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On the unimodality of multivariate symmetric distribution functions of class L. (English) Zbl 0379.60017


MSC:

60E05 Probability distributions: general theory
60F05 Central limit and other weak theorems
Full Text: DOI

References:

[1] Cuppens, R., (Decomposition of Multivariate Probability (1975), Academic Press: Academic Press New York) · Zbl 0363.60012
[2] Gnedenko, B. V.; Kolmogorov, A. N., (Limit Distributions for Sums of Independent Random Variables (1954), Addison-Wesley: Addison-Wesley Reading, Mass), (K. L. Chung, Tr.) · Zbl 0056.36001
[3] Kanter, M., Unimodality and dominance for symmetric random vectors, Trans. Amer. Math. Soc., 229, 65-86 (1976) · Zbl 0379.60015
[4] Lèvy, P., (Théorie de L’addition des Varaibles Aléatoires (1954), Gauthier-Villars: Gauthier-Villars Paris) · Zbl 0056.35903
[5] Olshen, R. A.; Savage, L. J., A generalized unimodality, J. Appl. Prob., 7, 21-34 (1970) · Zbl 0193.45102
[6] Ghurye, S. G., L’vov Gos Univ. Zap. Ser. Meh. Mat., 29, 5-44 (1954), from
[7] Tucker, H. G., (A Graduate Course in Probability (1962), Academic Press: Academic Press New York) · Zbl 0159.45702
[8] Urbanik, K., A representation of self-decomposable distributions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 16, 196-204 (1968)
[9] Urbanik, K., Self-decomposable probability distributions on \(R^m\). Self-decomposable probability distributions on \(R^m\), Zastos. Mat., 10, 91-97 (1969), (1969) · Zbl 0233.62003
[10] Urbanik, K., Lèvy’s probability on Euclidean spaces, Studia Math., 44, 119-148 (1972) · Zbl 0251.60022
[11] Wintner, A., Cauchy’s stable distributions and an “explicit formula” of Mellin, Amer. J. Math., 78, 819-861 (1956) · Zbl 0072.31903
[12] Wolfe, S. J., On the unimodality of \(L\) functions, Ann. Math. Statist., 42, 912-918 (1971) · Zbl 0219.60026
[13] Wolfe, S. J., On the unimodality of spherically symmetric stable distribution functions, J. Multivar. Anal., 5, 236-242 (1975) · Zbl 0318.60009
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