Simple proofs of two results on convolutions of unimodal distributions

Statistics and Probability Letters

Volumn 39, Issue 2, 1998, Pages 97-100

  Purkayastha, Sumitra ^a,b  

^a INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

^b INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Convolution; Khintchine's representation; Symmetry; Unimodality

Indexed keywords

EID: 0032135834     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(98)00013-3     Document Type: Article

References (6)

1. Dharmadhikari, S.W., Joag-Dev, K., 1983. Unimodality of symmetrized unimodality laws and related results. In Bickel, P.J., Doksum, K., Hodges, J.L. Jr. (Eds.), A Festschrift for Erich L. Lehmann, Wadsworth, Belmont, CA, pp. 131-139.
2. Dharmadhikari, S.W., Joag-Dev, K., 1988. Unimodality, Convexity, and Applications. Academic Press, New York.
3. Hodges, J.L., Lehmann, E.L., 1954. Matching in paired comparisons. Ann. Math. Statist. 25, 787-791.
4. Khintchine, A.Y., 1938. On unimodal distributions. Izv. Nauchno-Isled. Inst. Mat. Mech. Tomsk. Gos. Univ. 2, 1-7.
5. Shepp, L.A., 1962. Symmetric random walk. Trans. Amer. Math. Soc. 104, 144-153.
6. Wintner, A., 1938. Asymptotic Distributions and Infinite Convolutions. Edwards Brothers, Ann Arbor, MI.