The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

Land, technical progress and the falling rate of profit

The paper sets out a one sector growth model with a neoclassical production function in land and a capital-labour aggregate. Capital accumulates through capitalist saving, the labour supply is infinitely elastic at a subsistence wage and all factors may experience factor augmenting technical progress. The main result is that, if the elasticity of substitution between land and the capital-labour aggregate is less than one and if the rate of caital augmenting technical progress is strictly positive, then the rate of profit will fall to zero. The surprise is that this result holds regardless of the rate of land augmenting technical progress; that is, no amount of technical advance in agriculture can stop the fall in the rate of profit. The paper also discusses the relation of this result to the classical and Marxist literature and sets out the path of the relative price of land.

Competition for Procurement Shares

We propose a new procurement procedure which allocates shares of the total amount to be procured depending on the bids of suppliers. Among the properties of the mechanism are: (i) Bidders have an incentive to par- ticipate in the procurement procedure, as equilibrium payoffs are strictly positive. (ii) The mechanism allows to vary the extent to which affirma- tive action objectives, like promoting local industries, are pursued. (iii) Surprisingly, even accomplishing affirmative action goals, procurement ex- penditures might be lower than under a classical auction format. Keywords: Procurement Auction, Affirmative Action. JEL: C72, D44, H57

A theory of international conflict management and sanctioning

In this paper we analyze sanctioning policies in international law. We develop a model of international military conflict where the conflicting countries can be a target of international sanctions. These sanctions constitute an equilibrium outcome of an international political market for sanctions, where different countries trade political influence. We show that the level of sanctions in equilibrium is strictly positive but limited, in the sense that higher sanctions would exacerbate the military conflict, not reduce it. We then propose an alternative interpretation to the perceived lack of effectiveness of international sanctions, by showing that the problem might not be one of undersanctioning but of oversanctioning.

Strange nonchaotic attractors in Harper maps

We study the existence of strange nonchaotic attractors (SNA) in the family of Harper maps. We prove that for a set of parameters of positive measure, the map possesses a SNA. However, the set is nowhere dense. By changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a SNA.

Psychometric characteristics of the Spanish version of instruments to measure neck pain disability

Background: The NDI, COM and NPQ are evaluation instruments for disability due to NP. There was no Spanish version of NDI or COM for which psychometric characteristics were known. The objectives of this study were to translate and culturally adapt the Spanish version of the Neck Disability Index Questionnaire (NDI), and the Core Outcome Measure (COM), to validate its use in Spanish speaking patients with non-specific neck pain (NP), and to compare their psychometric characteristics with those of the Spanish version of the Northwick Pain Questionnaire (NPQ).Methods: Translation/re-translation of the English versions of the NDI and the COM was done blindly and independently by a multidisciplinary team. The study was done in 9 primary care Centers and 12 specialty services from 9 regions in Spain, with 221 acute, subacute and chronic patients who visited their physician for NP: 54 in the pilot phase and 167 in the validation phase. Neck pain (VAS), referred pain (VAS), disability (NDI, COM and NPQ), catastrophizing (CSQ) and quality of life (SF-12) were measured on their first visit and 14 days later. Patients' self-assessment was used as the external criterion for pain and disability. In the pilot phase, patients' understanding of each item in the NDI and COM was assessed, and on day 1 test-retest reliability was estimated by giving a second NDI and COM in which the name of the questionnaires and the order of the items had been changed.Results: Comprehensibility of NDI and COM were good. Minutes needed to fill out the questionnaires [median, (P25, P75)]: NDI. 4 (2.2, 10.0), COM: 2.1 (1.0, 4.9). Reliability: [ICC, (95%CI)]: NDI: 0.88 (0.80, 0.93). COM: 0.85 (0.75,0.91). Sensitivity to change: Effect size for patients having worsened, not changed and improved between days 1 and 15, according to the external criterion for disability: NDI: -0.24, 0.15, 0.66; NPQ: -0.14, 0.06, 0.67; COM: 0.05, 0.19, 0.92. Validity: Results of NDI, NPQ and COM were consistent with the external criterion for disability, whereas only those from NDI were consistent with the one for pain. Correlations with VAS, CSQ and SF-12 were similar for NDI and NPQ (absolute values between 0.36 and 0.50 on day 1, between 0.38 and 0.70 on day 15), and slightly lower for COM (between 0.36 and 0.48 on day 1, and between 0.33 and 0.61 on day 15). Correlation between NDI and NPQ: r = 0.84 on day 1, r = 0.91 on day 15. Correlation between COM and NPQ: r = 0.63 on day 1, r = 0.71 on day 15.Conclusion: Although most psychometric characteristics of NDI, NPQ and COM are similar, those from the latter one are worse and its use may lead to patients' evolution seeming more positive than it actually is. NDI seems to be the best instrument for measuring NP-related disability, since its results are the most consistent with patient's assessment of their own clinical status and evolution. It takes two more minutes to answer the NDI than to answer the COM, but it can be reliably filled out by the patient without assistance.

A Methodology to measure shareholder value orientation and shareholder value creation aimed at providing a research basis to investigate the link between both magnitudes

Does shareholder value orientation lead to shareholder value creation? This article proposes methods to quantify both, shareholder value orientation and shareholder value creation. Through the application of these models it is possible to quantify both dimensions and examine statistically in how far shareholder value orientation explains shareholder value creation. The scoring model developed in this paper allows quantifying the orientation of managers towards the objective to maximize wealth of shareholders. The method evaluates information that comes from the companies and scores the value orientation in a scale from 0 to 10 points. Analytically the variable value orientation is operationalized expressing it as the general attitude of managers toward the objective of value creation, investment policy and behavior, flexibility and further eight value drivers. The value creation model works with market data such as stock prices and dividend payments. Both methods where applied to a sample of 38 blue chip companies: 32 firms belonged to the share index IBEX 35 on July 1st, 1999, one company represents the “new economy” listed in the Spanish New Market as per July 1st, 2001, and 5 European multinational groups formed part of the EuroStoxx 50 index also on July 1st, 2001. The research period comprised the financial years 1998, 1999, and 2000. A regression analysis showed that between 15.9% and 23.4% of shareholder value creation can be explained by shareholder value orientation.

Growth of positive words and lower bounds of the growth rate for Thompson's group (F)p

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Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

A doubling measure on R(d) can charge a rectifiable curve

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An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

Two weight inequalities for discrete positive operators

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Hausdorff measure of quasicircles

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