Berrendero, José R.; Cárcamo, Javier Tests for stochastic orders and mean order statistics. (English) Zbl 1319.60032 Commun. Stat., Theory Methods 41, No. 7-9, 1497-1509 (2012). Summary: The aim of this article 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. Cited in 3 Documents MSC: 60E15 Inequalities; stochastic orderings 62G10 Nonparametric hypothesis testing 62E20 Asymptotic distribution theory in statistics 62N05 Reliability and life testing Keywords:convex order; dilation order; dispersive order; DMRL; exponential distribution; HNBUE; hypothesis testing; NBUE; order statistics; total time on test transform order; Weibull distribution PDFBibTeX XMLCite \textit{J. R. Berrendero} and \textit{J. Cárcamo}, Commun. Stat., Theory Methods 41, No. 7--9, 1497--1509 (2012; Zbl 1319.60032) Full Text: DOI Link References: [1] DOI: 10.1016/0167-7152(90)90140-3 · Zbl 0692.62043 [2] DOI: 10.1137/1.9780898719062 · Zbl 1172.62017 [3] DOI: 10.1016/j.csda.2008.12.012 · Zbl 1453.62034 [4] DOI: 10.1017/S026996480014104X · Zbl 0955.60019 [5] DOI: 10.1016/S0378-3758(99)00167-6 · Zbl 0953.62108 [6] DOI: 10.1016/j.jspi.2004.03.008 · Zbl 1065.62174 [7] DOI: 10.1016/S0167-7152(01)00075-X · Zbl 1052.62045 [8] DOI: 10.1007/BF02915440 · Zbl 1092.62105 [9] DOI: 10.1016/j.jspi.2008.11.010 · Zbl 1161.60304 [10] DOI: 10.1198/jbes.2010.07224 · Zbl 1214.62048 [11] DOI: 10.1239/jap/1158784940 · Zbl 1127.62046 [12] DOI: 10.1239/jap/1269610831 · Zbl 1200.62141 [13] DOI: 10.1016/S0167-7152(99)00166-2 · Zbl 0958.60011 [14] DOI: 10.1080/00949659808811891 · Zbl 0931.62085 [15] DOI: 10.1016/S0167-7152(99)00157-1 · Zbl 0977.62103 [16] Klefsjö B., Scand. J. Statist. 10 pp 65– (1983) [17] DOI: 10.1239/aap/1037990955 · Zbl 1031.62086 [18] DOI: 10.1006/jmva.2000.1954 · Zbl 1019.60028 [19] DOI: 10.1214/aoms/1177728551 · Zbl 0064.38403 [20] DOI: 10.1093/biomet/78.4.923 · Zbl 0850.62375 [21] Murthy D. N. P., Weibull Models (2004) · Zbl 1047.62095 [22] Rinne H., The Weibull Distribution. A Handbook (2009) · Zbl 1270.62040 [23] DOI: 10.1002/9780470316481 · Zbl 0538.62002 [24] Shaked M., Stochastic Orders (2006) [25] Shorack G. R., Empirical Processes with Applications to Statistics (1986) · Zbl 1170.62365 [26] DOI: 10.1007/s00362-006-0329-4 · Zbl 1114.60021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.