Some properties of the minimum and the maximum of random variables with joint logconcave distributions

It is shown that if (X ₁, X ₂, . . . , X _n ) is a random vector with a logconcave (logconvex) joint reliability function, then X _P = min _i∈P X _i has increasing (decreasing) hazard rate. Analogously, it is shown that if (X ₁, X ₂, . . . , X _n ) has a logconcave (logconvex) joint distribution function, then X ^P  = max _i∈P X _i has decreasing (increasing) reversed hazard rate. If the random vector is absolutely continuous with a logconcave density function, then it has a logconcave reliability and distribution functions and hence we obtain a result given by Hu and Li (Metrika 65:325–330, 2007). It is also shown that if (X ₁, X ₂, . . . , X _n ) has an exchangeable logconcave density function then both X _P and X ^P have increasing likelihood ratio.     

A queueing problem with correlated arrivals and correlated phase-type service zur theorie des rangtests

Summary This paper studies the steady-state behaviour of a discrete-time, single-channel, first-come-first-served queueing problem wherein (i) the arrivals at two consecutive time-marks are correlated (ii) the service is accomplished in phases and (iii) the completion of phases at two consecutive time-marks are correlated. The probability generating function (p.g.f.) of the number of phases waiting and in service is obtained. Further, the p.g.f. of queue length is obtained for the case when each unit demands only one phase of service, and the mean queue length is derived therefrom. Finally, the p.g.f. and the mean queue length are discussed for the special cases, (i) r=0,R≠0, (ii) r≠0,R=0, (iii) r=0,R=0, (iv) r≠0,R=−I, (v) r=0,R=−I, (vi) r=−I,R≠0, (vii) r=−I,R=0, (viii) r=I,R≠0, (ix) r=I,R=0, (x) r≠0,R=I, (xi) r=0,R=I, where r andR are the respective coefficients of correlation between arrivals and completion of phases at two consecutive time-marks.     

Book Reviews

Books reviewed: Biorcio, Roberto La Padania Promessa Cartocci, Roberto Fra Lega e Chiesa Diamanti, Ilvo La Lega: Geografia, Storia e Sociologia di un nuovo Soggetto Politico Diamanti, Ilvo Il Male del Nord: Lega, Localismo, Secessione Magatti, Mauro Tra Disordine e Scisma Mannheimer, Renato, (ed.) La Lega Lombarda Hebbert, Michael London Mazzette, Antonietta and Giancarlo Rovati (eds.) La Protesta dei ’forti”: Leghe del Nord e Partito Sardo d’Azione Pajetta, Giovanna Il Grande Camaleonte: Episodi, Passioni, Avventure del Leghismo Vicercati, Daniele I Lombardi alla nuova Crociati Veltz, Pierre Mondialism Villes et Territoires: L’economie Archipel Abromeit, Heidrun Democracy in Europe. Legitimising Politics in a Non‐state Polity Dietz, Henry and Gil Shidlo, (eds.) Urban Democratic Elections in Latin America Harrison, Bennett and Marcus Weiss Workforce Development Networks: Community‐based Organizations and Regional Alliances Sugrue, Thomas J. The Origins of the Urban Crisis. Race and Inequality in Postwar Detriot Wilford, Rich and Robert L. Miller (eds.) Women, Ethnicity and Nationalism: The Politics of Transition Jones, G.V. and P. Visaria Urbanisation in Large Developing Countries. China, Indonesia, Brazil and India Buiseret, David (eds.) Envisioning the City: Six Studies in Urban Cartography Taylor, Peter J. Modernities: A Geohistorical Interpretation     

Book reviews

Book reviewed in this article: Gutkind, P. C. W. and Wallerstein, I. , editors, 1977: The political economy of contemporary Africa. Mellor, J. R. 1977: Urban sociology in an urbanized society. Ragon, M. 1977: L'architecte, le prince et la démocratie: vers une démocratisation de l'architecture. d'Arvois, A. 1977: L'architecture du Prince. Dialectiques 20 Burlen, K. 1978: L'idéologique des architectes. Lamy, B. et Robirosa, A. 1976: Evolution de la profession d’ architecte. Stretton, H. 1976: Capitalism, socialism and the environment. Walton, J. and Masotti, L. H. , editors, 1976: The city in comparative perspective. Harloe, M. , editor, 1977: Captive cities. Brown, A. A., Licari, J. A., Neuberger, E. , editors, 1974; Urban and social economics in market and planned economies Wieviorka, M. 1977: L'état, le patronat et les consommateurs.     

