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Published: 25 May 2024

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1

Sanon, Abdramane, Alain P. K. Gomgnimbou, Hamadé Sigue, Kalifa Coulibaly, Cheick A. Bambara, Willifried Sanou, Sékou Fofana, and Hassan B. Nacro. "Performances économiques et financières de la fertilisation en riziculture pluviale stricte dans la zone sud soudanienne du Burkina Faso." International Journal of Biological and Chemical Sciences 15, no. 4 (November 19, 2021): 1581–94. http://dx.doi.org/10.4314/ijbcs.v15i4.22.

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La culture du riz joue un rôle décisif dans les moyens d'existence des producteurs. La production rizicole rencontre des difficultés liées aux coûts de fertilisation. L’étude avait pour objectif d’évaluer les performances économiques et financières des biodéchets et des fertilisants inorganiques en riziculture pluviale stricte. L’évaluation est faite suivante deux démarches : la première consiste à calculer et à comparer les indicateurs de performance, tandis que la deuxième repose sur une matrice de corrélation afin d’identifier les relations entre les indicateurs de performances économiques et financières et rendements de riz paddy. La performance agronomique des options de fertilisation a été évaluée par les rendements du riz paddy récolté dans un essai. A cet effet, un dispositif expérimental en Blocs de Fisher complètement randomisés avec quatre répétitions et dix traitements composites a été installé à la station de recherches de Farako-Ba au Burkina Faso, durant quatre campagnes agricoles de 2016 à 2019. Pour le calcul des indicateurs de performances économiques et financières, l’achat des engrais minéraux et des biodéchets, le coût de la main-d’œuvre pour collecter, transporter et incorporer les fertilisants, le prix moyen d’un kilogramme de riz paddy dans les différents marchés de la zone d’étude ont été prises en considération. Les résultats ont montré que les traitements Fumier de Poule+Urée, Fumier de Poule+Burkina Phosphate+Urée et Compost+Urée présentaient significativement les meilleures performances économiques du point de vue de la marge nette et de la productivité moyenne du travail. Les meilleurs taux de rentabilité interne et du ratio bénéfice sur coût sont enrégistrés par les traitements Fumier de Poule+Urée et Compost+Urée. Il ressort de l’analyse statistique des corrélations positives et significatives entre le rendement du riz paddy et les marges nettes d’une part et d’autre part entre le rendement du riz paddy et la productivité moyenne du travail. Dans un contexte de coûts élevés de la fertilisation, ces résultats révèlent l’intérêt de la combinaison de biodéchets (fumier de poule) avec les engrais minéraux en culture de riz pluvial strict pour une vulgarisation en milieu paysan.

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2

Heavens, A. F., M. Seikel, B. D. Nord, M. Aich, Y. Bouffanais, B. A. Bassett, and M. P. Hobson. "Generalized Fisher matrices." Monthly Notices of the Royal Astronomical Society 445, no. 2 (October 14, 2014): 1687–93. http://dx.doi.org/10.1093/mnras/stu1866.

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3

Heavens, Alan. "Generalisations of Fisher Matrices." Entropy 18, no. 6 (June 22, 2016): 236. http://dx.doi.org/10.3390/e18060236.

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4

Almestady, Mohammed S., and Alun O. Morris. "Fischer Matrices for Projective Representations of Generalized Symmetric Groups." Algebra Colloquium 16, no. 03 (September 2009): 449–62. http://dx.doi.org/10.1142/s1005386709000431.

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The aim of this work is to calculate the Fischer matrices for the covering groups of the Weyl group of type Bn and the generalized symmetric group. It is shown that the Fischer matrices are the same as those in the ordinary case for the classes of Sn which correspond to partitions with all parts odd. For the classes of Sn which correspond to partitions in which no part is repeated more than m times, the Fischer matrices are shown to be different from the ordinary case.

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5

Prins, Abraham Love. "On the Fischer matrices of a group of shape 21+2n + :G." Revista Colombiana de Matemáticas 56, no. 2 (April 17, 2023): 189–211. http://dx.doi.org/10.15446/recolma.v56n2.108379.

