A Different Way to Look at Random Variables

2016 ◽  
pp. 179-199
Author(s):  
Erio Castagnoli ◽  
Marzia De Donno ◽  
Gino Favero ◽  
Paola Modesti
Keyword(s):  
Decision Theory ◽  
Decision Maker ◽  
Classical Problem ◽  
Random Variables ◽  
Random Variable ◽  
Point Of View ◽  
Alternative Approach ◽  
The World ◽  
Sure Thing Principle ◽  
Points Of View

A classical problem in Decision Theory is to represent a preference preorder among random variables. The fundamental Debreu's Theorem states that, in the discrete case, a preference satisfies the so-called Sure Thing Principle if and only if it can be represented by means of a function that can be additively decomposed along the states of the world where the random variables are defined. Such a representation suggests that every discrete random variable may be seen as a “histogram” (union of rectangles), i.e., a set. This approach leads to several fruitful consequences, both from a theoretical and an interpretative point of view. Moreover, an immediate link can be found with another alternative approach, according to which a decision maker sorts random variables depending on their probability of outperforming a given benchmark. This way, a unified approach for different points of view may be achieved.

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (03) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variablesX1,X2, …,Xnare said to be totally negatively dependent (TND) if and only if the random variablesXiand ∑j≠iXjare negatively quadrant dependent for alli. Our main result provides, for TND 0-1 indicatorsX1,x2, …,Xnwith P[Xi= 1] =pi= 1 - P[Xi= 0], an upper bound for the total variation distance between ∑ni=1Xiand a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

Jules Verne’s ‘Around the World in 80 Days’: Multilingualism, Multiculturalism and Symbols

2021 ◽  
Vol 2021 ii (15) ◽  
pp. 146-182
Author(s):  
Haroula Hatzimihail ◽  
Ioannis Pantelidis
Keyword(s):  
Key Words ◽  
Age Groups ◽  
Literary Work ◽  
Point Of View ◽  
Social Classes ◽  
Jules Verne ◽  
The World ◽  
Semiotic Systems ◽  
Points Of View ◽  
Different Cultures

In this announcement, the various –linguistic and non-linguistic- symbols used in the literary work 'Around the world in 80 days', written by Jules Verne, are examined from an intertemporal and contemporary point of view. The references through these points of view, in matters of multiculturalism and multilingualism, are becoming classical in nature: they concern the necessity of the applied ability to communicate between individuals who belong to different social classes and age groups, speak the same or different languages, come from different cultures, with rights and obligations in their various areas of life, etc. Key-words: linguistics, multilingualism, multiculturalism, semiotics, semiotic systems, symbols

Random packing of an interval. II

1979 ◽  
Vol 11 (03) ◽  
pp. 591-602
Author(s):  
David Mannion
Keyword(s):  
Fine Particles ◽  
Random Variables ◽  
Random Variable ◽  
Difficult Problem ◽  
Random Packing ◽  
Point Of View ◽  
Initial Size ◽  
Moderate Size ◽  
The Individual

We showed in [2] that if an object of initial size x (x large) is subjected to a succession of random partitions, then the object is decomposed into a large number of terminal cells, each of relatively small size, where if Z(x, B) denotes the number of such cells whose sizes are points in the set B, then there exists c, (0 < ≦ 1), such that Z(x, B)x −c converges in probability, as x → ∞, to a random variable W. We show here that if a parent object of size x produces k offspring of sizes y 1, y 2, ···, y k and if for each k x - y 1 - y 2 - ··· - y k (the ‘waste’ or the ‘cover’, depending on the point of view) is relatively small, then for each n the nth cumulant, Ψ n (x, B), of Z(x, B) satisfies Ψ n (x, B)x -c → κ n (B), as x → ∞, for some κ n (B). Thus, writing N = x c , Z(x, B) has approximately the same distribution as the sum of N independent and identically distributed random variables (The determination of the distribution of the individual appears to be a difficult problem.) The theory also applies when an object of moderate size is broken down into very fine particles or granules.

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (3) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variables X1, X2, …, Xn are said to be totally negatively dependent (TND) if and only if the random variables Xi and ∑j≠iXj are negatively quadrant dependent for all i. Our main result provides, for TND 0-1 indicators X1, x2, …, Xn with P[Xi = 1] = pi = 1 - P[Xi = 0], an upper bound for the total variation distance between ∑ni=1Xi and a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

Bat or Batman?

