On monotone dependence functions of the quantile type

• Autorzy: Andrzej Krajka , Dominik Szynal
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1995-1996
• Tom: 23
• Numer: 1
• Strony: 51-72

Daty

wydano

1995

otrzymano

1994-01-13

poprawiono

1994-10-06

Twórcy

autor

Andrzej Krajka

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

autor

Dominik Szynal

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

Bibliografia

• [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.