@article{3fd5b102d055449cade76339fb49e78c,
title = "Strong unimodality of discrete order statistics",
abstract = "Alimohammadi et al. (2015) 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.",
keywords = "Discrete order statistics, Logconcavity, Strong modality, Unimodality",
author = "Bara Kim and Jeongsim Kim and Sungji Lee",
note = "Funding Information: We are grateful to the reviewers for valuable comments and suggestions, which greatly improved this paper.B. Kim{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2017R1A2B4012676 ). J. Kim{\textquoteright}s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2017R1D1A1B03029542 ). Funding Information: We are grateful to the reviewers for valuable comments and suggestions, which greatly improved this paper.B. Kim's research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1A2B4012676). J. Kim's research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03029542). Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",
year = "2018",
month = sep,
doi = "10.1016/j.spl.2018.04.018",
language = "English",
volume = "140",
pages = "48--52",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier",
}