Download PDF - On monotone dependence functions of the quantile typeAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On monotone dependence functions of the quantile type

Authors 1, 1

Affiliations

  1. Institute of Mathematics, M. Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Abstract

We introduce the concept of monotone dependence function of bivariate distributions without moment conditions. Our concept gives, among other things, a characterization of independent and positively (negatively) quadrant dependent random variables.

Keywords

ENG
associated random variables, quantile monotone dependence function, mixture of distribution functions, quantile, independent, positively (negatively) quadrant dependent random variables, monotone dependence function

Bibliography

  1. N. Blomquist, On a measure of dependence between two random variables, Ann. Math. Statist. 21 (1950), 593-600.
  2. K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1982), 286-295.
  3. T. Kowalczyk, General definition and sample counterparts of monotonic dependence functions of bivariate distributions, Math. Operationsforsch. Statist. Ser. Statist. 8 (1987), 351-369.
  4. T. Kowalczyk and E. Pleszczyńska, Monotonic dependence functions of bivariate distributions, Ann. Statist. 5 (1977), 1221-1227.
  5. T. Kowalczyk, E. Pleszczyńska and W. Szczesny, Evaluation of stochastic dependence, in: Statistical Inference. Theory and Practice, T. Bromek and E. Pleszczyńska (eds.), PWN, Warszawa, and Kluwer Academic Publishers, Dordrecht, 1991, 106-132.
  6. A. Krajka and D. Szynal, Nonparametric functional characteristics of dependence, C. R. Acad. Sci. Paris Sér. I 315 (1992), 1107-1112.
  7. L. Kubik, Sur un problème de M. D. Dugue, Comment. Math. (Prace Mat.) 13 (1969), 1-2.
  8. E. L. Lehmann, Some concepts of dependence, Ann. Math. Statist. 37 (1966), 1137-1153.
  9. B. Schweitzer et E. F. Wolff, Sur une mesure de dépendance pour les variables aléatoires, C. R. Acad. Sci. Paris Sér. A 283 (1976), 659-661.
  10. B. Schweitzer et E. F. Wolff, On nonparametric measures of dependence for random variables, Ann. Statist. 9 (1981), 879-885.
Applicationes Mathematicae
1995-1996/23/1
Export to PBN, Opens in new tab
Pages:
51-72
Main language of publication
English
Received
1994-01-13
Accepted
1994-10-06
Published
1995
Exact and natural sciences