Remarks about the Dugué problem

• Autorzy: Krakowiak W.
• Języki publikacji: EN

Abstrakty

EN

The paper presents some new results of the Dugué problem of finding the characteristic functions φ₁ and φ₂ such that (1 − c) φ₁ + cφ₂ = φ₁ φ₂, 0 < c < 1.

Słowa kluczowe

EN

Dugué problem; arithmetics of probability measures; characteristic functions

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2003
• Tom: Vol. 23, Fasc. 1
• Strony: 93--104
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Krakowiak W.

• Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] D. Dugué, Sur les fonctions méromorphes transformées Fourier de fonctions monotones, C. R. Acad. Sci. 208 (1939), p. 1547.
• [2] D. Dugué, Arithmétique des lois de probabilitiés, Mém. Sci. Math. 137, Gauthier-Villars, Paris 1957.
• [3] L. Kubik, Sur un problème de M. D. Dugué, Comment. Math. (Prace Mat.) 13 (1969), pp. 1-2.
• [4] H. J. Rossberg, Characterization of the exponential and the Pareto distributions by means of some properties of the distributions which the differences and quotiens of order statistics are subject to, Math. Operationsforsch. Statist. 3 (1972), pp. 207-216.
• [5] D. Szynal and A. Wolińska, On classes of couples of characteristic functions satisfying the condition of Dugué, Comment. Math. (Prace Mat.) 23 (1983), pp. 325-328.
• [6] S. Vallander, I. Ibragimov and N. Lindtrop, On limiting distributions for moduli of sequential differences of independent variables (in Russian), Teor. Veroyatnost. i Primenen. 14 (1969), pp. 693-707.
• [7] A. Wolińska, On a problem of Dugué, Lecture Notes in Math. 982, Springer, Berlin 1982, pp. 244-253.
• [8] A. Wolińska-Wełcz, On a solution of the Dugué problem, Probab. Math. Statist. 7 (1986), pp. 169-185.