Marginal distributions of sequential and generalized order statistics

Expressions for marginal distribution functions of sequential order statistics and generalized order statistics are presented without any restrictions imposed on the model parameters. The results are related to the relevation transform, to the distribution of the product of Beta distributed random variables, and to Meijers G-functions. Some selected applications in the areas of moments, conditional distributions, recurrence relations, and reliability properties are shown. Key words:Order statistics; Generalized order statistics; Sequential order statistics; Record values; Distribution theory; Meijers G-function; Recurrence relations; Reliability properties.     

Air pollution-mortality models: A demonstration of the effects of random measurement error

Errors of measurement have long been recognized as a chronic problem in statistical analysis. Although there is a vast statistical literature of multiple regression models estimating the air pollution-mortality relationship, this problem has been largely ignored. It is well known that pollution measures contain error, but the consequences of this error for regression estimates is not known. We use Lave and Seskin's air pollution model to demonstrate the consequences of random measurement error. We assume a range of 0% to 50% of the variance of the pollution measures is due to error. We find large differences in the estimated effects on mortality of the pollution variables as well as the other explanatory variables once this measurement error is taken into account. These results cast doubt on the usual regression estimates of the mortality effects of air pollution. More generally our results demonstrate the consequences of random measurement error in the explanatory variable of a multiple regression analysis and the misleading conclusions that may result in policy research if this error is ignored.     

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.     

PROPRIETORIAL CONTROL IN FAMILY FIRMS: SOME FUNCTIONS OF 'QUASI-ORGANIC' MANAGEMENT SYSTEMS

The purpose of this paper is to investigate the strategies of managerial control which are used by the proprietors of family-owned business enterprises. Interviews with the proprietors and senior managers of businesses in the building industry illustrate the ‘quasi-organic’ nature of management structures. These grant some autonomy to senior managers without threatening proprietorial decision-making prerogatives. Although the family firm has certain distinctive features, similar control strategies designed to ensure that delegated decisions are ‘reliable’ and ‘responsible’ are evident in various types of business enterprise. There is, then, scope for further comparative research within a conceptual framework which does not entirely divorce the family firm from other business organizations.     

Reduced Form Auctions Revisited

This note uses the Theorem of the Alternative to prove new results on the implementability of general, asymmetric auctions, and to provide simpler proofs of known results for symmetric auctions. The tradeoff is that type spaces are taken to be finite.     

Late entry,market shares and competitive survival: The case of synthetic fibers

This paper examines product policy in relation to the experience curve and product life cycle concepts in the context of the experience of the thirteen major firms in the Western European synthetic fibers industry. It examines the hypothesis based on Boston Consulting Group and the Profit Impact of Market Share (PIMS) evidence that late entrants to a market will be at a competitive disadvantage because they lack the accumulated experience of the pioneering firms. For each of the three main synthetic fibres, acrylic, nylon and polyester, it was found that the early entrants who established major market shares early in the growth phase of the product life cycle were able to maintain that leadership nearly twenty years later. In contrast not only did almost all the late entrants fail to achieve significant market shares but in the difficult market conditions between 1974 and 1981 they provided seven out of nine market withdrawals.     

Urban Regulations and the Price of Land and Housing in Korea

South Korea is a remarkable macroeconomic success story, but it has performed relatively poorly in one respect: the provision of high quality housing at reasonable prices. This paper analyzes the Korean housing market and the market for related inputs, with special emphasis on the regulatory environment.     

The Lifetime Distributional Impact of Government Health Outlays

This article examines the lifetime redistributive impact of government health outlays and finds that such outlays redistribute income from the lifetime rich to the lifetime poor and from men to women.