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In this paper, the Fischer matrices of the maximal subgroup G = 21+8+ : (U4(2):2) of U6(2):2 will be derived from the Fischer matrices of the quotient group Q = G/Z(21+8+) = 28 : (U4(2):2), where Z(21+8+) denotes the center of the extra-special 2-group 21+8+. Using this approach, the Fischer matrices and associated ordinary character table of G are computed in an elegantly simple manner. This approach can be used to compute the ordinary character table of any split extension group of the form 21+2n+ :G, n ∈ N, provided the ordinary irreducible characters of 21+2n+ extend to ordinary irreducible characters of its inertia subgroups in 21+2n+:G and also that the Fischer matrices M(gi) of the quotient group 21+2n+ :G/Z(21+2n+) = 22n:G are known for each class representative gi in G.

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6

Kagan, Abram, and Zinoviy Landsman. "Relation between the covariance and Fisher information matrices." Statistics & Probability Letters 42, no. 1 (March 1999): 7–13. http://dx.doi.org/10.1016/s0167-7152(98)00178-3.

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7

Böttcher, Albrecht, and Bernd Silbermann. "Toeplitz matrices and determinants with Fisher-Hartwig symbols." Journal of Functional Analysis 63, no. 2 (September 1985): 178–214. http://dx.doi.org/10.1016/0022-1236(85)90085-0.

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8

Bin, Meng. "Operator-valued free Fisher information of random matrices." Acta Mathematica Scientia 30, no. 4 (July 2010): 1327–37. http://dx.doi.org/10.1016/s0252-9602(10)60128-2.

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9

Böttcher, Albrecht, and Jani Virtanen. "Norms of Toeplitz Matrices with Fisher–Hartwig Symbols." SIAM Journal on Matrix Analysis and Applications 29, no. 2 (January 2007): 660–71. http://dx.doi.org/10.1137/06066165x.

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10

Lv, Songjun. "General Fisher information matrices of a random vector." Advances in Applied Mathematics 89 (August 2017): 18–40. http://dx.doi.org/10.1016/j.aam.2017.03.002.

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11

Moori, Jamshid, and Kenneth Zimba. "FISCHER-CLIFFORD MATRICES OFB(2, n)." Quaestiones Mathematicae 29, no. 1 (March 2006): 9–37. http://dx.doi.org/10.2989/16073600609486147.

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12

Iranmanesh, A. "Fischer Matrices of the Affine Groups." Southeast Asian Bulletin of Mathematics 25, no. 1 (July 2001): 121–28. http://dx.doi.org/10.1007/s10012-001-0121-2.

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13

List, R. J., and I. M. I. Mahmoud. "Fischer matrices for wreath productsGwS n." Archiv der Mathematik 50, no. 5 (May 1988): 394–401. http://dx.doi.org/10.1007/bf01196499.

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14

McGarvey, Richard, and John E. Feenstra. "Estimating rates of fish movement from tag recoveries: conditioning by recapture." Canadian Journal of Fisheries and Aquatic Sciences 59, no. 6 (June 1, 2002): 1054–64. http://dx.doi.org/10.1139/f02-080.

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Tag-recovery data are commonly used to estimate movement rates of fish stocks. Fishers report tagged fish found in their catch; however, not all recoveries are reported to fishery researchers and the rate of nonreporting is usually not known or is imprecisely estimated. To obviate the problem of nonreporting, an estimator of movement rates is proposed that does not use the number originally tagged but is fitted to the relative proportions recaptured in each cell in each time step subsequent to release. Rates of processes that occur in the tag-release spatial cell, such as short-term tagging mortality and survival, cancel from the predicted likelihood probabilities. Similarly, rates in the recapture cell for processes of ongoing tag loss, natural mortality, and tag nonreporting, if they can be reasonably approximated as uniform across cells, also cancel. Estimators are presented assuming one of two levels of auxiliary fishery inputs: (i) total mortality by cell or time step, or (ii) if mortality can be approximated as spatially uniform, effort totals in each cell, by time step. Yearly movement transition matrices were estimated for King George whiting (Sillaginodes punctata) in South Australia among 11 spatial cells from tag recoveries gathered over a period of three decades.

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15

Ali, Faryad, and Jamshid Moori. "The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24." Algebra Colloquium 17, no. 03 (September 2010): 389–414. http://dx.doi.org/10.1142/s1005386710000386.

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The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

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16

Yuan, Sihan, and Daniel J. Eisenstein. "Decorrelating the errors of the galaxy correlation function with compact transformation matrices." Monthly Notices of the Royal Astronomical Society 486, no. 1 (March 27, 2019): 708–24. http://dx.doi.org/10.1093/mnras/stz899.