Philosophy ◽  
1989 ◽  
Vol 64 (248) ◽  
pp. 207-217
Author(s):  
David Pugmire
Keyword(s):  
Conscious Experience ◽  
Mental States ◽  
Point Of View ◽  
Thomas Nagel ◽  
The World ◽  
Theories Of Mind ◽  
Points Of View

Thomas Nagel claimed that subjectivity is what distinguishes those states known in the vernacular as conscious or as experiences. And he argued that subjectivity eludes reductivist theories of mind, which are obliged to ignore it and hence to fail. I shall be concerned here primarily with the formulation of the concept of subjectivity. Nagel tried to delineate subjectivity in a well known phrase: ‘an organism has conscious mental states if and only if there is something it is like to be that organism—something it is like for the organism’. Nagel offers to explain this condition of being host to conscious experience as the organism's having a point of view on the world, a point of view which is its own and nothing else's, however much or little the world as disclosed by it may agree with what is presented from other points of view.

Going Nowhere: Nagel on Normative Objectivity

Philosophy ◽  
1990 ◽  
Vol 65 (254) ◽  
pp. 501-509 ◽  
Author(s):  
Marilyn Friedman
Keyword(s):  
Scientific Reasoning ◽  
Practical Reasoning ◽  
Point Of View ◽  
Reasons For Action ◽  
Thomas Nagel ◽  
The World ◽  
Objective Understanding ◽  
Points Of View ◽  
Objective Side

In The View from Nowhere, Thomas Nagel develops a theory of practical reasoning which attempts to give the personal, or subjective, point of view its due2 while still insisting on the objectivity of ethics.On the objective side, Nagel affirms that there are truths about values and reasons for action which are independent of the ways in which reasons and values appear to us, independent of our own particular beliefs and inclinations (p. 144). The objective foundation for these truths consists in a certain distinctive process of understanding. Objective understanding is explicated in terms of an objective standpoint, a standpoint defined as impersonal, that is, as detached from the subjective point of view. The objective standpoint is structured by a conception ‘of the world as centerless—as containing ourselves and other beings with particular points of view’ (p. 140). As with scientific reasoning, ‘we begin from our position inside the world and try to transcend it by regarding what we find here as a sample of the whole’ (p. 141).

scholarly journals Methodical aspects of statistical modeling of two-dimensional systems of random variables

2020 ◽  
Vol 1 (1) ◽  
pp. 43-57
Author(s):  
P. Kosobutskyy
Keyword(s):  
Statistical Modeling ◽  
Random Variables ◽  
Practical Interest ◽  
Statistical Processing ◽  
Random Variable ◽  
Point Of View ◽  
Original Research ◽  
Two Dimensional ◽  
Random Data ◽  
Statistical Regularities

According to the analysis of literature sources, the statistical processing of measurement results is not always given due attention. Unfortunately, appropriate algorithms are often limited to simplified statistical procedures, without the proper justification of the objective function, including to check the quality of processing of random data. Therefore, the author plans to publish a series of articles on statistical modeling, which will include the results of original research by the author and others. In this article are considered the methodological aspects of statistical modeling of two-dimensional systems with random data, physical substantiation of correlation regularities of statistical relations between random variables is given, since or the problem of establishing the law of distribution of random variable has practical interest from the point of view of modeling statistical regularities of model "signal + noise".

scholarly journals Dibalik Fakta dan Mitos Fenomena Super Blue “Blood” Moon

2018 ◽  
Vol 1 (1) ◽  
pp. 30
Author(s):  
Yunina Surtiana
Keyword(s):  
Temperature Shift ◽  
Point Of View ◽  
Natural Phenomenon ◽  
Natural Phenomena ◽  
The Moon ◽  
Literature Study ◽  
Library Research ◽  
The World ◽  
Scientific Phenomenon ◽  
Points Of View

This article discusses a natural phenomenon namely Super Blue (Blood) Moon (later to be referred as SBBM) in terms of scientific and mythical points of view. The method used in this study is literature study promoting library research as its instrument.Thus, as much literature as possible in a variety of types such as books, journals, and any articles is collected and later analyzed. Having synthesized the literature, this study finds out that in terms of science, it is a very phenomenal occurrence since there are three natural phenomena namely super moon, blood moon, and blue moon happening simultaneously. Researchers and scientists usually seize this moment for science. For instance, some of them study the temperature shift of the moon. In the meantime, in terms of mythical point of view, some beliefs starting from the moon fights with the sun, the moon is eaten by a dragon, and the moon contributes to maternal fertility, still exist among people around the world. In conclusion, there needs to be further socialization that SBBM is a scientific phenomenon and that it has nothing to do with the existing myths around the globe.  

