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

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.

scholarly journals On rough convergence variables of triple sequences

Analysis ◽  
2020 ◽  
Vol 40 (2) ◽  
pp. 85-88
Author(s):  
Nagarajan Subramanian ◽  
Ayhan Esi
Keyword(s):  
Convergence In Distribution ◽  
Fundamental Theory ◽  
Mathematical Properties ◽  
Convergence Almost Surely ◽  
The Relationship ◽  
Convergence In Mean

AbstractTriple sequence convergence plays an extremely important role in the fundamental theory of mathematics. This paper contains four types of convergence concepts, namely, convergence almost surely, convergence incredibility, trust convergence in mean, and convergence in distribution, and discuss the relationship among them and some mathematical properties of those new convergence.

New Stochastic Orders Based on Double Truncation

1997 ◽  
Vol 11 (3) ◽  
pp. 395-402 ◽  
Author(s):  
Jorge Navarro ◽  
Felix Belzunce ◽  
Jose M. Ruiz
Keyword(s):  
Likelihood Ratio ◽  
Random Variable ◽  
Stochastic Orders ◽  
Likelihood Ratio Order ◽  
Reliability Measures ◽  
Life Distributions ◽  
The Relationship ◽  
Double Truncation

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.

A Feature-Segmentation Model of Short-Term Visual Memory

Perception ◽  
10.1068/p3320 ◽  
2002 ◽  
Vol 31 (5) ◽  
pp. 579-589 ◽  
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.

scholarly journals On comparison of the principles of equivalent utility and its applications

2019 ◽  
Vol 11 (2) ◽  
pp. 240-249
Author(s):  
M. Chudziak
Keyword(s):  
Decision Making ◽  
Probability Space ◽  
Random Variable ◽  
Insurance Premium ◽  
Behavioral Models ◽  
Decision Making Under Risk ◽  
Rank Dependent Utility ◽  
Positive Homogeneity ◽  
Bounded Random Variable ◽  
Negative Real Number

An insurance premium principle is a way of assigning to every risk, represented by a non-negative bounded random variable on a given probability space, a non-negative real number. Such a number is interpreted as a premium for the insuring risk. In this paper the implicitly defined principle of equivalent utility is investigated. Using the properties of the quasideviation means, we characterize a comparison in the class of principles of equivalent utility under Rank-Dependent Utility, one of the important behavioral models of decision making under risk. Then we apply this result to establish characterizations of equality and positive homogeneity of the principle. Some further applications are discussed as well.

scholarly journals Gaps in Discrete Random Samples

2009 ◽  
Vol 46 (04) ◽  
pp. 1038-1051 ◽  
Author(s):  
Rudolf Grübel ◽  
Paweł Hitczenko
Keyword(s):  
Analysis Of Algorithms ◽  
Sufficient Conditions ◽  
Borderline Case ◽  
Convergence In Probability ◽  
Enumerative Combinatorics ◽  
Random Samples ◽  
The Family ◽  
Heavy Tailed ◽  
Convergence Almost Surely ◽  
Necessary And Sufficient

Let (X i ) i∈ℕ be a sequence of independent and identically distributed random variables with values in the set ℕ0 of nonnegative integers. Motivated by applications in enumerative combinatorics and analysis of algorithms we investigate the number of gaps and the length of the longest gap in the set {X 1,…,X n } of the first n values. We obtain necessary and sufficient conditions in terms of the tail sequence (q k ) k∈ℕ0 , q k =P(X 1≥ k), for the gaps to vanish asymptotically as n→∞: these are ∑ k=0 ∞ q k+1/q k <∞ and limk→∞ q k+1/q k =0 for convergence almost surely and convergence in probability, respectively. We further show that the length of the longest gap tends to ∞ in probability if q k+1/q k → 1. For the family of geometric distributions, which can be regarded as the borderline case between the light-tailed and the heavy-tailed situations and which is also of particular interest in applications, we study the distribution of the length of the longest gap, using a construction based on the Sukhatme–Rényi representation of exponential order statistics to resolve the asymptotic distributional periodicities.

Convergence Results for r-Iterated Means of the Denominators of the Lüroth Series

2016 ◽  
Vol 11 (2) ◽  
pp. 179-203
Author(s):  
Rita Giuliano
Keyword(s):  
Convergence In Probability ◽  
Convergence In Distribution ◽  
Asymptotic Results ◽  
Arithmetic Means ◽  
Convergence Results ◽  
Weighted Means

Abstract In the present paper we extend two classic asymptotic results concerning convergence in probability and convergence in distribution for the denominators of the Lüroth series and obtain new theorems concerning the same two kinds of convergence for the r-iterated arithmetic means of such denominators. These results are extended to r-iterated weighted means.

scholarly journals On the convergence of quadratic variation for compound fractional Poisson processes

2012 ◽  
Vol 15 (2) ◽  
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.

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

1961 ◽  
Vol 2 (2) ◽  
pp. 229-242 ◽  
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.

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

2018 ◽  
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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