Optimale Aufteilung des Stichprobenumfangs bei mehreren Merkmalen

Zusammenfassung Es wird gezeigt, daß sich das vonNeyman undTschuprow für ein einziges Merkmal gelöste Problem der optimalen Aufteilung des Stichprobenumfangs auf vorgegebene Schichten auf ein nichtlineares Programm mit linearen Restriktionen und nichtlinearer Zielfunktion zurückführen läßt. Auf Grund der Konvexitätseigenschaft der Zielfunktion ergibt sich, daß das Minimum der Zielfunktion (Minimum der Streuung des Stichprobenmittels ) stets eindeutig ist. Der beiNeyman undTschuprow mögliche Fall, daß sich in derh-ten Schicht ein Stichprobenumfang ergibt, der größer als der Umfang in der Gesamtheit ist, kann hier nicht auftreten.Durch Einführung einer verallgemeinerten Streuung wird das Problem der optimalen Aufteilung bei vorgegebener Schichtung imk-dimensionalen Merkmalsraum aufk Merkmale verallgemeinert. Es wird gezeigt, daß diese verallgemeinerte Streuung (=Zielfunktion eines nichtlinearen Programms) im allgemeinen nicht über dem ganzen konvexen Bereich der zulässigen Lösungen konvex (von unten) ist. Ein Teilbereich des zulässigen Bereichs, über dem die Zielfunktion konvex ist, wird angegeben. Schließlich werden hierzu vergleichende Ergebnisse gebracht.     

Book Reviews

Books reviewed: Bernard Jouve and Christian Lefèvre, (eds.) Villes, métropoles. Les nouveaux territoires du politique Sheridan Bartlett, Roger Hart, David Satterthwaite, Ximena de la Barra and Alfredo Missair, Cities for children: children's rights, poverty and urban management Daniel J. Monti Jr., The American city: a social & cultural history Andrew E.G. Jonas and David Wilson, (eds.) The urban growth machine: critical perspectives two decades later Dieter Dettke, (ed.) The challenges of globalization for Germany's social democracy: a political agenda for the 21st century Gösta Esping‐Andersen, Social foundations of postindustrial economies Michael Mortimore and William M. Adams Working the Sahel: environment and society in northern Nigeria> Stefan Hedlund, Russia's ‘market’ economy. A bad case of predatory capitalism Alexander Reichl, Reconstructing Times Square: politics and culture in urban development David Byrne, Social exclusion OECD, The response of higher education institutions to regional needs Felix Driver and David Gilbert, (eds.) Imperial cities: landscape, display and identity     

Pahl and Lojkine on the state: a comment

La relation entre i'état et le développement social peut entre analysée à partir de trois niveaux interconnectés:

• 1 Au niveau de la théorie et de la méthodologie. C'est ce que font Lojkine et Pahl.
• 2 A un niveau général, mais concernant des types théoriquement differenciés d'organisations sociales (c'est à dire, sociétés capitalistes avancées, sociététés socialistes. etc.). C'est le niveau qui concerne cet auteur le plus.
• 3 Au niveau d'une société donnée, durant une période historique déterminéee. C'est à ce niveau que les autres travaux de Lojkine ont été faits.

