Rekursionsformeln für die zentralen Momente derPólya- und der Beta-Verteilung

Zusammenfassung In der vorliegenden Arbeit werden insbesondere explizite Darstellungen der gewöhnlichen Momente und Rekursionsformeln für die zentralen Momente derPólya- und Beta-Verteilung hergeleitet. Dazu werden gewisse positive lineare Polynom-Operatoren der Approximationstheorie benutzt, die speziell auch die bekannten Bernstein-Polynome enthalten. Die Sätze sind deshalb sehr allgemein formuliert, um sie auch in der Approximationstheorie anwenden zu können.

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Summary In this paper some explicit representations of the moments about zero and recurrence formulas of the central moments for thePólya- and Beta-distribution are given. For this purpose certain positive linear polynomial operators of approximation theory are used. These operators contain in particular the well-known Bernstein-polynomials. The theorems are formulated in a general way to use them in approximation theory.

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Die Vorbereitung dieses Artikels wurde unterstützt von der Deutschen Forschungs-Gemeinschaft.     

Eine zweifache Verallgemeinerung der Pólya-Verteilung und ihre verschiedenen Deutungen

Zusammenfassung Die erste Verallgemeinerung der Pólya-Verteilung durch Ziehungen aus einer Urne, die Kugeln ins verschiedenen Farben enthält, wird aufr Ziehungsgruppen verallgemeinert und entspricht damit einer Überschreitungswahrscheinlichkeit beir+1 Serien von Stichproben und einer Wartezeitverteilung (Gruppe vons–1 Warteperioden) bei einer geeignet gefüllten Urne mit Kugeln inr Farben sowie der Transponierungswahrscheinlichkeit bei einem Kugelziehungsproblem und weiteren Deutungen; die interessierenden Varianzen und Kovarianzen werden angegeben und mit denen einer verallgemeinerten hypergeometrischen Verteilung verglichen.

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Summary The first generalization ofPólya's distribution by taking balls from an urn with balls ins colours is generalized tor series of takings and thus corresponds to a generalized distribution of exceendances, a certain waiting-problem, to a law of succession and certain other interpretations. Variances and covariances are calculated and compared with those of a generalized hypergeometric distribution.

     

Charakterisierung der zweiseitigen Exponentialverteilung

LetF () be a family of distribution functions with a translation parameter such thatF (0) has a densityf. It is well known that each sample median is a maximum likelihood estimate of , iff belongs to the classE of all bilateral exponential densities which are symmetric about 0. Here it is shown that, conversely,fE holds, either if there is an evenm such that for every sample of sizem each median is an MLE of , or if there is an infinite setM such that for every sample of any sizemM at least one median is an MLE of .     

Optimal variance- and efficiency-balanced designs for one- and two-way elimination of heterogeneity

Summary In this paper, a series ofE-optimal non-binary variance balanced (block or row-column) designs and a series ofE-optimal non-binary efficiency balanced (block or row-column) designs are provided in certain broad classes of competing designs. Furthermore, their high efficiencies by the usualA- andD-optimality criteria are shown.     

Environmental policy in the two-country-case

Summary The paper analyzes the problem how environmental policy affects sector structure, the allocation of resources, relative price (and comparative advantage) and national income in a two-country case with varying terms of trade. The frame of reference is a two-sector model in which production generates pollutants as a joint product. If a country exports the pollution-intensively produced commodity environmental policy will improve its terms of trade under suitable conditions with respect to demand. Whereas in the political debate the negative effect of environmental policy on the international competiveness of a country is stressed, the terms-of-trade effect gives more leeway to environmental policy. The effects on output, export, imports and the other variables of the system are discussed.Help for calculating the results is acknowledged to J. Eichberger. I acknowledge helpful comments from an anonymous referee. I am also grateful to the Deutsche Forschungsgemeinschaft for financial support.