scholarly journals Measuring Independence between Statistical Randomness Tests by Mutual Information

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 741
Author(s):  
Jorge Augusto Karell-Albo ◽  
Carlos Miguel Legón-Pérez  ◽  
Evaristo José Madarro-Capó  ◽  
Omar Rojas ◽  
Guillermo Sosa-Gómez
Keyword(s):  
Mutual Information ◽  
Correlation Coefficient ◽  
Linear Correlation ◽  
Statistical Dependency ◽  
Nonlinear Correlations ◽  
Randomness Tests ◽  
Dependency Detection

The analysis of independence between statistical randomness tests has had great attention in the literature recently. Dependency detection between statistical randomness tests allows one to discriminate statistical randomness tests that measure similar characteristics, and thus minimize the amount of statistical randomness tests that need to be used. In this work, a method for detecting statistical dependency by using mutual information is proposed. The main advantage of using mutual information is its ability to detect nonlinear correlations, which cannot be detected by the linear correlation coefficient used in previous work. This method analyzes the correlation between the battery tests of the National Institute of Standards and Technology, used as a standard in the evaluation of randomness. The results of the experiments show the existence of statistical dependencies between the tests that have not been previously detected.

scholarly journals Operational Risk Aggregation Based on Business Line Dependence: A Mutual Information Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Wenzhou Wang ◽  
Limeng Shi ◽  
Xiaoqian Zhu
Keyword(s):  
Mutual Information ◽  
Correlation Coefficient ◽  
Linear Correlation ◽  
Risk Estimation ◽  
Pearson Correlation ◽  
Operational Risk ◽  
Random Variable ◽  
Data Set ◽  
Risk Aggregation ◽  
Business Line

The dependencies between different business lines of banks have serious effects on the accuracy of operational risk estimation. Furthermore, the dependencies are far more complicated than simple linear correlation. While Pearson correlation coefficient is constructed based on the hypothesis of a linear association, the mutual information that measures all the information of a random variable contained in another random variable is a powerful alternative. Based on mutual information, the generalized correlation coefficient which can capture both linear and nonlinear correlation can be derived. This paper models the correlation between business lines by mutual information and normal copula. The experiment on a real-world Chinese bank operational risk data set shows that using mutual information to model the dependencies between business lines is more reasonable than linear correlation.

A selection of remarks on the measurement of correlations between variables of a panel data structure

2021 ◽  
Vol 66 (5) ◽  
pp. 7-25
Author(s):  
Mieczysław Kowerski ◽  
Jarosław Bielak
Keyword(s):  
Panel Data ◽  
Correlation Coefficient ◽  
Linear Correlation ◽  
Stock Exchange ◽  
Panel Data Analysis ◽  
Correlation Coefficients ◽  
Data Dependencies ◽  
Construction Companies ◽  
Advantages And Disadvantages ◽  
Warsaw Stock Exchange

Many articles featuring panel data modelling tend to begin their considerations with an introduction of the Pearson linear correlation coefficients matrix between the analysed variables. The aim of the article is to prove such an approach unsuitable in the analysis of panel data dependencies. Instead, an attempt has been made to propose a more appropriate measure – a correlation coefficient between the empirical and fitted values of the dependent variable of the estimated panel model (with fixed or random effects) in relation to the variable whose dependency towards the dependent variable is being studied. Pearson’s linear correlation coefficient does not reflect the basic advantage of panel data, which is the ability to provide information about the dependencies of the studied phenomena simultaneously in time and space. The fact that one observation relates to object i during period t and another to object j during period t + 1 is irrelevant for the calculation of the coefficient. Pearson’s coefficient, however, can be used when conducting sub-calculations in panel data analysis. The presented considerations have been illustrated by the calculations of the relationships between the structure of capital and the profitability and size of 17 construction companies listed on the Warsaw Stock Exchange in the years 2009–2018 (170 observations) which created a balanced panel. A specification of the advantages and disadvantages of the proposed solution was formulated on the basis of the calculations.

