Distribution of Order Statistics for Discrete Parents with Applications to Censored Sampling
Abstract
This paper studies distributions of order statistics (o.s.'s) from a general discrete parent, and is intended to explicitly present those distributions in such a way that the results are applicable in practice. The possibility of ties is one of the main reasons that the discrete case is more difficult than the continuous case. The new concept of a 'tie-run' is defined in this paper as a subchain consisting of equal real numbers, which makes it feasible to explicitly express the joint probability mass function of k discrete o.s.'s, and also conditional distributions of discrete o.s.'s. This paper shows that discrete o.s.'s possess a property that parallels Tukey's (Ann. Math. Statist. 18 (1947) 529-539) implication for conditional distributions of continuous o.s.'s. Finally, several examples are given to illustrate the utility of the results. © 1995.
Recommended Citation
G. Gan and L. J. Bain, "Distribution of Order Statistics for Discrete Parents with Applications to Censored Sampling," Journal of Statistical Planning and Inference, vol. 44, no. 1, pp. 37 - 46, Elsevier, Jan 1995.
The definitive version is available at https://doi.org/10.1016/0378-3758(95)92781-5
Department(s)
Mathematics and Statistics
Keywords and Phrases
Censored sampling; Conditional distribution; Discrete order statistics; Maximum likelihood estimation
International Standard Serial Number (ISSN)
0378-3758
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Elsevier, All rights reserved.
Publication Date
01 Jan 1995