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Abstract Covariance matrix estimation is a persistent challenge for cosmology, often requiring a large number of synthetic mock catalogues. The off-diagonal components of the covariance matrix also make it difficult to show representative error bars on the 2-point correlation function (2PCF) since errors computed from the diagonal values of the covariance matrix greatly underestimate the uncertainties. We develop a routine for decorrelating the projected and anisotropic 2PCF with simple and scale-compact transformations on the 2PCF. These transformation matrices are modelled after the Cholesky decomposition and the symmetric square root of the Fisher matrix. Using mock catalogues, we show that the transformed projected and anisotropic 2PCF recover the same structure as the original 2PCF while producing largely decorrelated error bars. Specifically, we propose simple Cholesky-based transformation matrices that suppress the off-diagonal covariances on the projected 2PCF by ${\sim } 95{{\ \rm per\ cent}}$ and that on the anisotropic 2PCF by ${\sim } 87{{\ \rm per\ cent}}$. These transformations also serve as highly regularized models of the Fisher matrix, compressing the degrees of freedom so that one can fit for the Fisher matrix with a much smaller number of mocks.

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17

Forrester, P. J. "Log-gases, random matrices and the Fisher-Hartwig conjecture." Journal of Physics A: Mathematical and General 26, no. 5 (March 7, 1993): 1179–91. http://dx.doi.org/10.1088/0305-4470/26/5/035.

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18

Liu, Jing, Xiao-Xing Jing, Wei Zhong, and Xiao-Guang Wang. "Quantum Fisher Information for Density Matrices with Arbitrary Ranks." Communications in Theoretical Physics 61, no. 1 (January 2014): 45–50. http://dx.doi.org/10.1088/0253-6102/61/1/08.

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19

Singthongchai, Jatsada, Noppakun Thongmual, and Nirun Nitisuk. "Parametric test based on the bootstrapping approach for the MANOVA under a Behrens-Fisher problem." Model Assisted Statistics and Applications 19, no. 1 (March 14, 2024): 61–69. http://dx.doi.org/10.3233/mas-231449.

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This article presents a comparison of multivariate normal mean vectors under covariance positive definite matrices. We introduce an improved parametric bootstrap (IPB) approach for addressing the multivariate Behrens-Fisher problem, specifically focusing on cases with unequal covariance matrices. Additionally, we evaluate the performance of the IPB test by comparing it with three existing tests: the parametric bootstrap (PB) test, the generalized variable (GV) test, and the Johansen test. Through Monte Carlo simulation, our results demonstrate that both the IPB test and the PB test exhibit superior control over Type I error rates compared to the GV and Johansen tests. Notably, the IPB test outperforms the PB test in terms of controlling Type I error rates. Consequently, our study concludes that the IPB test represents a preferred statistical method for testing the equality of mean vectors in the multivariate Behrens-Fisher problem.

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20

Giurgescu, Patricia. "Entropy considerations in the noncommutative setting." International Journal of Mathematics and Mathematical Sciences 24, no. 12 (2000): 807–19. http://dx.doi.org/10.1155/s0161171200004567.

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An analogue of the classical link between the relative entropy and Fisher information entropy is presented in the context of free probability theory. Several generalizations of the relative entropy in terms of density matrices are also discussed.

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21

Shawky, A. I., and R. A. Bakoban. "Exponentiated Gamma Distribution: Different Methods of Estimations." Journal of Applied Mathematics 2012 (2012): 1–23. http://dx.doi.org/10.1155/2012/284296.

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The exponentiated gamma (EG) distribution and Fisher information matrices for complete, Type I, and Type II censored observations are obtained. Asymptotic variances of the different estimators are derived. Also, we consider different estimators and compare their performance through Monte Carlo simulations.

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22

Nielsen, Frank. "A Simple Approximation Method for the Fisher–Rao Distance between Multivariate Normal Distributions." Entropy 25, no. 4 (April 13, 2023): 654. http://dx.doi.org/10.3390/e25040654.

