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Variance Laplacian: Quadratic Forms in StatisticsEasyChair Preprint 821, version historyVersion | Date | Pages | Version notes |
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1 | March 12, 2019 | 12 | | 2 | April 5, 2019 | 16 | (1) Bounding all eigenvalues using Lemma 4 (2) Spectral Representation of Variance Laplacian matrix (3) Probabilistic interpretation of Tsallis Entropy | 3 | June 11, 2019 | 20 | (1) Unit Random processes ( and the variance values ) are related to unit random processes (2) New results on the Laplacian matrix associated with Variance of a discrete random variable are included | 4 | July 6, 2019 | 23 | (1) Characterization of Entropic Quadratic Forms ( satisfying reasonable axioms ) is discussed (2) Relationship between Tsallis Entropy and Renyii entropy is discussed. | 5 | August 9, 2019 | 28 | (1) Relationship between Renyi entropy and Tsallis entropy is derived (2) Lemma 5 ( new lemma ) is proved and its probabilistic interpretation is provided (3) Generalized Verhulst maps are discussed | 6 | September 5, 2019 | 33 | (1) Matrix Logistic Map and the associaited generalized Verhulst dynamical system is defined and the dynamic behavior is studied (2) Lemma 7 is generalized (3) Minor mistakes are corrected | 7 | September 20, 2019 | 36 | (1) Lemma 8 is proved (2) Existing inequality is reasoned to be tighter than Cauchy-Schwarz inequality. (3) Jensen inequality based inequalities are discussed. | 8 | November 1, 2019 | 38 | (1) Entire New Section ( i.e. Section 5 ) is added. It deals with approximation of Gibbs- Shannon Entropy and the associated Information theoretic results. (2) Mutual Information based on approximations is computed | 9 | November 16, 2021 | 40 | Covariance matrix of two random variables which assume same values is proved to be Laplacian. The leading diagonal sums of variance Laplacian matrix are proved to be the autocorrelation coefficients of PMF vector Eigenvalues of Variance Laplacian matrix are bounded in a tighter manner |
Keyphrases: Eigenvectors, Laplacian matrix, eigenvalues, quadratic form, variance |
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