Serious Analytical and Conceptual Errors in Bilirubin Binding Studies

PEDIATRICS ◽  
1981 ◽  
Vol 67 (6) ◽  
pp. 935-936
Author(s):  
Charles E. Ahlfors
Keyword(s):  
Correlation Coefficient ◽  
Linear Correlation ◽  
Accurate Method ◽  
Binding Studies ◽  
Low Correlation ◽  
Total Capacity ◽  
Bilirubin Binding

The unexpectedly high and 1:1 correlation among fluorometric, Sephadex, and peroxidase determinations of total and reserve bilirubin binding capacities as reported by Cashore et al1 is quite remarkable considering the serious analytical and conceptual errors in the article, the previously observed lack of linear correlation between the fluorometer and 2-(4'-hydroxybenzene)azobenzoic acid (HABA),2 and the relatively low correlation coefficient (.92) observed when the peroxidase test is compared with itself on different instruments.3 The addition of sufficient bilirubin to near saturation of the first site should make the fluorometer a reasonably accurate method of assessing "true" total capacity (usually thought to be 1 mole of bilirubin bound per mole of albumin).

scholarly journals Correlation of plasma concentrations of cystatin C and creatinine to inulin clearance in a pediatric population

1998 ◽  
Vol 44 (6) ◽  
pp. 1334-1338 ◽  
Author(s):  
Douglas Stickle ◽  
Barbara Cole ◽  
Karl Hock ◽  
Keith A Hruska ◽  
Mitchell G Scott
Keyword(s):  
Correlation Coefficient ◽  
Cystatin C ◽  
Linear Correlation ◽  
Pediatric Patients ◽  
Plasma Concentrations ◽  
Age Groups ◽  
Inulin Clearance ◽  
Blood Concentrations ◽  
Group A ◽  
Group B

Abstract Measurement of blood concentrations of cystatin C (cysC), a cysteine protease inhibitor present in human plasma, has been suggested for use as an indicator of glomerular filtration rate (GFR) in a manner analogous to the use of plasma creatinine (SCR). In this study, cysC and SCR were measured in plasma from pediatric patients (4–19 years) with renal disease for whom a “gold standard” measurement of GFR via inulin clearance (CIN) was available. The data analyses were divided into two age groups: group A (4–12 years, n = 26) and group B (12–19 years, n = 34). For both age groups, the linear correlation coefficient of [cysC]−1 vs CIN (mL/min/1.73 m2) (r = 0.765 for group A and r = 0.869 for group B) was less than that of the linear correlation coefficient of [SCR]−1 vs CIN (r = 0.841 for group A and r = 0.892 for group B). As a single measurement for detection of abnormal GFR, however, the optimum receiver-operator characteristic point for cysC measurement (for group A at cysC >1.2 mg/L, sensitivity = 80%, specificity = 91%; and for group B at cysC >1.4 mg/L, sensitivity = 87%, specificity = 100%) was numerically superior to that for SCR measurement (for group A at SCR >8.0 mg/L, sensitivity = 67%, specificity = 100%; and for group B at SCR >9.0 mg/L, sensitivity = 91%, specificity = 91%), using a reference value for normal GFR of CIN > 90 mL/min/1.73 m2. However, these differences were not statistically significant. CysC measurement appears to be broadly equivalent to SCR measurement for estimation of GFR in pediatric patients.

EEG TRANSFER ENTROPY TRACKS CHANGES IN INFORMATION TRANSFER ON THE ONSET OF VISION

2012 ◽  
Vol 17 ◽  
pp. 9-18 ◽  
Author(s):  
M. D. MADULARA ◽  
P. A. B. FRANCISCO ◽  
S. NAWANG ◽  
D. C. AROGANCIA ◽  
C. J. CELLUCCI ◽  
...  
Keyword(s):  
Mutual Information ◽  
Information Transfer ◽  
Occipital Lobe ◽  
Transfer Entropy ◽  
The Other ◽  
Information Measures ◽  
Eyes Closed ◽  
Eyes Open ◽  
Almost All ◽  
Nonlinear Correlations

We investigate the pairwise mutual information and transfer entropy of ten-channel, free-running electroencephalographs measured from thirteen subjects under two behavioral conditions: eyes open resting and eyes closed resting. Mutual information measures nonlinear correlations; transfer entropy determines the directionality of information transfer. For all channel pairs, mutual information is generally lower with eyes open compared to eyes closed indicating that EEG signals at different scalp sites become more dissimilar as the visual system is engaged. On the other hand, transfer entropy increases on average by almost two-fold when the eyes are opened. The largest one-way transfer entropies are to and from the Oz site consistent with the involvement of the occipital lobe in vision. The largest net transfer entropies are from F3 and F4 to almost all the other scalp sites.

scholarly journals Comparison of Emission Measurement Methods for Electromagnetic Disturbances in the Frequency Range from 30 MHz to 300 MHz for LED Lamps According to EN 55015