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We present a simple method to approximate the Fisher–Rao distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating the Fisher–Rao distances between successive nearby normal distributions on the curves by the square roots of their Jeffreys divergences. We consider experimentally the linear interpolation curves in the ordinary, natural, and expectation parameterizations of the normal distributions, and compare these curves with a curve derived from the Calvo and Oller’s isometric embedding of the Fisher–Rao d-variate normal manifold into the cone of (d+1)×(d+1) symmetric positive–definite matrices. We report on our experiments and assess the quality of our approximation technique by comparing the numerical approximations with both lower and upper bounds. Finally, we present several information–geometric properties of Calvo and Oller’s isometric embedding.

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23

Mislevy, Robert J., and Kathleen M. Sheehan. "Information Matrices in Latent-Variable Models." Journal of Educational Statistics 14, no. 4 (December 1989): 335–50. http://dx.doi.org/10.3102/10769986014004335.

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The Fisher, or expected, information matrix for the parameters in a latent-variable model is bounded from above by the information that would be obtained if the values of the latent variables could also be observed. The difference between this upper bound and the information in the observed data is the “missing information.” This paper explicates the structure of the expected information matrix and related information matrices, and characterizes the degree to which missing information can be recovered by exploiting collateral variables for respondents. The results are illustrated in the context of item response theory models, and practical implications are discussed.

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24

CHENG, Zheng-Dong, Yu-Jin ZHANG, Xiang FAN, and Bin ZHU. "Study on Discriminant Matrices of Commonly-used Fisher Discriminant Functions." Acta Automatica Sinica 36, no. 10 (December 21, 2010): 1361–70. http://dx.doi.org/10.3724/sp.j.1004.2010.01361.

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25

Wang, Qinwen, and Jianfeng Yao. "Extreme eigenvalues of large-dimensional spiked Fisher matrices with application." Annals of Statistics 45, no. 1 (February 2017): 415–60. http://dx.doi.org/10.1214/16-aos1463.

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26

Vong, Seak-Weng, and Xiao-Qing Jin. "Unitarily Invariant Norms of Toeplitz Matrices with Fisher–Hartwig Singularities." SIAM Journal on Matrix Analysis and Applications 29, no. 3 (January 2007): 850–54. http://dx.doi.org/10.1137/070681065.

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27

GOLOSNOY, VASYL, and HELMUT HERWARTZ. "DYNAMIC MODELING OF HIGH-DIMENSIONAL CORRELATION MATRICES IN FINANCE." International Journal of Theoretical and Applied Finance 15, no. 05 (August 2012): 1250035. http://dx.doi.org/10.1142/s0219024912500355.

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A class of dynamic factor and dynamic panel models is proposed for daily high dimensional correlation matrices of asset returns. These flexible semiparametric predictors process ultra high frequency information and allow to exploit both realized correlation matrices and exogenous factors for forecasting purposes. The Fisher-z transformation offers the transmission from (factor and panel) time series models operating on unrestricted random variables to bounded correlation forecasts. Our methodology is contrasted with prominent alternative correlation models. Based on economic performance criteria dynamic factor models turn out to carry the highest predictive content.

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28

Wilson, Robert A. "Matrix generators for Fischer's group Fi24." Mathematical Proceedings of the Cambridge Philosophical Society 113, no. 1 (January 1993): 5–8. http://dx.doi.org/10.1017/s0305004100075733.

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AbstractIn this paper we show how to construct 781 × 781 matrices over GF(3), generating the largest of the three Fischer groups. For some purposes these are more useful than the permutations on 306936 points, as they require only one-sixth of the storage space. We also construct generators for its triple cover, as 1566 × 1566 matrices over GF(2), and for the derived group thereof, as 783 × 783 matrices over GF(4).

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29

ARTSTEIN-AVIDAN, S., D. FLORENTIN, and Y. OSTROVER. "REMARKS ABOUT MIXED DISCRIMINANTS AND VOLUMES." Communications in Contemporary Mathematics 16, no. 02 (April 2014): 1350031. http://dx.doi.org/10.1142/s0219199713500314.

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In this note we prove certain inequalities for mixed discriminants of positive semi-definite matrices, and mixed volumes of compact convex sets in ℝn. Moreover, we discuss how the latter are related to the monotonicity of an information functional on the class of convex bodies, which is a geometric analogue of the classical Fisher information.

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30

Lin, Minghua. "Fischer type determinantal inequalities for accretive–dissipative matrices." Linear Algebra and its Applications 438, no. 6 (March 2013): 2808–12. http://dx.doi.org/10.1016/j.laa.2012.11.016.

