Nguyen, Truc T.; Gupta, Arjun K.; Nguyen, Diem M.; Dinh, Khoan T. A location-scale family generated by a given symmetric distribution and the sample variance. (English) Zbl 1068.62011 Far East J. Theor. Stat. 15, No. 2, 235-249 (2005). Summary: Let \(X_i\), \(i=1,\dots,n\), \(n\geq 2\), be a random sample from a distribution \(F\) of a location scale family of distribution \(F_0((x-\mu)/ \sigma)\), \(\mu\) is some real number, \(\sigma>0\) for some given distributions \(F_0\). Assume that \(F_0\) is a symmetric distribution with finite moments of all orders and is determined by its moments. Two characterizations of \(F_0((x-\mu)/\sigma)\) based on the distribution function \(G_n\) of \(\sum^n_{i=1}(X_i-\overline X)^2/\sigma^2\), are given. Cited in 1 Document MSC: 62E10 Characterization and structure theory of statistical distributions 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62N05 Reliability and life testing Keywords:normal distribution; chi-square distribution; homogeneous polynomial; sequences of equations; moments PDFBibTeX XMLCite \textit{T. T. Nguyen} et al., Far East J. Theor. Stat. 15, No. 2, 235--249 (2005; Zbl 1068.62011)