A measure of inaccuracy in concomitants of ordered random variables under Farlie-Gumbel-Morgenstern family

In communication theory, for possible outcomes of an experiment, we have two basic problems for the statement of the experimenter: we may not have enough information (vague statement) or some of the information may be incorrect, which make inaccurate in either or both of these situations. In this article, a measure of inaccuracy and its residual between distributions of concomitants of generalized order statistics (1os) and parent random variable are extended. Results of inaccuracy for family distributions and stochastic comparisons are obtained. Furthermore, some properties of the proposed measure are discussed. The unique characterization of the distribution function of parent random variable by the inaccuracy is shown.

Comprehensive Homeland Security: Developing a Domestic Protection Force for the United States

The ideation and execution of American homeland security has substantially evolved over the past fifteen years from a vague statement of principles to a very concrete, professional, and institutionalized field, with a cabinet-level department associated with various aspects of its practice. However, homeland security in the United States – defined as the protection of citizens, property, and interests beginning at international borders and expanding inward – is not yet fully developed or even secure in its own roles. As the evolution of both the theory and the practice continues, an important principle – analogous to one in the field of national security – must be sufficiently addressed and acted upon: the physical act of protecting sovereign territory.

Vagueness and Legal Theory

The use of vague language in law has important implications for legal theory. Legal philosophers have occasionally grappled with those implications, but they have not come to grips with the characteristic phenomenon of vagueness: the sorites paradox. I discuss the paradox, and claim that it poses problems for some legal theorists (David Lyons, Hans Kelsen, and, especially, Ronald Dworkin). I propose that a good account of vagueness will have three consequences for legal theory: (i) Theories that deny that vagueness in formulations of the law leads to discretion in adjudication (including Dworkin's) cannot accommodate “higher-order” vagueness, (ii) A legal theory should accept that the law is partly indeterminate when it can be stated in vague language, (iii) However, the traditional formulation of the indeterminacy claim, that a vague statement is “neither true nor false” in a borderline case, is misconceived and should be abandoned.

How To Find The Right Subdivision Into Tariff Classes

By intuition, the subdivision of an insurance portfolio into a number of classes is said to be good if it reflects the heterogeneity of the portfolio in an efficient way. To illustrate this rather vague statement we take the following very simple example:The portfolio consists of 20 independent risks, 10 of them producing an expected loss ratio of say 30% each (type A risks) and 80% each (type B risks) respectively.This “natural” subdivision is certainly better than, for instance, no subdivision at all;or, the finest possible subdivision with 20 classes consisting of only 1 risk each (because there is no point in differentiating between risks of the same type);or, 5 classes each containing two A- and two B-risks (here the number of classes is unnecessarily high and the heterogeneity has been completely wiped out; statistics based on this subdivision would even make us believe that the portfolio is totally homogeneous).As a matter of fact, the above “natural” subdivision is—of course!—the best of all subdivisions, it is the optimal subdivision in this case.In practice, however, as we all know, it is not easy to find the optimal subdivision. For one thing, the inherent structure or “natural” subdivision is not known a priori and secondly, for many different reasons, we can only choose from a limited number of subdivisions and not from all theoretically possible solutions. Note that even with only 20 risks there are 58.1012 possibilities of subdividing the portfolio. Thus, in practice, there is only a relatively small number of admissible subdivisions and the optimal one may not be among them, but we still need some sort of statistical criterion to choose the best one from these admissible subdivisions.

On Optimal Simulations of Econometric Models

In a recent note [Rouzier (1973, a)] we indicated a method for correcting certain parameters of an econometric model in order to minimize a weighted sum of mean square errors for the endogenous variables. A crude justification of this method was that, since the equations are generally estimated separately, there is no obvious reason why the complete model should lead to consistent solutions. Indeed, when a model is being constructed, there are implicit interactions whose effects are not revealed until numerical simulations are performed. The final run of a model differs a lot from the first one because the builder adds subjective informations to the results of the estimation. But when changing a coefficient, or when opting for another specification, he is probably paying a price in terms of the economic meaning of certain trade-offs. This is a rather vague statement, but we think that this study is able to contribute to a more complete understanding of the mechanisms of our models. In this paper, we intend to show that the above mentioned method can in fact be used not only to improve the performances, but also as a tool to analyze the trade-offs of a model.