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31

Ali, Faryad. "The Fischer–Clifford Matrices of a Maximal Subgroup of the Sporadic Simple Group of Held." Algebra Colloquium 14, no. 01 (March 2007): 135–42. http://dx.doi.org/10.1142/s1005386707000132.

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The Held group He discovered by Held [10] is a sporadic simple group of order 4030387200 = 210.33.52.73.17. The group He has 11 conjugacy classes of maximal subgroups as determined by Butler [5] and listed in the 𝔸𝕋𝕃𝔸𝕊. Held himself determined much of the local structure of He as well as the conjugacy classes of its elements. Thompson calculated the character table of He . In the present paper, we determine the Fischer–Clifford matrices and hence compute the character table of the non-split extension 3·S7, which is a maximal subgroups of He of index 226560 using the technique of Fischer–Clifford matrices. Most of the computations were carried out with the aid of the computer algebra system 𝔾𝔸ℙ.

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32

Hiai, Fumio, Dénes Petz, and Yoshimichi Ueda. "A Free Logarithmic Sobolev Inequality on the Circle." Canadian Mathematical Bulletin 49, no. 3 (September 1, 2006): 389–406. http://dx.doi.org/10.4153/cmb-2006-039-7.

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AbstractFree analogues of the logarithmic Sobolev inequality compare the relative free Fisher information with the relative free entropy. In the present paper such an inequality is obtained for measures on the circle. The method is based on a random matrix approximation procedure, and a large deviation result concerning the eigenvalue distribution of special unitary matrices is applied and discussed.

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33

CHEN, YONGXIN, TRYPHON T. GEORGIOU, and ALLEN TANNENBAUM. "Interpolation of matrices and matrix-valued densities: The unbalanced case." European Journal of Applied Mathematics 30, no. 3 (May 8, 2018): 458–80. http://dx.doi.org/10.1017/s0956792518000219.

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We propose unbalanced versions of the quantum mechanical version of optimal mass transport that is based on the Lindblad equation describing open quantum systems. One of them is a natural interpolation framework between matrices and matrix-valued measures via a quantum mechanical formulation of Fisher-Rao information and the matricial Wasserstein distance, and the second is an interpolation between Wasserstein distance and Frobenius norm. We also give analogous results for the matrix-valued density measures, i.e., we add a spatial dependency on the density matrices. This might extend the applications of the framework to interpolating matrix-valued densities/images with unequal masses.

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34

SU, Gulumbe, B. Shehu, and S. Dahiru. "ON SOME SOLUTIONS OF THE MULTIVARIATE BEHRENS FISHER PROBLEM." Journal of Mathematical Sciences & Computational Mathematics 2, no. 2 (January 1, 2021): 322–35. http://dx.doi.org/10.15864/jmscm.2211.

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Multivariate Behrens-Fisher Problem is a problem that deals with testing the equality of two means from multivariate normal distribution when the covariance matrices are unequal and unknown. However, there is no single procedure served as a better performing solution to this problem, Adebayo (2018). In this study effort is made in selecting five different existing procedures and examined their power and rate to which they control type I error using a different setting and conditions observed from previous studies. To overcome this problem a code was designed via R Statistical Software, to simulate random normal data and independently run 1000 times using MASS package in other to estimate the power and rate at which each procedure control type I error. The simulation result depicts that, in a setting when variance covariance matrices S1 > S2 associated with a sample sizes (n1 > n2) in Table 4.1, 4.2, 4.5, and 4.6, shows that, Adebayos’ procedure performed better but at a sample sizes (n1 = n2 and n1 < n2) Hotelling T2 is recommended in terms of power. For type I error rate where robustness and nominal level matters we found that under some settings none of the procedure maintained nominal level as revealed in Table 4.11 and 4.15. The results presented in Table 4.9 to 4.16 shows that when nominal level matters Krishnamoorthy came first, followed by Adebayos’, Yaos’, Johansons’ then Hotelling T2 were recommended in the sequentially under the settings used in this study.

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35

Peeters, Ralf L. M., and Bernard Hanzon. "Symbolic computation of Fisher information matrices for parametrized state-space systems." Automatica 35, no. 6 (June 1999): 1059–71. http://dx.doi.org/10.1016/s0005-1098(99)00004-7.

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36

Klein, André, and Peter Spreij. "Tensor Sylvester matrices and the Fisher information matrix of VARMAX processes." Linear Algebra and its Applications 432, no. 8 (April 2010): 1975–89. http://dx.doi.org/10.1016/j.laa.2009.06.027.

