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Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences. (English) Zbl 1076.60024

The authors define generalized absolute Lorenz curves (GALC) that include as special cases the classical and generalized L-statistics as well as the absolute Lorenz curve. The GALC are based on strictly stationary and ergodic sequences of random variables. The main result extends the strong law obtained in D. Gilat and R. Helmers [Commentat. Math. Univ. Carol. 38, 187–192 (1997; Zbl 0889.60029)] by relaxing the condition that the sequence of random variables is absolutely regular (or weakly Bernoullian). Removing this assumption means the results can be applied to a broader class of sequences including some long-range dependent sequences.

MSC:

60F15 Strong limit theorems

Citations:

Zbl 0889.60029
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