La critique faite par Pahl des perspectives marxistes est rejetés comme étant superficielle, par contre il est reconnu que i'?uvre de Poulantzas manque de perspective historique et dialectique. Mais i'analyse marxiste des institutions politiques dépend d'une interprétation correcte de la relation entre structure et superstructure, et ce point est développé par i'auteur. Une critique est faite des théories élitistes et historicistes. La typologie historiciste de Runciman est considérée comme étant inadéquate, car elle ne peut ětre appliquée à la réalité historique, et en dernier lieu, ne peut expliquer pourquoi les relations état-société montrent tant de variations. Les définitions marxistes de i'état sont insuffisantes et ont besoin d'ětre dévéloppées. A propos, les travaux de Lojkine et de Poulantzas sont critiqués comme étant réductivistes et non-dialectiques. La question des origines sociales de la démocratie est introduite afin de développer une perspective analytique satisfaisante qui pourrait prendre en compte les faits historiques des révolutions nationales en Europe de l'Ouest, au Japon et aux Etats-Unis. L'accent est mis sur le role de la classe ouvrière, le concept d'hégémonie, l'exercise du pouvoir hégémonique, et plus précisement quand la classe hégémonique n'est pas dominante. Une bonne analyse marxiste des relations état-société doit pouvoir envisager les tendences et les conditions actuelles de l'accumulation du capital, en conjonction avec les intérěts des groupes monopolistes. Cet essai fini par une brěve discussion des tendences actuelles dans ces domaines.     

Tests und Konfidenzintervalle für exponentielle Verteilungen und deren Anwendung auf einige diskrete Verteilungen

Zusammenfassung Es werden Verteilungen betrachtet, die (bezüglich irgendeines Ma?es) eine Dichte der GestaltC(ϑ) exp [ϑ x] besitzen. Für solche Verteilungen werden (ein- und zweiseitige) Tests und Konfidenzintervalle mit gewissen Optimalit?tseigenschaften entwickelt, und zwar fürϑ, für die Differenzϑ ₁ −ϑ ₂, sowie für einige Versionen desk-Stichproben Problems. Sodann werden einige Hilfss?tze über den bedingten Erwartungswert und die bedingte Varianz von zweiparametrigen Verteilungen abgeleitet, die bezüglich des einen Parameters reproduktiv sind und eine bezüglich des zweiten Parameters ersch?pfende und vollst?ndige Funktion besitzen. Schlie?lich werden die allgemeinen Ergebnisse auf einige diskrete Verteilungen (Binomial, Poisson, negativ Binomial, Pascal) angewendet und der Zusammenhang mit verschiedenen bekannten Tests diskutiert.

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Summary Probability distributions are considered which (with respect to any measure) possess a density function of the typeC(ϑ) exp [ϑ x]. For distributions of this type (one and twosided) tests and confidence intervals with some optimal properties are given, namely forϑ, for the differenceϑ ₁ −ϑ ₂, and for several versions of thek-sample problem. Furthermore, some lemmas concerning the conditional expectation and the conditional variance are proved for two-parameter families of distributions which are reproductive in one parameter and possess a complete statistic, sufficient for the second parameter. Finally the general results are applied to some discrete distributions (binomial, Poisson, negative binomial, Pascal) and the relationship to several fairly known tests is discussed.

     

Structural instability of the core

Let σ be a q-rule, where any coalition of size q, from the society of size n, is decisive. Let w(n,q)= 2q-n+1 and let W be a smooth ‘policy space’ of dimension w. Let U(W)^N be the space of all smooth profiles on W, endowed with the Whitney topology. It is shown that there exists an ‘instability dimension’ w^*(σ) with 2w^*(σ)w(n,q) such that:

1. (i) if ww^*(σ), and W has no boundary, then the core of σ is empty for a dense set of profiles in U(W)^N (i.e., almost always),

2. (ii) if ww^*(σ)+1, and W has a boundary, then the core of σ is empty, almost always,

3. (iii) if ww^*(σ)+1 then the cycle set is dense in W, almost always,

4. (iv) if ww^*(σ)+2 then the cycle set is also path connected, almost always.

The method of proof is first of all to show that if a point belongs to the core, then certain generalized symmetry conditions in terms of ‘pivotal’ coalitions of size 2q−n must be satisfied. Secondly, it is shown that these symmetry conditions can almost never be satisfied when either W has empty boundary and is of dimension w(n,q) or when W has non-empty boundary and is of dimension w(n,q)+1.     

