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.

---

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.     

On the optimality of limit cycles in dynamic economic systems

The purpose of this paper is to derive conditions for the optimality of a limit cycle in a dynamic economic system and to interpret them economically. A fairly general two-state continuous-time nonlinear optimal control problem is considered. It turns out that for this class of models three different economic mechanisms can be identified as the possible source of limit cycles. One relates to an intertemporal substitution effect expressed in terms of complementarity over time, the second one is a dominating cross effect between the state variables of the system (i.e., the capital stocks in our model), and the third one is positive growth at the equilibrium.We acknowledge the helpful comments by William A. Brock, Gerhard Sorger, Franz Wirl, and two anonymous referees. The research was partly supported by the Austrian Science Foundation under contract No. P6601.     

Separating small and big fish: The case of income tax evasion

This paper proposes to offer the taxpayer a choice of tax-enforcement schemes for self-selection. More specifically, the taxpayer should have the possibility of opting for the prevailing regime with a certain penalty on the evaded tax or for an alternative regime with a higher penalty on the evaded tax but a reduced tax rate. It is shown that this leads to a separation of taxpayers characterized by a relatively high degree of evasion (H-evaders) from taxpayers who evade only a relatively small amount of tax (L-evaders). Furthermore, the procedure is not self-defeating, it is effectively possible to direct the efforts of auditing towards the H-evaders. At the end of the game the L-evaders experience a welfare gain, the H-evaders are induced to reduce their evasion activities and the government can expect higher yields.We wish to thank Johann K. Brunner and two anonymous referees for many helpful comments.     

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.     

The core of some location games

An important problem in Location Theory is that of assigning plants to locations in an optimal manner. In the context of this problem, recognizing interplant transportation costs, Koopmans and Beckmann (1957) introduced the Quadratic Assignment Problem (QAP). It is shown in this paper that when the QAP is formulated as a cooperative location game, its core may be empty. By contrast, the core of the game corresponding to thelinear assignment problem (where transportation costs are disregarded) is assured to be non-empty. Some conditions under which the core is non-empty are discussed.I am grateful to two anonymous referees of this journal for their comments.