scholarly journals On statistical independence and no-correlation for a pair of random variables taking two values: Classical and quantum

2018 ◽  
Vol 2018 (8) ◽  
Author(s):  
Toru Ohira
Keyword(s):  
Random Variables ◽  
Statistical Independence

scholarly journals Random Permutations, Non-Decreasing Subsequences and Statistical Independence

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1415
Author(s):  
Jesús E. García ◽  
Verónica A. González-López
Keyword(s):  
Random Variables ◽  
Continuous Data ◽  
Random Permutations ◽  
Statistical Independence ◽  
Independence Test ◽  
Independence Tests ◽  
Present Procedure ◽  
Longest Increasing Subsequence

In this paper, we show how the longest non-decreasing subsequence, identified in the graph of the paired marginal ranks of the observations, allows the construction of a statistic for the development of an independence test in bivariate vectors. The test works in the case of discrete and continuous data. Since the present procedure does not require the continuity of the variables, it expands the proposal introduced in Independence tests for continuous random variables based on the longest increasing subsequence (2014). We show the efficiency of the procedure in detecting dependence in real cases and through simulations.

On statistical independence and zero correlation in several dimensions

1960 ◽  
Vol 1 (4) ◽  
pp. 492-496 ◽  
Author(s):  
H. O. Lancaster
Keyword(s):  
Canonical Form ◽  
Arbitrary Number ◽  
Random Variables ◽  
Summable Function ◽  
Statistical Independence ◽  
Bivariate Distributions ◽  
Canonical Correlations ◽  
Zero Correlation ◽  
Maximal Correlation

Bivariate distributions, subject to a condition of φ2 boundedness to be defined later, can be written in a canonical form. Sarmanov [4] used such a form to deduce that two random variables are independent if and only if the maximal correlation of any square summable function, ξ (x1), of the first variable with any square summable function, η(x2), of the second variable is zero. This is equivalent to the condition that the canonical correlations are all zero. The theorem of Sarmanov [4] was proved without any restriction in Lancaster [2] and the proof is now extended to an arbitrary number of dimensions.

DEMPSTER COMBINATION RULE WITH BOOLEAN-LIKE PROCESSED BELIEF FUNCTIONS

2001 ◽  
Vol 09 (01) ◽  
pp. 105-121 ◽  
Author(s):  
IVAN KRAMOSIL
Keyword(s):  
Empirical Data ◽  
Random Variables ◽  
Unit Interval ◽  
Probability Measures ◽  
Belief Functions ◽  
Statistical Independence ◽  
Combination Rule ◽  
Real Numbers

It is a well-known fact that the Dempster combination rule for combination of uncertainty degrees coming from two or more sources is legitimate only if the combined empirical data, charged with uncertainty and taken as random variables, are statistically (stochastically) independent. We shall prove, however, that for a particular but large enough class of probability measures, an analogy of Dempster combination rule, preserving its extensional character but using some nonstandard and boolean-like structures over the unit interval of real numbers, can be obtained without the assumption of statistical independence of input empirical data charged with uncertainty.

scholarly journals Joint Probability Distribution of Streamflows and Tides in Estuaries

1987 ◽  
Vol 18 (4-5) ◽  
pp. 237-246 ◽  
Author(s):  
G. V. Loganathan ◽  
C. Y. Kuo ◽  
J. Yannaccone
Keyword(s):  
Probability Distribution ◽  
Chesapeake Bay ◽  
Random Variables ◽  
Joint Probability ◽  
Original Data ◽  
Joint Probability Distribution ◽  
Statistical Independence ◽  
Probability Of Occurrence ◽  
Traditional Assumption ◽  
Box Cox Transformation

A procedure for estimating the joint probability of occurrence of correlated extreme tides and corresponding freshwater flows in estuaries is presented. The method uses the Box-Cox transformation to transform the original data to near normality, and therefore the search for a parent distribution is avoided. It is also shown that the traditional assumption of statistical independence for the jointly distributed random variables may lead to the underestimation of flows and tidal heights. The methodology is applied to the Rappahannock River in Virginia which flows into the Chesapeake Bay.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

The Constructive Thinking Inventory: Factorial Structure in Healthy Individuals and Patients with Chronic Skin Diseases

1998 ◽  
Vol 14 (3) ◽  
pp. 226-233 ◽  
Author(s):  
Jürgen Hoyer ◽  
Mechthild Averbeck ◽  
Thomas Heidenreich ◽  
Ulrich Stangier ◽  
Karin Pöhlmann ◽  
...  
Keyword(s):  
Skin Diseases ◽  
Principal Component ◽  
Initial Study ◽  
Statistical Independence ◽  
Constructive Thinking ◽  
Global Factor ◽  
Emotional Coping ◽  
Factor Congruence ◽  
Chronic Skin ◽  
Chronic Skin Diseases

Epstein's “Constructive Thinking Inventory” (CTI) was developed to measure the construct of experiential intelligence, which is based on his cognitive-experiential self-theory. Inventory items were generated by sampling naturally occurring automatic cognitions. Using principal component analysis, the findings showed a global factor of coping ability as well as six main factors: Emotional Coping, Behavioral Coping, Categorical Thinking, Personal Superstitious Thinking, Esoteric Thinking, and Naive Optimism. We tested the replicability of this factor structure and the amount of statistical independence (nonredundancy) between these factors in an initial study of German students (Study 1, N = 439) and in a second study of patients with chronic skin disorders (Study 2, N = 187). Factor congruence with the original (American) data was determined using a formula proposed by Schneewind and Cattell (1970) . Our findings show satisfactory factor congruence and statistical independence for Emotional Coping and Esoteric Thinking in both studies, while full replicability or independence could not be found in both for the other factors. Implications for the use and further development of the CTI are discussed.

On the Mathematical Basis of Zelen’s Prerandomized Designs

1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann
Keyword(s):  
Clinical Trial ◽  
Normal Distribution ◽  
Random Variables ◽  
Small Samples ◽  
Selection Effects ◽  
Sample Sizes ◽  
Mathematical Basis ◽  
Additional Assumptions

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

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