorm(p, interval = c(-10, 10), tail = c("lower.tail", "upper.tail", "both.tails"), 
             mean = 0, corr = NULL, sigma = NULL, maxpts = 25000, abseps = 0.001, 
             releps = 0, ...)

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

       p: probability.

interval: a vector containing the end-points of the interval to be
          searched by 'uniroot'.

    tail: specifies which quantiles should be computed. 'lower.tail'
          gives the quantile x for which  P[X <= x] = p, 'upper.tail'
          gives x with  P[X > x] = p and  'both.tails' leads to x  with
          P[-x <= X <= x] = p.

    mean: the mean vector of length n. 

    corr: the correlation matrix of dimension n.

   sigma: the covariance matrix of dimension n. Either 'corr' or
          'sigma' can be specified. If 'sigma' is given, the problem is
          standardized. If neither 'corr' nor 'sigma' is given, the
          identity matrix is used for 'sigma'. 

  maxpts: maximum number of function values as integer. 

  abseps: absolute integration error tolerance as double. 

  releps: relative integration error tolerance as double. 

     ...: additional paramters to be passed to 'uniroot'.

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

     Only equicoordinate quantiles are computed, i.e., the quantiles in
     each dimension coincide. Currently, the distribution function is
     inverted by  using the 'uniroot' function which may result in
     limited accuracy of the  quantiles.

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

     A list with four components: 'quantile' and 'f.quantile'  give the
     location of the quantile and the value of the function evaluated
     at that point. 'iter' and 'estim.prec' give the number  of
     iterations used and an approximate estimated precision from
     'uniroot'.

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

     'pmvnorm', 'qmvt'

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

     qmvnorm(0.95, sigma = diag(2), tail = "both")

