Belomestnyi, D. V.; Prokhorov, A. V. Reconstruction of a general distribution from the distribution of a linear statistics. (English. Russian original) Zbl 1052.60014 Mosc. Univ. Math. Bull. 58, No. 2, 1-6 (2003); translation from Vestn. Mosk. Univ., Ser. I 2003, No. 2, 3-8 (2003). The authors discuss the problem on renewal of the distribution of independent similarly distributed random values \(\,X_1,\dots,X_m\,\) by the distribution of linear statistics \(\,L=\beta_1X_1+\dots+\beta_mX_m\), \(\,\beta_k>0\). A univalence criterion is obtained for such renewal and its stability is studied. Reviewer: R. K. Azimov (Andizhan) Cited in 1 Document MSC: 60E05 Probability distributions: general theory 60E10 Characteristic functions; other transforms Keywords:renewal of general distribution; linear statistics PDF BibTeX XML Cite \textit{D. V. Belomestnyi} and \textit{A. V. Prokhorov}, Mosc. Univ. Math. Bull. 58, No. 2, 3--8 (2003; Zbl 1052.60014); translation from Vestn. Mosk. Univ., Ser. I 2003, No. 2, 3--8 (2003)