scholarly journals Analysis of the folded normal distribution of a random variable

2021 ◽  
pp. 111-122
Author(s):  
Степан Алексеевич Рогонов ◽  
Илья Сергеевич Солдатенко
Keyword(s):  
Probability Distribution ◽  
Analytical Solution ◽  
Normal Distribution ◽  
Random Variables ◽  
Random Variable ◽  
Point Of View ◽  
Practical Solution ◽  
Absolute Value ◽  
Actual Error ◽  
Folded Normal Distribution

Анализ поведения случайных величин после различных преобразований можно применять при решении многих нетривиальных задач. В частности, решения, которые невозможно выразить аналитически, с точки зрения практической применимости способны давать результаты с точностью, достаточной для вычислений, вынося невыразимую невязку аналитического решения далеко за рамки требуемой погрешности. В настоящей работе исследовано поведение модуля нормально распределенной случайной величины и выяснено, при каких условиях можно пренебречь операцией взятия абсолютного значения и аппроксимировать модуль случайной величины {\it похожим} распределением вероятностей. The analysis of the behavior of random variables after various transformations can be used in the practical solution of many non-trivial problems. In particular, solutions that cannot be expressed purely analytically, from the point of view of practical applicability, are able to give results with accuracy sufficient for real calculations, taking the inexpressible discrepancy of the analytical solution far beyond the actual error. In this paper, the behavior of the modulus of a normally distributed random variable is investigated and it is found out under what conditions it is possible to neglect the operation of taking an absolute value and approximate the modulus of a random variable with a {\it similar} probability distribution.

scholarly journals SUBCOLL SUBCOLLOQUIAL MESURA AL MESURATIVE PHRASEOL TIVE PHRASEOLOGICAL UNI OGICAL UNITS IN THE S IN THE CULTURE OF THE PEOPLES OF THE WORLD

2021 ◽  
Vol 5 (4) ◽  
pp. 67-75
Author(s):  
Nodirjon Bakhromalievich Otaqulov ◽  
Keyword(s):  
Point Of View ◽  
World Culture ◽  
Main Attention ◽  
The World ◽  
Symbolic Meanings ◽  
Points Of View ◽  
Definition Of ◽  
Linguistic Units ◽  
The Relationship ◽  
Linguistic Material

Introduction. This article examines the use of subcolloquial mesurative phraseological units in the French, Uzbek and Russian languages from the point of view of reflecting in them the relationship between language and cultural semantics. Its purpose is to determine the similarities and differences between subcolloquial mesurative phraseological units, taking into account the main symbolic meanings of numbers in world culture. The article examines the subcolloquial mesurative units in French, Uzbek and Russian, their place in the linguistic picture of the world, as well as their use in proverbs, sayings and phraseological units. Various points of view of scientists-linguists are considered, in particular, that the category of time is a category of a wide heterogeonic plan and finds a peculiar reflection in the linguistic picture of the world. The questions of the use of the subcolloquial mesurative unit of time in lexical, phraseological units, as well as in proverbs and sayings in French, Uzbek and Russian are touched upon. The conclusions are supported by the factual linguistic material of the indicated languages. Materials and methods. The study used the methods of component and stylistic analysis within the framework of the linguistic picture of the world based on the system-structural paradigms. It is noted that subcolloquial mesurative phraseological units differ from other linguistic units in that they provide imagery, expressiveness and emotionality to speech. The main attention is paid to the definition of national and cultural features of phraseological units with subcolloquial mesurative components of the French, Uzbek and Russian languages, expressing different socio-cultural cultures of the world. Results and discussion. Scientific novelty lies in the study of determining the sources of phraseological units with subcolloquial mesurative components in the French, Uzbek and Russian languages on the basis of phraseological units. An analysis of the generality and specificity in the meanings of the subcolloquial mesuratic phraseological units of the compared languages was carried out. This analysis involves the study of the semantics of subcolloquial mesuratic phraseological units, the mechanisms of nomination and associative links existing in them, the consciousness and properties of the mentality of the three peoples

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