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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.

MSC:
60E05 Probability distributions: general theory
60E10 Characteristic functions; other transforms
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