Book Reviews

Book reviewed in this article: Beechey, V. and Perkins, T. 1987: A matter of hours: women, part-time work and the labour market. Darden, J.T., Child Hill, R., Thomas, J. and Thomas, R. 1987: Detroit: race and uneven development. Duncan, S. and Goodwin, M. 1988: The local state and uneven development. Eades, J. editor, 1987: Migrants, workers and the social order. Henderson, J. and Karn, V. 1987: Race, class and housing: inequality and the allocation of public housing in Britain. Hughes, J.W. and Sternlieb, G. 1987: The dynamics of America's housing. Jenkins, R. and Solomos, J. editors, 1987: Racism and equal opportunity policies in the 1980s. Linge, G.J.R. editor, 1988: Peripheralisation and industrial change. Lubeck, P.M. 1987: Islam and urban labour in northern Nigeria: the making of a Muslim working class. Massey, D. 1987: Nicaragua. Matzerath, H. 1985: Urbanisierung in Preußen 1815–1914. Page, E.C and Goldsmith, M.J. editors, 1987: Central and local government relations: a comparative analysis of west European unitary states. Hoffman-Martinot, V. 1987: Finances et pouvoir local: l'expérience allemande. Pradilla, E. 1984: Contribucion a la critica de la teoría urbana: del espacio a la crisis urbana. Pradilla, E. 1987: Capital, estado y vivienda en América Latina. Reade, E. 1987: British town and country planning. Savage, M. 1987: The dynamics of working-class politics: the labour movement in Preston 1880–1940. Teague, P. editor, 1987: Beyond the rhetoric: politics, the economy and social policy in Northern Ireland. Wilson, G. 1987: Money in the family.     

Productivity efficiencies in Ukrainian polyclinics: lessons for health system transitions from differential responses to market changes

Ukraine’s recent elections revealed deep divisions between eastern regions, which favored central economic planning, and western regions, which preferred more free market reforms. This study compares polyclinics in Ukraine to see if the inflexibility of Soviet-style planned economies results in lower economic efficiency in eastern regions. Using data from two geopolitical regions, Data Envelopment Analysis (DEA) scores for polyclinic efficiencies are modeled as a function of demographic and economic determinants. Surprisingly, results indicate that polyclinics in western Ukraine are less efficient. Possible explanations, including case mix intensity, responsiveness to local preferences, physician entrepreneurial behavior and a legacy of inequitable funding, are discussed.

What Is the Economic Meaning of FDH?

The central feature of the FDH model is the lack of convexity for its production possibility set, TF. Starting with n observed (distinct) decision making units DMU_k , each defined by an input-output vector p _k = [y _k -x _k], domination is defined by ordinary vector inequalities. DMU_k is said to dominate DMU_j if p _k ≥ p _j , p _k ≠ p _j . The FDH production possibility set TF consists of the observed DMU_j together with all input-output vectors p=[y_k,?x_k] with y ≥ 0, x ≥ 0, y ≠ 0, x ≠ 0 which are dominated by at least one of the observed DMU_j. DMU_k is defined as “FDH efficient” if no DMU_j dominates it. In the BCC (or variable return to scale) DEA model the production possibility set TB consists of the observed DMU_k together with all input-output vectors dominated by any convex combination of them and DMU_k is DEA efficient if it is not dominated by any p in TB. In the DEA model, economic meaning is established by the introduction of (non negative) multiplier (price) vectors w = [u,v]. If DMU_k is undominated (in TB) then there exists a positive multiplier vector w for which (a) w ^T p _k = u ^T y _k ? v ^T x _k ≥ w ^T p for every p ∈ TB. In everyday language, the net return (or profit) for DMU_k relative to the given multiplier vector w is at least as great as that for any production possibility p. On the other hand, if DMU_k is FDH but not DEA efficient then it is proved that there exists no positive multiplier vector >w for which (a) holds, i.e. for any positive w there exists at least one DMU_j for which w ^T p _j > w^T p _k . Since, therefore, FDH efficiency does not guarantee price efficiency what is its economic significance? Without economic significance, how can FDH be considered as being more than a mathematical system however logically soundly it may be conceived?

     

On unordering Horvitz and Thompson'sT 1 class of linear estimators

Summary When elements of a finite population are sampled with varying probability selection at each draw,Horvitz andThompson [1952] have formulated certain classes of linear estimators to bear on the problem of providing a smaple appraisal of the population total.Horvitz andThompson's T ₁ class is an ordered one, which was examined by the present author [1967 b]. For some sampling procedures a best estimator exists for theT ₁ class. Subsequently the present author [1967 c] appliedMurthy's technique [Murthy 1967] of unordering an ordered estimator and derived a more efficient estimator. The present paper is concerned with applyingMurthy's technique to theT ₁ class itself, and examining the unorderedT ₁ class. Curiously enough, it is noted that the condition of unbiasedness is sufficient to completely specify the unorderedT ₁ class for the sampling procedure considered here.Research sponsored by Marathwada University, Aurangabad, India; under Grant No. Research-12-68-69/3314-16.     

