On the Relationship between the Conditional and Unconditional Distribution of a Random Variable

The purpose of this paper is to study definitions and characterizations of orders based on reliability measures related with the doubly truncated random variable X[x, y] = (X|x ≤ X ≤ y). The relationship between these orderings and various existing orderings of life distributions are discussed. Moreover, we give two new characterizations of the likelihood ratio order based on double truncation. These new orders complete a general diagram between orders defined from truncation.

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A Feature-Segmentation Model of Short-Term Visual Memory

Perception ◽

10.1068/p3320 ◽

2002 ◽

Vol 31 (5) ◽

pp. 579-589 ◽

Cited By ~ 13

Author(s):

Koji Sakai ◽

Toshio Inui

Keyword(s):

Visual Memory ◽

Random Variable ◽

Short Term ◽

Pattern Complexity ◽

Convex Part ◽

Good Account ◽

Feature Segmentation ◽

Short Term Visual Memory ◽

The Relationship ◽

Response Feature

A feature-segmentation model of short-term visual memory (STVM) for contours is proposed. Memory of the first stimulus is maintained until the second stimulus is observed. Three processes interact to determine the relationship between stimulus and response: feature encoding, memory, and decision. Basic assumptions of the model are twofold: (i) the STVM system divides a contour into convex parts at regions of concavity; and (ii) the value of each convex part represented in STVM is an independent Gaussian random variable. Simulation showed that the five-parameter fits give a good account of the effects of the four experimental variables. The model provides evidence that: (i) contours are successfully encoded within 0.5 s exposure, regardless of pattern complexity; (ii) memory noise increases as a linear function of retention interval; (iii) the capacity of STVM, defined by pattern complexity (the degree that a pattern can be handled for several seconds with little loss), is about 4 convex parts; and (iv) the confusability contributing to the decision process is a primary factor in deteriorating recognition of complex figures. It is concluded that visually presented patterns can be retained in STVM with considerable precision for prolonged periods of time, though some loss of precision is inevitable.

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On the convergence of quadratic variation for compound fractional Poisson processes

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-012-0023-2 ◽

2012 ◽

Vol 15 (2) ◽

Cited By ~ 5

Author(s):

Enrico Scalas ◽

Noèlia Viles

Keyword(s):

Stochastic Process ◽

Random Variable ◽

Quadratic Variation ◽

Poisson Processes ◽

Renewal Processes ◽

The Relationship ◽

Compound Renewal Processes

AbstractThe relationship between quadratic variation for compound renewal processes and M-Wright functions is discussed. The convergence of quadratic variation is investigated both as a random variable (for given t) and as a stochastic process.

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The general theory of canonical correlation and its relation to functional analysis

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700026707 ◽

1961 ◽

Vol 2 (2) ◽

pp. 229-242 ◽

Cited By ~ 29

Author(s):

E. J. Hannan

Keyword(s):

Linear Combination ◽

Canonical Correlation ◽

Random Variables ◽

Random Variable ◽

Finite Variance ◽

Finite Sample ◽

Standard Description ◽

Joint Distributions ◽

Gaussian Case ◽

The Relationship

The classical theory of canonical correlation is concerned with a standard description of the relationship between any linear combination of ρ random variablesxs, and any linear combination ofqrandom variablesytinsofar as this relation can be described in terms of correlation. Lancaster [1] has extended this theory, forp=q= 1, to include a description of the correlation of any function of a random variablexand any function of a random variabley(both functions having finite variance) for a class of joint distributions ofxandywhich is very general. It is the purpose of this paper to derive Lancaster's results from general theorems concerning the spectral decomposition of operators on a Hilbert space. These theorems lend themselves easily to the generalisation of the theory to situations wherepandqare not finite. In the case of Gaussian, stationary, processes this generalisation is equivalent to the classical spectral theory and corresponds to a canonical reduction of a (finite) sample of data which is basic. The theory also then extends to any number of processes. In the Gaussian case, also, the present discussion-is connected with the results of Gelfand and Yaglom [2] relating to the amount of information in one random process about another.

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Information Theory as a consistent framework for quantification and classification of landscape patterns

10.1101/383281 ◽

2018 ◽

Cited By ~ 2

Author(s):

Jakub Nowosad ◽

Tomasz F. Stepinski

Keyword(s):

