Tiago de Oliveira, J. Statistical choice of non-separated one-parameter models. (English) Zbl 0731.62083 Trab. Estad. Invest. Oper. 36, No. 2, 138-152 (1985). The purpose of this paper is to study the asymptotic choice between two models \(\{\) F(x\(| \alpha)\), \(\alpha\in A\subseteq {\mathbb{R}}\}\) and \(\{\) G(x\(| \beta \}\), \(\beta\in B\subseteq {\mathbb{R}}\}\), A and B being intervals but such that for \((\alpha_ 0,\beta_ 0)\), and only for this pair, we have \(F(x| \alpha_ 0)=G(x| \beta_ 0).\) As examples consider the models with distribution functions \(F(x| \alpha)=x^{\alpha}\) \((0<\alpha <+\infty)\) and \(G(x| \beta)=1-(1- x)^{\beta}\) \((0<\beta <+\infty)\) on the support [0,1] which coincide for the uniform distribution \((\alpha_ 0=1\), \(\beta_ 0=1)\) or the models with densities \(f(x| \alpha)=\alpha x^{\alpha -1}e^{- x^{\alpha}}\) (Weibull distribution) \((0<\alpha <+\infty)\) and \(g(x| \beta)=(\Gamma (\beta))^{-1}x^{\beta -1}e^{-x}\) (gamma distribution) \((0<\beta <+\infty)\), on the support \({\mathbb{R}}_+\), which coincide for the exponential distribution \((\alpha_ 0=1\), \(\beta_ 0=1)\). MSC: 62F99 Parametric inference 62F03 Parametric hypothesis testing Keywords:choice of statistical models; one-sided tests; two-sided tests; one- parameter models; asymptotic choice PDFBibTeX XMLCite \textit{J. Tiago de Oliveira}, Trab. Estad. Invest. Oper. 36, No. 2, 138--152 (1985; Zbl 0731.62083) Full Text: DOI EuDML References: [1] M. G. KENDALL and A. STUART (1961):The Advanced Theory of Statistics, vol. II, C. Griffin and Cy. · Zbl 0416.62001 [2] J. TIAGO DE OLIVEIRA (1981): “Statistical choice of univariate extreme models,Statistical Distributions in Scientific Work, vol. 6, D. Reidell and Cy. · Zbl 0484.62036 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.