One-step R-estimation in linear models with stable errors

Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α$\alpha$-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step R-estimation method and investigate its asymptotic performances under stable densities. Contrary to traditional least squares, the proposed R-estimators remain root-n$n$ consistent (the optimal rate) under the whole family of stable distributions, irrespective of their asymmetry and tail index. While parametric stable-likelihood estimation, due to the absence of a closed form for stable densities, is quite cumbersome, our method allows us to construct estimators reaching the parametric efficiency bounds associated with any prescribed values (_α0,_b0)$({\alpha }_0,b_0)$ of the tail index α$\alpha$ and skewness parameter b$b$, while preserving root-n$n$ consistency under any (α,b)$(\alpha ,b)$ as well as under usual light-tailed densities. The method furthermore avoids all forms of multidimensional argmin computation. Simulations confirm its excellent finite-sample performances.     

Criterion-robust optimal product designs for discrimination between nested response surface models

Consider the problem of discriminating between two rival response surface models and estimating parameters in the identified model. To construct designs serving for both model discrimination and parameter estimation, the M _γ-optimality criterion, which puts weight γ (0≤γ≤1) for model discrimination and 1 − γ for parameter estimation, is adopted. The corresponding M _γ-optimal product design is explicitly derived in terms of canonical moments. With the application of the maximin principle on the M _γ-efficiency of any M _γ'-optimal product design, a criterion-robust optimal product design is proposed.     

BOOK REVIEWS

Book Review in this Article Alvesson , Mats . Organization Theory and Technocratic Consciousness. Dawson , Sandra . Analysing Organizations. Rowbottom , Ralph and Billis , David . Organizational Design. Moores , Brian . (Ed.) Are They Being Served? Boddy , David and Buchanan , David A. Managing New Technology. Francis , Arthur . New Technology At Work. Warner , Malcolm . (Ed.), Management Reforms In China.     

Ready or Not? Homosexuality,Unit Cohesion,and Military Readiness

The U.S. military argues that homosexuals are unfit for service because their presence compromises military readiness and unit cohesion. Based on this assumption, it continues to discharge homosexuals at an average rate of approximately 925 per year. On the other hand, the extant research suggests that homosexuals are no more disruptive to military life than their heterosexual counterparts. By integrating the legal and scientific literature, this paper examines the soundness of the military’s assumptions and aims to improve our understanding of the issues involved. Within this context, the efficacy of the military’s “Don’t Ask, Don’t Tell, Don’t Pursue” policy and whether it is in the best interest of the military and its soldiers and sailors is discussed.

Scharfe untere und obere Schranken für die Wahrscheinlichkeit der Realisation vonk untern Ereignissen

Summary LetA ₁,...,A _n be events in a probability space (,A,W). We denote byL _k the event, that at leastk events among then eventsA ₁,...A _n occur, and byK _k the event, that exactlyk events occur. If only the inequalities _i W(A _i ) _i ,i=1,...,n, are known, we calculate sharp lower and upper bounds forW(L _k ) andW(K _k ). These bounds only depend onn, k and _i , _i ,i=1,...,n. They are relevant, when treating combined tests or confidence procedures.     

The Relationship Among Union Membership, Facets of Satisfaction and Intent to Leave: Further Evidence on the Voice Face of Unions

This study examined the impact of union membership on employees’ intent to leave their jobs across a number of facets of satisfaction, as a further test of unions’ voice face. Among the findings were that there were significant relationships between job, compensation, benefits, working conditions, and immediate supervisor satisfaction and intent to leave one’s job for nonunion employees. In contrast, only the relationship between job satisfaction and intent to leave was significant for union employees. Finally, over the facets of satisfaction where one would expect unions to have the most influence, the relationship between intent to leave one’s job and satisfaction was greater for nonunion employees than for union employees. These results provide a great deal of support for the effect of unions’ voice face.