A Power Comparison of Homogeneity Tests in Mixtures of Exponentials.pdfVIP

DISCUSSION PAPERS IN STATISTICSAND ECONOMETRICSSEMINAR OF ECONOMIC AND SOCIAL STATISTICSUNIVERSITY OF COLOGNENo. 3/97A Power Comparison ofHomogeneity Testsin Mixtures of ExponentialsbyKarl MoslerWilfried SeidelChristoph Jaschinger DISKUSSIONSBEITRAGE ZURSTATISTIK UND OKONOMETRIESEMINAR FUR WIRTSCHAFTS- UND SOZIALSTATISTIKUNIVERSITAT ZU KOLNAlbertus-Magnus-Platz, D-50923 Koln, Deutschland DISCUSSION PAPERS INSTATISTICS AND ECONOMETRICSSEMINAR OF ECONOMIC AND SOCIAL STATISTICSUNIVERSITY OF COLOGNENo. 3/97A Power Comparisonof Homogeneity Testsin Mixtures of ExponentialsbyKarl Mosler1Wilfried Seidel2Christoph Jaschinger1October 1997AbstractThe empirical power of several test procedures is studied which test forhomogeneity against mixtures of exponential distributions.AMS 1991 subject classications. Primary 62G10; secondary 62N05.Key words and phrases. Mixture components, mixture diagnosis, survival analysis,hazard models, overdispersion, goodness-of-t, likelihood ratio tests. 1Seminar fur Wirtschafts{ und Sozialstatistik, Universitat zu Koln, D-50923 Koln2Institut fur Statistik und Quantitative Okonomik, Universitat der Bundeswehr HamburgD-22039 Hamburg 1 Homogeneity Tests in Mixtures of Exponenti-alsIn survival analysis the distribution of a lifetimeY can often be modeled by a mixtureof exponential distributions; for some theory and applications see the recent surveyby McLachlan (1995). Then, with some unknown mixing distribution  on IR+, thesurvival function readsS(y) = P [Y y] = ZIR+ e yud(u); y  0: (1)We assume that  has nite fourth moment and RIR+ ud(u) 0. An importantproblem in many applications is whether, given the data,  is concentrated at somesingle point u0 0, in other words, whether Y follows a non-mixed exponentialdistribution with mean u0, or not.For testing the null hypothesis,H0 : (fu0g) = 1 at some u0 0; (2)i.e., \H0 : Y has density 1u0 exp( yu0 ), several approaches are practical, amongthem tests for overdispersion, likelih