On testing the equality in dispersion of two probability distributions

Marzec, Leszek; Marzec, Paweł

doi:10.1093/biomet/78.4.923

Cited by 17 publications

(6 citation statements)

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“…Therefore, in this important case, the finiteness of the expectation is all what is needed to ensure the asymptotic normality whereas the asymptotic behavior of most related test statistics in the literature involves the existence of the second moment. See for instance, Aly (1990, Theorem 2.1), Marzec and Marzec (1991 …”

Section: Testing Stochastic Equality Against Strict Dominancementioning

confidence: 99%

Tests for the Second Order Stochastic Dominance Based onL-Statistics

Berrendero

Cárcamo

2011

Journal of Business & Economic Statistics

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We use some characterizations of convex and concave-type orders to define discrepancy measures useful in two testing problems involving stochastic dominance assumptions. The results are connected with the mean value of the order statistics and have a clear economic interpretation in terms of the expected cumulative resources of the poorest (or richest) in random samples. Our approach mainly consists in comparing the estimated means in ordered samples of the involved populations. The test statistics we derive are functions of L-statistics and are generated through estimators of the mean order statistics. We illustrate some properties of the procedures with simulation studies and an empirical example.

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Section: Testing Stochastic Equality Against Strict Dominancementioning

confidence: 99%

Tests for the Second Order Stochastic Dominance Based onL-Statistics

Berrendero

Cárcamo

2011

Journal of Business & Economic Statistics

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“…For instance, Aly (1990) and Marzec and Marzec (1991) considered the dispersive order, Belzunce et al (2000Belzunce et al ( , 2005b) the dilation order, Belzunce et al (2001) the right spread order, Kochar et al (2002) the new better than used in expectation (NBUE) order, Belzunce et al (2005a) the total time on test transform order, Berrendero and Cárcamo (2010) the convex-type orders.…”

Section: Introductionmentioning

confidence: 99%

Tests for Stochastic Orders and Mean Order Statistics

Berrendero

Cárcamo

2012

Communications in Statistics - Theory and Methods

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The aim of this note is to emphasize the fact, not observed previously in the literature, that many discrepancy measures used in tests related to different stochastic orders can be expressed as expectations of order statistics. In this way, we provide a new meaning to the corresponding test statistics which allows us to understand better, and potentially improve, the testing procedures. As illustration, we consider tests to detect overdispersion with respect to a specific probability model. In this setting, a test for the Weibull distribution is discussed in detail.

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“…Many researchers (Doksum (1969), Lewis and Thompson (1981), Shaked (1982), Emad-Eldin Aly (1990), Bartoszewicz and Bednarski (1990), Marzec and Marzec (1991) among others) have proposed tests for testing dispersive ordering of two distributions. Many researchers (Doksum (1969), Lewis and Thompson (1981), Shaked (1982), Emad-Eldin Aly (1990), Bartoszewicz and Bednarski (1990), Marzec and Marzec (1991) among others) have proposed tests for testing dispersive ordering of two distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Testing procedures for this and some other dispersive orders have been developed by Doksum (1969), Emad-Eldin Aly (1990), as well as Marzec and Marzec (1991). Marzec and Marzec (1991) defined…”

Section: Introductionmentioning

confidence: 99%