Information Theory ◽

Landscape Ecology ◽

Real Life ◽

Random Variable ◽

Landscape Patterns ◽

Life Patterns ◽

Changing Patterns ◽

Correlated Information ◽

The Relationship

AbstractContextQuantitative grouping of similar landscape patterns is an important part of landscape ecology due to the relationship between a pattern and an underlying ecological process. One of the priorities in landscape ecology is a development of the theoretically consistent framework for quantifying, ordering and classifying landscape patterns.ObjectiveTo demonstrate that the Information Theory as applied to a bivariate random variable provides a consistent framework for quantifying, ordering, and classifying landscape patterns.MethodsAfter presenting Information Theory in the context of landscapes, information-theoretical metrics were calculated for an exemplar set of landscapes embodying all feasible configurations of land cover patterns. Sequences and 2D parametrization of patterns in this set were performed to demonstrate the feasibility of Information Theory for the analysis of landscape patterns.ResultsUniversal classification of landscape into pattern configuration types was achieved by transforming landscapes into a 2D space of weakly correlated information-theoretical metrics. An ordering of landscapes by any single metric cannot produce a sequence of continuously changing patterns. In real-life patterns, diversity induces complexity – increasingly diverse patterns are increasingly complex.ConclusionsInformation theory provides a consistent, theory-based framework for the analysis of landscape patterns. Information-theoretical parametrization of landscapes offers a method for their classification.

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Löytyä-verbin konstruktioiden yhteydessä esiintyvä subjektin sijanvaihtelu

Eesti ja soome-ugri keeleteaduse ajakiri Journal of Estonian and Finno-Ugric Linguistics ◽

10.12697/jeful.2021.12.1.01 ◽

2021 ◽

Vol 12 (1) ◽

pp. 11-39

Author(s):

Rodolfo Basile ◽

Ilmari Ivaska

Keyword(s):

Regression Analysis ◽

Word Order ◽

Random Variable ◽

Point Of View ◽

Case Alternation ◽

Part Of Speech ◽

Subject Number ◽

The Subject ◽

Semantic Variables ◽

The Relationship

Abstrakti. Artikkeli tarkastelee löytyä-verbin konstruktioiden nominatiivi- ja partitiivisubjektin vaihtelua. Aineistona on korpuksista poimittu 779 havainnon satunnaisotos, jota tarkastellaan sekä kvantitatiivisesti tilastollisin menetelmin että kvalitatiivisesta näkökulmasta. Tutkimus pyrkii selvittämään, mitkä muuttujat vaikuttavat löytyä-verbin sisältävien lauseiden subjektien sijanvalintaan. Valikoidut muuttujat ovat subjektin luku, subjektin jaollisuus, subjektin sanaluokka, sanajärjestys, aikamuoto, subjektin ja verbin välinen kongruenssi sekä subjektin lemma, joka toimii satunnaismuuttujana. Regressioanalyysin keinoin subjektin sijanvalintaa ennustetaan mainittujen muuttujien ja niiden välisten vuorovaikutussuhteiden avulla. Laadullisessa analyysissa käsitellään myös näiden morfosyntaktisten ja semanttisten seikkojen vaikutusta lauseen eksistentiaalisuuden sekä subjektin kvantiteetin ja definiittisyyden tulkintaan. Abstract. Rodolfo Basile, Ilmari Ivaska: Subject case alternation in constructions containing the Finnish verb löytyä. This article examines the nominative-partitive subject alternation occurring with constructions containing the Finnish verb löytyä. The material used is taken from corpora and consists of a random sample of 779 observations, analyzed both quantitatively by means of statistical methods, and from a qualitative point of view. The research aims at investigating which variables influence the case alternation of subjects of constructions containing the verb löytyä. The chosen variables are subject number, subject divisibility, subject part of speech, word order, tense, agreement and subject lemma, the only random variable. With the help of regression analysis, the subject case is predicted on the basis of said variables and of interactions between them. The qualitative analysis will also discuss the relationship these morphosyntactic and semantic variables have with the existential interpretations of the clause as well as with the subject quantity and definiteness. Kokkuvõte. Rodolfo Basile, Ilmari Ivaska: Subjekti käändevaheldus löytyä-verbiga konstruktsioonides. Artiklis uuritakse nominatiivi- ja partitiivikujulise subjekti vaheldumist soome keele löytyä-verbi sisaldavates konstruktsioonides. 779 vaatlust sisaldavat korpustest pärinevat juhuvalimit analüüsitakse nii kvantitatiivsete kui ka kvalitatiivsete meetoditega. Uurimuse eesmärk on välja selgitada, millised tegurid löytyä-verbi sisaldavate konstruktsioonide subjekti käändevalikut mõjutavad. Käsitletavad tegurid on subjekti arv, loendatavus, sõnaliik, konstruktsiooni sõnajärg, ajavorm ning subjekti ja verbi ühildumine. Juhusliku muutujana kaasatakse ka subjekti lemma. Regressioonanalüüsi abil ennustatakse subjekti käändevalikut mainitud tegurite ja nendevaheliste koosmõjude kaudu. Kvalitatiivse analüüsi käigus arutletakse ka selle üle, milline on nimetatud morfosüntaktiliste ja semantiliste tegurite mõju lause eksistentsiaalsele tõlgendusele ning subjekti kvantiteedile ja definiitsusele.

