Strong unimodality of discrete order statistics. (English) Zbl 1463.62145
Summary: M. Alimohammadi et al. [ibid. 103, 176–185 (2015; Zbl 1328.62282)] showed that the smallest and largest order statistics from a discrete strongly unimodal distribution, are strongly unimodal. In this note, we generalize their result to all order statistics, which proves their conjecture.
MSC:
| 62G30 | Order statistics; empirical distribution functions |
| 60E05 | Probability distributions: general theory |
Citations:
Zbl 1328.62282References:
| [1] | Alam, K., Unimodality of the distribution of an order statistic, Ann. Math. Stat., 43, 2041-2044, (1972) · Zbl 0251.62031 |
| [2] | Alimohammadi, M.; Alamatsaz, M. H.; Cramer, E., Discrete strong unimodality of order statistics, Statist. Probab. Lett., 103, 176-185, (2015) · Zbl 1328.62282 |
| [3] | Arnold, B. C.; Balakrishnan, N.; Nagaraja, H. N., A first course in order statistics, (2008), SIAM Philadelphia · Zbl 1172.62017 |
| [4] | Barlow, R. E.; Proschan, F., Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Stat., 37, 1574-1592, (1966) · Zbl 0149.15402 |
| [5] | Cramer, E., Logconcavity and unimodality of progressively censored order statistics, Statist. Probab. Lett., 68, 83-90, (2004) · Zbl 1095.62059 |
| [6] | Dharmadhikari, S.; Joag-Dev, K., Unimodality, convexity, and applications, (1988), Academic Press Boston · Zbl 0646.62008 |
| [7] | Huang, J. S.; Ghosh, M., A note on strong unimodality of order statistics, J. Amer. Statist. Assoc., 77, 929-930, (1982) · Zbl 0507.62048 |
| [8] | Keilson, J.; Gerber, H., Some results for discrete unimodality, J. Amer. Statist. Assoc., 66, 386-389, (1971) · Zbl 0236.60017 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
