Chebyshev–Edgeworth expansions for distributions of generalised Hotelling-type statistics based on random size samples

The general transfer theorem for the distribution function of asymptotically normal statistics was generalized on the Hotelling-type statistics case and analog of general transfer theorem for the distribution function of Hotelling-type statistics with random size was proved. It allowed to obtain the Chebyshev–Edgeworth expansion for initial Hotelling-type statistics. The explicit form of the Chebyshev–Edgeworth expansion was obtained for the case when the random sample size distribution is the negative binomial distribution shifted by 1. The limit distribution for this case was F-distribution. The Cornish–Fisher expansion was obtained for the special case of parameter of random sample size. The computational experiment was conducted and graphs were plotted for Chebyshev–Edgeworth expansion illustration.