scholarly journals GENERALIZED MEAN OF ORDER $t$ VIA BOX AND COX'S TRANSFORMATION

1994 ◽  
Vol 25 (2) ◽  
pp. 125-141
Author(s):  
VICENTE QUESADA ◽  
INDER JEET TANEJA
Keyword(s):  
Transformation Function ◽  
Shannon’S Entropy ◽  
Information Theoretic ◽  
Shannon's Entropy ◽  
Relative Information ◽  
Information Theoretic Measures ◽  
Two Measures ◽  
The Mean ◽  
Generalized Mean ◽  
Jensen Difference

Mean of order $t$ and Box and Cox's transformation function are very famous in the literature of mathematics and statistics respectively. In this paper, we have derived some standard inequalities from the mean of order $t$ and studied some interesting properties of Box and Cox's transformation function. A compos- iterelation of these two measures, calling generalized mean of order $t$ or unified $(t,s)$-mean is considered. The unified $(t,s)$-mean leads us to very important gen- eralized information theoretic measures. These measures include generalizations of Shannon's entropy, Kullback-leibler's relative information, Kerridge's inaccu- racy, J-divergence, Jensen difference dive~gence measure, etc. Properties of unified $(t,s)$-mean are also studied.

Large-sample confidence intervals of information-theoretic measures in linguistics

2020 ◽  
Vol 6 (1) ◽  
pp. 19-54
Author(s):  
Ryan Ka Yau Lai ◽  
Youngah Do
Keyword(s):  
Maximum Likelihood ◽  
Corpus Linguistics ◽  
Delta Method ◽  
Confidence Bounds ◽  
Likelihood Estimator ◽  
Information Theoretic ◽  
Leibler Divergence ◽  
Information Theoretic Measures ◽  
Data Points ◽  
Measure Of Uncertainty

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.

scholarly journals Optimized permutation testing for information theoretic measures of multi-gene interactions

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
James M. Kunert-Graf ◽  
Nikita A. Sakhanenko ◽  
David J. Galas
Keyword(s):  
Large Scale ◽  
Permutation Test ◽  
Association Studies ◽  
Genome Wide Association Studies ◽  
Permutation Testing ◽  
Exact Test ◽  
Information Theoretic ◽  
Information Theoretic Measures ◽  
Full Analysis ◽  
Computational Bottleneck

Abstract Background Permutation testing is often considered the “gold standard” for multi-test significance analysis, as it is an exact test requiring few assumptions about the distribution being computed. However, it can be computationally very expensive, particularly in its naive form in which the full analysis pipeline is re-run after permuting the phenotype labels. This can become intractable in multi-locus genome-wide association studies (GWAS), in which the number of potential interactions to be tested is combinatorially large. Results In this paper, we develop an approach for permutation testing in multi-locus GWAS, specifically focusing on SNP–SNP-phenotype interactions using multivariable measures that can be computed from frequency count tables, such as those based in Information Theory. We find that the computational bottleneck in this process is the construction of the count tables themselves, and that this step can be eliminated at each iteration of the permutation testing by transforming the count tables directly. This leads to a speed-up by a factor of over 103 for a typical permutation test compared to the naive approach. Additionally, this approach is insensitive to the number of samples making it suitable for datasets with large number of samples. Conclusions The proliferation of large-scale datasets with genotype data for hundreds of thousands of individuals enables new and more powerful approaches for the detection of multi-locus genotype-phenotype interactions. Our approach significantly improves the computational tractability of permutation testing for these studies. Moreover, our approach is insensitive to the large number of samples in these modern datasets. The code for performing these computations and replicating the figures in this paper is freely available at https://github.com/kunert/permute-counts.

Insights into codeswitching from online communication: Effects of language preference and conditions arising from vocabulary richness

2021 ◽  
pp. 1-7
Author(s):  
Laurie Beth Feldman ◽  
Vidhushini Srinivasan ◽  
Rachel B. Fernandes ◽  
Samira Shaikh
Keyword(s):  
Online Communication ◽  
Language Preference ◽  
Lexical Diversity ◽  
Information Theoretic ◽  
Vocabulary Richness ◽  
Twitter Data ◽  
Language Mixing ◽  
Communication Effects ◽  
Information Theoretic Measures ◽  
Spanish Bilinguals

Abstract Twitter data from a crisis that impacted many English–Spanish bilinguals show that the direction of codeswitches is associated with the statistically documented tendency of single speakers to prefer one language over another in their tweets, as gleaned from their tweeting history. Further, lexical diversity, a measure of vocabulary richness derived from information-theoretic measures of uncertainty in communication, is greater in proximity to a codeswitch than in productions remote from a switch. The prospects of a role for lexical diversity in characterizing the conditions for a language switch suggest that communicative precision may induce conditions that attenuate constraints against language mixing.

scholarly journals Information-Theoretic Measures and Modeling Stock Market Volatility: A Comparative Approach

