Domains of attraction of the real random vector \((X,X^2)\) and applications. (English) Zbl 1265.60011

Omey, Edward; Van Gulck, Stefan

Publ. Inst. Math., Nouv. Sér. 86(100), 41-53 (2009).

This is an extension of results by the first author [Stochastics 80, No. 2–3, 211–227 (2008; Zbl 1138.60018)], to the case when the variables under consideration are real, not necessarily positive. Applying the results to the vector \(\left(\sum^n_{i=1}X_i,\;\sum^n_{i=1}X_i^2\right)\) enables the authors to discuss the asymptotic behavior of the sample variance \(s^2_{n-1}\), the sample coefficient of the variation SV\((n)\), the sample dispersion SD\((n)\) and the noncentral \(t\)-statistic \(t(n)\).

Reviewer: Slobodanka Janković (Beograd)

MSC:

60E05

Probability distributions: general theory

Keywords:

sample variance; sample coefficient of variation; noncentral \(t\)-statistic

Citations:

Zbl 1138.60018