Estimate the statistical dimension and variance from sample data

estim_statdim_var estimates the statistical dimension and the variance of intrinsic volumes from samples from the corresponding bivariate chi-bar-squared distribution.

estim_statdim_var(d, m_samp)

Arguments

d	the dimension of the bivariate chi-bar squared distribution.
m_samp	two-column matrix whose rows from iid samples from the bivariate chi-bar-squared distribution corresponding to the cone

Value

The output of estim_statdim_var is a two-element list consisting of the esimated statistical dimension delta and variance var,

See also

rbichibarsq, ellips_rbichibarsq, polyh_rbichibarsq_gen, polyh_rbichibarsq_ineq

Package: conivol

Examples

v <- circ_ivols(10,pi/8)
m_samp <- rbichibarsq(10^4,v)
estim_statdim_var(10, m_samp)
#> $delta
#> [1] 2.171754
#> 
#> $var
#> [1] 2.451442
#> 

# true values:
list( delta=sum((1:length(v)-1)*v),
      var=sum((1:length(v)-1)^2*v)-sum((1:length(v)-1)*v)^2 )
#> $delta
#> [1] 2.12358
#> 
#> $var
#> [1] 2.229463
#>