Risks ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 89
Author(s):  
Muhammad Sheraz ◽  
Imran Nasir
Keyword(s):  
Stock Market ◽  
Stock Returns ◽  
Stock Exchange ◽  
Approximate Entropy ◽  
Market Volatility ◽  
Comparative Approach ◽  
Stock Market Volatility ◽  
Information Theoretic ◽  
Information Theoretic Measures ◽  
Garch Modeling

The volatility analysis of stock returns data is paramount in financial studies. We investigate the dynamics of volatility and randomness of the Pakistan Stock Exchange (PSX-100) and obtain insights into the behavior of investors during and before the coronavirus disease (COVID-19 pandemic). The paper aims to present the volatility estimations and quantification of the randomness of PSX-100. The methodology includes two approaches: (i) the implementation of EGARCH, GJR-GARCH, and TGARCH models to estimate the volatilities; and (ii) analysis of randomness in volatilities series, return series, and PSX-100 closing prices for pre-pandemic and pandemic period by using Shannon’s, Tsallis, approximate and sample entropies. Volatility modeling suggests the existence of the leverage effect in both the underlying periods of study. The results obtained using GARCH modeling reveal that the stock market volatility has increased during the pandemic period. However, information-theoretic results based on Shannon and Tsallis entropies do not suggest notable variation in the estimated volatilities series and closing prices. We have examined regularity and randomness based on the approximate entropy and sample entropy. We have noticed both entropies are extremely sensitive to choices of the parameters.

Measuring the Complexity of Additive Manufacturing Supply Chains

2017 ◽  
Author(s):  
Ardeshir Raihanian Mashhadi ◽  
Sara Behdad
Keyword(s):  
Supply Chain ◽  
Additive Manufacturing ◽  
Supply Chains ◽  
Product Complexity ◽  
Information Theoretic ◽  
Manufacturing Method ◽  
Management Domain ◽  
Information Theoretic Measures ◽  
Production Cycles ◽  
Supply Planning

Complexity has been one of the focal points of attention in the supply chain management domain, as it deteriorates the performance of the supply chain and makes controlling it problematic. The complexity of supply chains has been significantly increased over the past couple of decades. Meanwhile, Additive Manufacturing (AM) not only revolutionizes the way that the products are made, but also brings a paradigm shift to the whole production system. The influence of AM extends to product design and supply chain as well. The unique capabilities of AM suggest that this manufacturing method can significantly affect the supply chain complexity. More product complexity and demand heterogeneity, faster production cycles, higher levels of automation and shorter supply paths are among the features of additive manufacturing that can directly influence the supply chain complexity. Comparison of additive manufacturing supply chain complexity to its traditional counterpart requires a profound comprehension of the transformative effects of AM on the supply chain. This paper first extracts the possible effects of AM on the supply chain and then tries to connect these effects to the drivers of complexity under three main categories of 1) market, 2) manufacturing technology, and 3) supply, planning and infrastructure. Possible impacts of additive manufacturing adoption on the supply chain complexity have been studied using information theoretic measures. An Agent-based Simulation (ABS) model has been developed to study and compare two different supply chain configurations. The findings of this study suggest that the adoption of AM can decrease the supply chain complexity, particularly when product customization is considered.

scholarly journals ASSESSMENT OF URBAN SPRAWL USING SHANNON’S ENTROPY AND FRACTAL ANALYSIS: A CASE STUDY OF ATAKUM, ILKADIM AND CANIK (SAMSUN, TURKEY)

2017 ◽  
Vol 25 (3) ◽  
pp. 264-276 ◽  
Author(s):  
Derya OZTURK
Keyword(s):  
Urban Sprawl ◽  
Fractal Analysis ◽  
Urban Form ◽  
Entropy Method ◽  
Shannon’S Entropy ◽  
Analysis Method ◽  
Maximum Likelihood Classification ◽  
Shannon's Entropy ◽  
Box Counting

Urban sprawl is one of the most important problems in urban development due to its negative environmental and societal impacts. Therefore, the spatial pattern of urban growth should be accurately analyzed and well understood for effective urban planning. This paper focuses on urban sprawl analysis in the Atakum, Ilkadim and Canik districts of Samsun, Turkey. In this study, urban sprawl was examined over a period of 24 years using Shannon's entropy and fractal analysis based on remote sensing and Geographic Information System (GIS). The built-up areas in 1989, 2000 and 2013 were extracted from Landsat TM/ETM+/OLI images using the maximum likelihood classification method, and urban form changes in the 1989–2013 period were investigated. The Shannon's entropy method was used to determine the degree of urban sprawl, and a fractal analysis method based on box counting was used to characterize the urban sprawl. The results show that Atakum, Ilkadim and Canik experienced important changes and have considerable sprawl and complex characteristics now. The study also revealed that there is no monotonic relationship between Shannon's entropy and fractal dimension.

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