Sigma_fun {degross}

Variance-covariance of sample central moments (root-n approximation) given the vector mu with the theoretical moments of order 1 to 8. CAREFUL: the result must be divided by n (= sample size)!

Description

Variance-covariance of sample central moments (root-n approximation) given the vector mu with the theoretical moments of order 1 to 8. CAREFUL: the result must be divided by n (= sample size)!

Usage

Sigma_fun(mu)

Arguments

mu

Vector of length 8 with the first 8 theoretical central moments.

Value

Variance-covariance matrix of the first four sample central moments (CAREFUL: a division by the sample size is further required !)

Author(s)

Philippe Lambert [e-mail]

References

Lambert, P. (2021) Moment-based density and risk estimation from grouped summary statistics. arXiv:2107.03883.

Examples

mu = numeric(8)
dfun = function(x) dgamma(x,10,5)
mu[1] = integrate(function(x) x*dfun(x),0,Inf)$val
for (j in 2:8) mu[j] = integrate(function(x) (x-mu[1])^j*dfun(x),0,Inf)$val
Sigma_fun(mu)