The Malleability of Man in Chinese Marxism

“Human nature changes” – a vague statement acceptable to Marx and to Engels, to Stalin and to Mao. The point is: what is it that changes, under what conditions does it change, and what is the nature of the change? The article that follows is a case study of the interaction between the concrete cultural and social dimensions of a given country and a philosophical concept that has made its way into that country's official ideology. It examines the idea of the malleability of human nature in contemporary China. The concept is of monumental importance in Chinese Marxism, and examination of its evolution and implications will illuminate the Chinese definition of social class, and the causes of a nationwide crisis in the educational system in 1958 that foreshadowed the dramatic 1966 closing of all schools and their subsequent restructuring. Most important, the analysis clarifies the meaning of a term so often used in discussions of Chinese thought and so rarely understood.

The Holy Alliance: Prerequisites, Creation and Plans for Establishing International Law

The article describes the prerequisites, the creation and the plans of the Holy Alliance to establish international law and order. The end of the Napoleonic wars was marked by the Congress of Vienna. Its participants sought to restore the rule of the nobility in the conquered states of Napoleon. Based on the so-called principle of legitimacy, Congress supported the restoration on the thrones of former dynasties and noble orders in many countries. In the first place, each of the participating countries sought to meet their invasive goals, to profit from the redistribution of Europe and the colonies. In order to consolidate the conquests of, Alexander I initiated the formation of a permanent organization – the Holy Alliance. It was a kind of ideological and military-political superstructure over the “Viennese system” of diplomatic relations, founded under the guise of Christianity. The text of the union treaty in its form and content was atypical, unlike other international agreements. This has led many international law professionals to treat it as a declaration. The organization had existed until the mid-19th century before the Crimean War, although contradictions in the alliance have been around since the 1920s. The treaty of the Holy Alliance was concluded in Paris on September 14 (26) 1815 by the governments of Russia, Austria and Prussia. It was a rather vague statement about the mutual assistance and cooperation of all Christian states. Under the terms of the treaty, everyone who recognized him could join the alliance. After approval, almost all European rulers, except the Pope, the head of the Christian world who considered his signature superfluous, and the Turkish Sultan who professed Islam, joined him. England also did not join the alliance, though proposals from the founders were. It should be said that in England, the treaty was treated with the greatest caution. The absence of the Holy See’s signature in England did not prevent her from being an active participant in all its congresses. The original task of the Holy Alliance was to fulfill the role of a communication platform in which the leading powers of the world would coordinate their actions to ensure peace in Europe, preventing aggression that could harm the security of international law and order on the continent. With varying success, but in the first years of existence of the alliance these goals were achieved. The Holy Alliance was the first collective security institution in the world after the Napoleonic wars.

Reading in Mathematics

Sometimes the teacher thinks that the students cannot work verbal problems because they do not have the ability to read. This is a vague statement because the act of reading is very complex, involving many skills and understandings. What docs the teacher mean when he says the student cannot read? Does this mean that the student cannot pronounce well, does not read smoothly, does not understand the concepts, or does not understand the technical words used in the problem? Stating that a student cannot read is making use of the catch-all word that may mean any number of things.

Villamaninite, a new mineral

Early in 1914 a parcel of copper-nickel-cobalt ore, weighing several tons, was received in London for valuation from the 'Cármenes mine, Spain'. This somewhat vague statement of locality refers without doubt to the group of mines in the district of Cármenes, province of León, situated about 6 km. E.N.E. of Viilamanín, a statisn on the railway from Gijon to León and about 40 km. N. of the latter city. The ores of these mines are described as consisting of sulphide minerals of copper, cobalt, and nickel in a gangue of dolomite.

On the Valuation of Benefits Dependent upon Promotion to a Higher Status

The suggestion has been made to me by Mr. George King, to write a paper upon an interesting problem which recently occupied our joint attention.A brief statement of the case is as follows :In a great public service there are certain well-defined ranks, the upper ones of which are exclusively recruited by promotion from the lower ones. There are limiting ages of retirement in each rank, and in the event of an officer reaching the fixed age without being promoted he is retired on a pension. The scale of pension depends mainly on length of service, varying of course with each rank, and, as the majority enter in the lowest rank between comparatively narrow limits of age, it is sufficient to deduce an average rate of pension at each age in the various ranks. The problem is to find what amount of annual contribution, uniform throughout future service, should be made in respect of each officer now in the service, of whatever age or rank, in order to provide for the ultimate charge for pensions.In the particular case presented there were six ranks to be dealt with, and it was understood that the calculations were to be made at 3 per-cent compound interest. I trust I may be excused for this vague statement of the case, but I could hardly be more explicit without being too definite. I shall refer to these ranks throughout as first, second, third ranks, &c., where the first is understood to mean the highest.