Stochastic Independence

1997 ◽  
pp. 121-146
Author(s):  
Bert Fristedt ◽  
Lawrence Gray
Keyword(s):  
Stochastic Independence

THE FIVE INDEPENDENCES AS NATURAL PRODUCTS

2003 ◽  
Vol 06 (03) ◽  
pp. 337-371 ◽  
Author(s):  
NAOFUMI MURAKI
Keyword(s):  
Probability Theory ◽  
Natural Products ◽  
Tensor Product ◽  
Natural Product ◽  
Free Product ◽  
Noncommutative Probability ◽  
Stochastic Independence ◽  
Boolean Product ◽  
Probability Spaces ◽  
Noncommutative Probability Theory

Let [Formula: see text] be the class of all algebraic probability spaces. A "natural product" is, by definition, a map [Formula: see text] which is required to satisfy all the canonical axioms of Ben Ghorbal and Schürmann for "universal product" except for the commutativity axiom. We show that there exist only five natural products, namely tensor product, free product, Boolean product, monotone product and anti-monotone product. This means that, in a sense, there exist only five universal notions of stochastic independence in noncommutative probability theory.

scholarly journals Assembling a consistent set of sentences in relational probabilistic logic with stochastic independence

2009 ◽  
Vol 7 (2) ◽  
pp. 137-154 ◽  
Author(s):  
Cassio Polpo de Campos ◽  
Fabio Gagliardi Cozman ◽  
José Eduardo Ochoa Luna
Keyword(s):  
Probabilistic Logic ◽  
Stochastic Independence

scholarly journals Disaggregative Invariance of Daily Precipitation

1997 ◽  
Vol 36 (6) ◽  
pp. 721-734 ◽  
Author(s):  
Roman Krzysztofowicz ◽  
Thomas A. Pomroy
Keyword(s):  
Empirical Evidence ◽  
Diurnal Cycle ◽  
Daily Precipitation ◽  
Precipitation Amount ◽  
Total Precipitation ◽  
Stochastic Independence ◽  
Precipitation Forecasting ◽  
Precipitation Timing ◽  
Temporal Disaggregation ◽  
Precipitation Records

Abstract Disaggregative invariance refers to stochastic independence between the total precipitation amount and its temporal disaggregation. This property is investigated herein for areal average and point precipitation amounts accumulated over a 24-h period and disaggregated into four 6-h subperiods. Statistical analyses of precipitation records from 1948 to 1993 offer convincing empirical evidence against the disaggregative invariance and in favor of the conditional disaggregative invariance, which arises when the total amount and its temporal disaggregation are conditioned on the timing of precipitation within the diurnal cycle. The property of conditional disaggregative invariance allows the modeler or the forecaster to decompose the problem of quantitative precipitation forecasting into three tasks: (i) forecasting the precipitation timing; (ii) forecasting the total amount, conditional on timing; and (iii) forecasting the temporal disaggregation, conditional on timing. Tasks (ii) and (iii) can be performed independently of one another, and this offers a formidable advantage for applications.

Stochastic Independence

1967 ◽  
pp. 57-76
Author(s):  
HOWARD G. TUCKER
Keyword(s):  
Stochastic Independence

On the stochastic independence properties of hard-core distributions

COMBINATORICA ◽  
1997 ◽  
Vol 17 (3) ◽  
pp. 369-391 ◽  
Author(s):  
Jeff Kahn ◽  
P. Mark Kayll
Keyword(s):  
Hard Core ◽  
Stochastic Independence ◽  
Independence Properties

scholarly journals RELATIONS BETWEEN STOCHASTIC ORDERINGS AND GENERALIZED STOCHASTIC PRECEDENCE

2015 ◽  
Vol 29 (3) ◽  
pp. 329-343 ◽  
Author(s):  
Emilio De Santis ◽  
Fabio Fantozzi ◽  
Fabio Spizzichino
Keyword(s):  
Random Variables ◽  
Stochastic Ordering ◽  
Stochastic Independence ◽  
Stochastic Orderings ◽  
Stochastic Dependence ◽  
Natural Concept ◽  
Decisions Under Risk ◽  
Stochastic Precedence ◽  
Special Classes

The concept of stochastic precedence between two real-valued random variables has often emerged in different applied frameworks. In this paper, we analyze several aspects of a more general, and completely natural, concept of stochastic precedence that also had appeared in the literature. In particular, we study the relations with the notions of stochastic ordering. Such a study leads us to introducing some special classes of bivariate copulas. Motivations for our study can arise from different fields. In particular, we consider the frame of Target-Based Approach in decisions under risk. This approach has been mainly developed under the assumption of stochastic independence between “Prospects” and “Targets”. Our analysis concerns the case of stochastic dependence.

Le Modele De Rasch

1988 ◽  
Vol 31 ◽  
pp. 57-70
Author(s):  
John H.A.L. de Jong
Keyword(s):  
Rasch Model ◽  
Reliability And Validity ◽  
Test Reliability ◽  
Stochastic Independence ◽  
Validation Procedure ◽  
Local Stochastic Independence ◽  
The One ◽  
Definition Of ◽  
Latent Traits ◽  
The Rasch Model

This paper provides an elementary introduction to the one parameter psychometric model known as the Rasch model. It explains the basic principles underlying the model and the concepts of unidimensionality, local stochastic independence, and additivity in non-mathematical terms. The requirements of measurement procedures, the measurement of latent traits, the control on model fit, and the definition of a trait are discussed. It is argued that the Rasch model is particularly appropriate to understand the mutual dependence of test reliability and validity. Examples from foreign language listening comprehension tests are used to illustrate the application of the model to a test validation procedure.

The distribution of the maximum of a random number of random variables with applications

1973 ◽  
Vol 10 (01) ◽  
pp. 122-129 ◽  
Author(s):  
Janos Galambos
Keyword(s):  
Service Time ◽  
Joint Distribution ◽  
Random Number ◽  
Random Variables ◽  
Stochastic Independence ◽  
Fixed Integer ◽  
Number Of Components ◽  
Distribution Of The Maximum ◽  
Distribution Of Elements ◽  
Mild Assumption

The asymptotic distribution of the maximum of a random number of random variables taken from the model below is shown to be the same as when their number is a fixed integer. Applications are indicated to determine the service time of a system of a large number of components, when the number of components to be serviced is not known in advance. A much slighter assumption is made than the stochastic independence of the periods of time needed for servicing the different components. In our model we assume that the random variables can be grouped into a number of subcollections with the following properties: (i) the random variables taken from different groups are asymptotically independent, (ii) the largest number of elements in a subgroup is of smaller order than the overall number of random variables. In addition, a very mild assumption is made for the joint distribution of elements from the same group.

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