Short notes on Charlier's method for expansion of frequency functions in series

Abstract

1. In 1905 Charlier outlined some methods for the expansion of functions in series. ¹ C. V. L. Charlier, Über die Darstellung willkürlicher Funktionen (Meddelanden från Lunds Observatorium, Ser. I, nr 27). Particularly he was dealing with frequency functions, but the method has a more general application. As is well known there were two kinds of developments considered, namely in terms of the differentials and in terms of the differences of a conveniently chosen developing function. The outstanding examples are — respectively — the expansions of the so called types A and B. The difference series has later gained a special attention by its deduction being attached to the theory for generating functions. ² I. V. Uspensky, On Ch. Jordan's Series for Probability (Annals of Mathematics, Vol. 32, 1931). The true pivotal function in this respect seems, however, to be the moment generating function. In the following notes it will be shown that the differential series as well as difference series built up by the advancing and the central differences are obtainable in a similar way. By employing some convenient cumulants the different expansions can be written down compactly in symbolic forms which reveal their mutual formal relations. It will further be observed that Charlier's method of expansion is the inversion of a method indicated by Abel.     

On the epidemiology of injury in developing countries: A one-year emergency room-based surveillance experience from León,Nicaragua

Background Regularly available data has been shown to be inadequate for developing, implementing, and evaluating injury prevention and control programs in Nicaragua. A specific prevention-oriented local injury surveillance system has therefore been set up in the city of León. Objectives The aim of this paper is to describe the epidemiology of fatal and non-fatal injuries over a one-year period in a well-defined local population in Nicaragua, as emerging from the perspective of emergency room and inpatient treatments over a one-year period. Methods A hospital-based injury surveillance system was established to collect data for different levels of severity. All treated unintentional and intentional injuries were registered, including information on the external causes according to the ICD-9. Results Of all emergency room visits, 15.9% (9,970) were injuries. For every death due to injuries, there were 31 hospital admissions and 253 emergency room visits. Home and street/roads were the main arenas for the accidents. The estimated underreporting rate was about 6%, and in 20.3% of the cases, no E-code was assigned. The overall incidence and mortality rates were 56.2 per 1,000 and 20 per 100,000 inhabitants, respectively. However, comparison with a parallel household survey showed that the reporting rate of the surveillance system is only about 9%. The overall ratio of male to female injury rates was 2.1 to 1. The main causes of non-fatal injuries were falls, whereas the main cause of death was traffic accidents. Conclusions Hospital discharge and emergency room data systems are effective and feasible means for collecting the data needed to prevent injuries. However, in a country like Nicaragua with limited access to hospital health services, it is necessary to supplement such a system with additional sources of information in order to gain a more comprehensive picture of injury occurrence.     

Interpersonal similarity and knowledge sharing within multinational organizations

Previous research has established that interpersonal similarity can influence knowledge sharing in such a way that similar people are more likely to share knowledge than those who are dissimilar. We contribute to the literature by showing that in the MNC context, cultural and functional similarity can become more powerful sources of bias than more commonly assumed demographic characteristics such as gender or seniority. This may be driven by the salience of such boundaries in the MNC: while demographic characteristics are more broadly distributed, cultural and functional barriers create more defined and observable faultlines, often coinciding with unit boundaries. We further argue that it may not be similarity as such that matters but rather its positive impact on different dimensions of social capital, which mediate the relationship between similarity and knowledge sharing. These microfoundations of inter-unit knowledge exchange point to important theoretical and practical implications for international management.     

Profits,dividends and industry restructuring: the Swedish paper and pulp industry between 1945 and 1977

This paper explores the role of profit distribution in the restructuring of the Swedish paper and pulp (P&P) industry between 1945 and 1977. In addressing this issue, we will draw on the life-cycle theory and market imperfection arguments to examine whether the less profitable firms shared more of their profits as dividends, or remained on the market longer by reinvesting the majority of the profits. Our study shows that an increasing share of the profits was distributed to owners over time, and thus less profit was reinvested in industrial renewal. We find that the observed general upward trend in dividends can be attributed to the decline in profit and firm legacy, as firms in the Swedish P&P industry kept dividends up while reducing reinvestment as their profit margins decreased over time. Our study shows that the market imperfections related to capital taxation and investment funds increased rather than decreased dividends.     

A Simple Improvement of the IV‐estimator for the Classical Errors‐in‐Variables Problem

Two measures of an error‐ridden variable make it possible to solve the classical errors‐in‐Variable problem by using one measure as an instrument for the other. It is well known that a second IV‐estimate can be obtained by reversing the roles of the two measures. We explore the optimal linear combination of these two estimates. In a Monte Carlo study, we show that the gain in precision is significant. The proposed estimator also compares well with full information maximum likelihood under normality. We illustrate the method by estimating the capital elasticity in the Norwegian ICT‐industry.     

On the Gram series on Pearson's system of frequency functions

Abstract

Among the manifold frequency curves that may conceivably arise when it is assumed that, instead of the variate χ itself, a function of the latter, u = ψ(χ), is normally distributed, the logarithmic normal curve occupies a unique position for two reasons: it can be theoretically deduced from a slightly modified elementary error hypothesis and it is applicable in practice to different cases.     

Balancing the trade-off between learning prospects and spillover risks: MNC subsidiaries’ vertical linkage patterns in developed countries

This paper investigates local vertical linkages of foreign subsidiaries and the dual role of such linkages as conduits for learning as well as potential channels for spillovers to competitors. On the basis of data from 97 subsidiaries, we analyze the quality of such linkages under varying levels of competition and subsidiary capabilities. Our theoretical development and the results from the analysis document a far more complex and dynamic relationship between levels of competition and MNCs’ local participation in knowledge intensive activities, i.e. learning and spillovers, than previous studies do. We find a curvilinear relationship between the extent of competitive pressure and the quality of local linkages confirming our argument of a trade-off between learning prospects and spillover risks. Furthermore, the level of subsidiary capabilities moderates this relationship.