2019 ◽  
Vol 63 (2) ◽  
pp. 106-111
Author(s):  
Kazimierz Kamuda ◽  
Dariusz Klepacki ◽  
Kazimierz Kuryło ◽  
Wiesław Sabat
Keyword(s):  
Correlation Coefficient ◽  
Linear Correlation ◽  
Traditional Method ◽  
Measurement Methods ◽  
The Other ◽  
Emission Measurement ◽  
Frequency Range ◽  
Statistical Tools ◽  
Equivalent Method ◽  
Electromagnetic Disturbances

The results of measurements of electromagnetic disturbances emitted by LED lamps, in the frequency range from 30 MHz to 300 MHz, which were made using two methods described in the EN 55015/2013 standard have been presented in the paper. In order to compare both methods, each tested lamp was first measured using the traditional method described in Section4.4.2 and then tested by an alternative, equivalent method described in Annex B of the above-mentioned standard. The comparison of results for both methods indicates that using first method, a given LED lamp emits disturbances below the acceptable limits, while the same LED lamp tested with the second method emits disturbances that are at the limit of admissible values. Additionally, used statistical tools in the form of calculated linear correlation coefficient show that the nature of the emission of disturbances measured for the same lamp is very comparable in both methods. The reference of these quasi-peak values to the permissible limits applicable in one or the other method may lead to different decisions.

scholarly journals Isotherm Studies for the Sorption of Metal Ions on to Peat

1998 ◽  
Vol 16 (1) ◽  
pp. 51-66 ◽  
Author(s):  
G. Mckay ◽  
B. Vong ◽  
J.F. Porter
Keyword(s):  
Metal Ions ◽  
Correlation Coefficient ◽  
Linear Correlation ◽  
Langmuir Equation ◽  
Single Component ◽  
Equilibrium Isotherms ◽  
Cobalt Nickel ◽  
Saturation Capacity ◽  
Best Fit

The adsorption of five single-component metal ions, namely, copper, cadmium, cobalt, nickel and zinc, on to peat has been studied. Equilibrium isotherms were measured and analysed using three methods: Langmuir, Freundlich and Redlich–Peterson. Overall the Langmuir equation gave the best fit based on a linear correlation coefficient. The Langmuir equation was used to determine the monolayer saturation capacity for each of the metals on peat. These sorption capacities are: cadmium, 99.47 μmol/g (11.18 mg/g) peat; cobalt, 446.93 μmol/g (26.34 mg/g) peat; copper, 198.31 μmol/g (12.60 mg/g) peat; nickel, 113.24 μmol/g (6.65 mg/g) peat; and zinc, 141.93 μmol/g (9.28 mg/g) peat.

scholarly journals Univariate and Multivariate Analysis of Phosphorus Element in Fertilizers Using Laser-Induced Breakdown Spectroscopy

Sensors ◽  
2019 ◽  
Vol 19 (7) ◽  
pp. 1727 ◽  
Author(s):  
Baohua Zhang ◽  
Pengpeng Ling ◽  
Wen Sha ◽  
Yongcheng Jiang ◽  
Zhifeng Cui
Keyword(s):  
Multivariate Analysis ◽  
Correlation Coefficient ◽  
Linear Correlation ◽  
Matrix Effect ◽  
Rapid Detection ◽  
Accurate Method ◽  
P Element ◽  
Characteristic Line ◽  
Least Squares Regression ◽  
The Matrix

Rapid detection of phosphorus (P) element is beneficial to the control of compound fertilizer production process and is of great significance in the fertilizer industry. The aim of this work was to compare the univariate and multivariate analysis of phosphorus element in compound fertilizers and obtain a reliable and accurate method for rapid detection of phosphorus element. A total of 47 fertilizer samples were collected from the production line; 36 samples were used as a calibration set, and 11 samples were used as a prediction set. The univariate calibration curve was constructed by the intensity of characteristic line and the concentration of P. The linear correlation coefficient was 0.854 as the existence of the matrix effect. In order to eliminate the matrix effect, the internal standardization as the appropriate methodology was used to increase the accuracy. Using silicon (Si) element as an internal element, a linear correlation coefficient of 0.932 was obtained. Furthermore, the chemometrics model of partial least-squares regression (PLSR) was used to analysis the concentration of P in fertilizer. The correlation coefficient was 0.977 and 0.976 for the calibration set and prediction set, respectively. The results indicated that the LIBS technique coupled with PLSR could be a reliable and accurate method in the quantitative determination of P element in complex matrices like compound fertilizers.

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