Total positivity and dependence of order statistics

Author:

Amo Enrique de1,Quesada-Molina José Juan2,Úbeda-Flores Manuel1

Affiliation:

1. Department of Mathematics, University of Almería, 04120 Almería, Spain

2. Department of Applied Mathematics, University of Granada, 18071 Granada, Spain

Abstract

<abstract><p>In this comprehensive study, we delve deeply into the concept of multivariate total positivity, defining it in accordance with a direction. We rigorously explore numerous salient properties, shedding light on the nuances that characterize this notion. Furthermore, our research extends to establishing distinct forms of dependence among the order statistics of a sample from a distribution function. Our analysis aims to provide a nuanced understanding of the interrelationships within multivariate total positivity and its implications for statistical analysis and probability theory.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference21 articles.

1. K. Jogdeo, Concepts of dependence, in Encyclopedia of Statistical Sciences, vol. 1, (eds. S. Kotz and N.L. Johnson) New York: Wiley, 1982,324–334.

2. P. Čížek, R. Weron, W. Härdle, Statistical Tools for Finance and Insurance, Berlin: Springer, 2005. http://dx.doi.org/10.1007/978-3-642-18062-0

3. R. E. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing: Probability Models, Silver Spring, MD: To Begin With, 1981.

4. H. Joe, Multivariate Models and Dependence Concepts, London: Chapman & Hall, 1997. http://dx.doi.org/10.1201/9780367803896

5. S. Karlin, Total Positivity, Stanford, CA: Stanford University Press, 1968.

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