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Antistarshapedness, dispersiveness and mixtures

Published online by Cambridge University Press:  14 July 2016

James Lynch
James Lynch*
Affiliation:
University of South Carolina
*
∗Postal address: Department of Statistics, University of South Carolina, Columbia, SC 29208, USA.
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Abstract

Classes of distributions are defined in terms of antistarshapedness or dispersiveness. Necessary and sufficient conditions are given for these classes to be closed under mixtures. These conditions characterize distributions with log-concave densities.

Keywords

MIXTUREQUANTILE PLOTSLOG CONCAVE
Type
Short Communications
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 265 - 269
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research carried out in part at The Pennsylvania State University, and supported in part by U.S. Army Research Office Grant No. DAA G29-84K-0007.

References

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt Rinehart and Winston, Inc., New York.Google Scholar
Bickel, P. J. and Lehmann, E. L. (1979) Descriptive statistics for nonparametric models IV: spread. In Contributions to Statistics — Jaroslav Hajek Memorial Volume, 33–40.Google Scholar
Doksum, K. (1969) Starshaped transformations and the power of rank tests. Ann. Math. Statist. 40, 1167–1176.Google Scholar
Droste, W. and Wefelmeyer, W. (1985) A note on strong unimodality and dispersity. J. Appl. Prob. 22, 235–239.Google Scholar
Leon, R. and Lynch, J. (1983) Preservation of life distribution classes under reliability operations. Math. Operat. Res. 8, 159–169.Google Scholar
Lewis, T. and Thompson, J. W. (1981) Dispersive distributions, and the connection between dispersivity and strong unimodality. J. Appl. Prob. 18, 76–90.10.2307/3213168Google Scholar
Lynch, J., Mimmack, G. and Proschan, F. (1983) Dispersive ordering results. Adv. Appl. Prob. 15, 889–891.10.2307/1427332Google Scholar
Saunders, I. W. (1978) Locating bright spots in a point process. Adv. Appl. Prob. 10, 587–612.Google Scholar
Saunders, I. W. and Moran, P. A. P. (1978) On the quantiles of the gamma and F distributions. J. Appl. Prob. 15, 426–432.Google Scholar
Shaked, M. (1980) On mixtures from exponential families. J. R. Statist. Soc. B 42, 192–198.Google Scholar
Shaked, M. (1982) Dispersive ordering of distributions. J. Appl. Prob. 19, 310–320.10.2307/3213483Google Scholar
Schweder, T. (1982) On the dispersion of mixtures. Scand. J. Statist. 9, 165–169.Google Scholar