Summary
The paper presents nonparametric tests on different pairs of hypotheses which involve that two probability distributions are stochastically ordered. Let F and G be two probability distribution functions on the reals. First, we consider the null hypothesis that F is stochastically larger than G holds against the alternative that this is not the case. Second, the null that either F is stochastically larger than G or G is stochastically larger than F holds is tested against the alternative that this is not the case. Third, homogeneity, i.e. F = G, is taken as the null hypothesis, and F stochastically larger than G as the alternative. The tests employ Smirnov’s supremum statistic in various ways. A new statistic is introduced which is the minimum of the two one-sided Smirnov statistics. Related nonparametric test statistics are shortly surveyed. Applications include location tests with ordinal data, expected utility decisions under risk, comparisons of system reliability and specification tests for duration models.
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© 1995 Physica-Verlag Heidelberg
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Mosler, K. (1995). Testing Whether Two Distributions are Stochastically Ordered or Not. In: Rinne, H., Rüger, B., Strecker, H. (eds) Grundlagen der Statistik und ihre Anwendungen. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-93636-4_12
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DOI: https://doi.org/10.1007/978-3-642-93636-4_12
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