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Exit Condition for Probabilistic Assessment Using Monte Carlo Method

Transactions of the VŠB - Technical University of Ostrava Civil Engineering Series ◽

10.2478/v10160-010-0014-3 ◽

2010 ◽

Vol 10 (1) ◽

pp. 1-9

Author(s):

Jakub Valihrach ◽

Petr Konečný

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Monte Carlo Method ◽

Optimization Design ◽

Random Variable ◽

Probability Of Failure ◽

Probabilistic Assessment ◽

Theoretical Derivation ◽

The Monte Carlo Method ◽

The Relationship

Exit Condition for Probabilistic Assessment Using Monte Carlo Method This paper introduces a condition used to exit a probabilistic assessment using the Monte Carlo simulation, and to evaluate it with regard to the relationship between the computed estimate of the probability of failure and the target design probability. The estimation of probability of failure is treated as a random variable, considering its variance that is dependent on the number of performed Monte Carlo simulation steps. After theoretical derivation of the decision condition, it is tested numerically with regard to its accuracy and computational efficiency. The condition is suitable for optimization design using the Monte Carlo method.

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Reliability Research of Masonry Column Strengthened with CFRP Based on Monte-Carlo Method

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.163-167.3079 ◽

2010 ◽

Vol 163-167 ◽

pp. 3079-3083

Author(s):

Li Li ◽

Hong Yi Jiang ◽

Yi Zheng ◽

Yu Lin Yang ◽

Mei Zhu Sun

Keyword(s):

New Technology ◽

Axial Loading ◽

Random Variable ◽

Reinforced Plastics ◽

Reinforced Masonry ◽

Brick And Mortar ◽

The Stability ◽

Relationship Of ◽

The Relationship ◽

Engineering Personnel

CFRP(Carbon Fiber Reinforced Plastics) reinforced structure, as one kind of new technology, has been applied extensively in concrete structure, and CFRP reinforced masonry structure has been began studying and applied. But reliability research of masonry strengthened with CFRP is less, which restrains applying of CFRP. In the paper, Combined with the theory of reliability and tests, supposed that it is basic random variable that strength of brick and mortar and geometry dimension of members and effect of load, it is established that the stability probabilistic formula of brick column reinforced by CFRP under axial-loading. Its reliability is calculated, by means of Matlab. Under the action of different loads and total loads being constant, it is analyzed that the relationship of index of reliability and ratio of loading effect. Some useful results are gotten. And the result calculated is reasonable and reliable and it may supply engineering personnel with computer basis.

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Simulating Emergency Department Boarding Using a Difference Equation

10.1101/2020.03.19.20039040 ◽

2020 ◽

Author(s):

Edward G. Brown ◽

Patricia K. Howard ◽

Daniel Moore

Keyword(s):

Emergency Department ◽

Difference Equation ◽

Random Variable ◽

Status Quo ◽

Time Interval ◽

Simulation Methods ◽

The Status ◽

Relationship Of ◽

The Relationship ◽

Patient Presentation

AbstractBackgroundThis paper aims to provide a model that can be used to simulate the effect of patient presentation counts on ED boarder counts and investigate strategies that might be used for managing ED boarding levels.MethodsA boarding simulation model is constructed using a random variable and two regressions that are linked together in a difference equation. The simulation is run under varying constraints, including time interval, presentation counts, and boarder count threshold. Bootstrapping is used to run the simulation a large number of times so that mean and medians can be calculated along with confidence intervals.ResultsThe method outlined in this paper can be used to simulate the effect of presentation levels on ED boarder counts. Using these methods one can derive quantifiable estimates of time that an emergency department might meet or exceed a particular boarder count threshold.ConclusionsThese simulation methods can help an emergency department understand the dynamics of the system in the status quo of normal operations and quantify the relationship of presentation counts and throughput to the hospital. We are hopeful that others may use these methods, adapting, developing, and testing for their own institutions.

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HUBUNGAN ANTARA KONVERGEN HAMPIR PASTI, KONVERGEN DALAM PELUANG, DAN KONVERGEN DALAM SEBARAN

Jurnal Matematika UNAND ◽

10.25077/jmu.2.2.10-16.2013 ◽

2013 ◽

Vol 2 (2) ◽

pp. 10

Author(s):

Vira Agusta ◽

Dodi Devianto ◽

Hazmira Yozza

Keyword(s):

Probability Space ◽

Random Variable ◽

Convergence In Probability ◽

Convergence In Distribution ◽

Convergence Almost Surely ◽

The Relationship

Let fXng be a sequence of random variable dened on a probability space ( ; F; P). In this paper, we studied about the relationship between the convergence almost surely, convergence in probability, and convergence in distribution. If the sequenceof random variable convergence almost surely to a random variable X then fXng convergence in probability to X. If the sequence of random variable fXng convergence in probability to a random variable X then fXng convergence in distribution to X.

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