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37

Sellentin, Elena, Miguel Quartin, and Luca Amendola. "Breaking the spell of Gaussianity: forecasting with higher order Fisher matrices." Monthly Notices of the Royal Astronomical Society 441, no. 2 (May 12, 2014): 1831–40. http://dx.doi.org/10.1093/mnras/stu689.

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38

Huillet, Thierry E. "On Discrete-Time Multiallelic Evolutionary Dynamics Driven by Selection." Journal of Probability and Statistics 2010 (2010): 1–27. http://dx.doi.org/10.1155/2010/580762.

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We revisit some problems arising in the context of multiallelic discrete-time evolutionary dynamics driven by fitness. We consider both the deterministic and the stochastic setups and for the latter both the Wright-Fisher and the Moran approaches. In the deterministic formulation, we construct a Markov process whose Master equation identifies with the nonlinear deterministic evolutionary equation. Then, we draw the attention on a class of fitness matrices that plays some role in the important matter of polymorphism: the class of strictly ultrametric fitness matrices. In the random cases, we focus on fixation probabilities, on various conditionings on nonfixation, and on (quasi)stationary distributions.

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39

Wang, Benju, and Yun Zhang. "Fischer Type Log-Majorization of Singular Values on Partitioned Positive Semidefinite Matrices." Journal of Function Spaces 2021 (August 31, 2021): 1–5. http://dx.doi.org/10.1155/2021/7211498.

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In this paper, we establish a Fischer type log-majorization of singular values on partitioned positive semidefinite matrices, which generalizes the classical Fischer's inequality. Meanwhile, some related and new inequalities are also obtained.

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40

Almestady, Mohammed, and Alun O. Morris. "Fischer Matrices for Generalised Symmetric Groups—A Combinatorial Approach." Advances in Mathematics 168, no. 1 (June 2002): 29–55. http://dx.doi.org/10.1006/aima.2001.2043.

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41

Mwanzia Musyoka, David, Lydia N. Njuguna, Abraham Love Prins, and Lucy Chikamai. "On a maximal subgroup of the orthogonal group O⁺₈(3)." Proyecciones (Antofagasta) 41, no. 1 (February 1, 2022): 137–61. http://dx.doi.org/10.22199/issn.0717-6279-4778.

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The orthogonal simple group 0 (3) has three conjugacy classes of maximal subgroups of the form 36:L4(3). These groups are all isomorphic to each other and each group has order 4421589120 with index 1120 in 0 (3). In this paper, we will compute the ordinary carácter table of one of these classes of maximal subgroups using the technique of Fischer-Clifford matrices. This technique is very efficient to compute the ordinary character table of an extension group Ḡ = N.G and especially where the normal subgroup N of Ḡ is an elementary abelian p-group. The said technique reduces the computation of the ordinary character table of Ḡ to find a handful of so-called Fischer-Clifford matrices of Ḡ and the ordinary or projective character tables of the inertia factor groups of the action of Ḡ on N.

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42

Lee, Eun-Taik, and Hee-Chang Eun. "Optimal sensor placements using modified Fisher information matrix and effective information algorithm." International Journal of Distributed Sensor Networks 17, no. 6 (June 2021): 155014772110230. http://dx.doi.org/10.1177/15501477211023022.

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This article presents an optimal sensor placement algorithm for modifying the Fisher information matrix and effective information. The modified Fisher information matrix and effective information are expressed using a dynamic equation constrained by the condensed relationship of the incomplete mode shape matrix. The mode shape matrix row corresponding to the master degree of freedom of the lowest-contribution Fisher information matrix and effective information indices is moved to the slave degree of freedom during each iteration to obtain an updated shape matrix, which is then used in subsequent calculations. The iteration is repeated until the target sensors attain the targeted number of modes. The numerical simulations are then applied to compare the optimal sensor placement results obtained using the number of installed sensors, and the contribution matrices using the Fisher information matrix and effective information approaches are compared based on the proposed parameter matrix. The mode-shape-based optimal sensor placement approach selects the optimal sensor layout at the positions to uniformly allocate the entire degree of freedom. The numerical results reveal that the proposed F-based and effective information–based approaches lead to slightly different results, depending on the number of parameter matrix modes; however, the resulting final optimal sensor placement is included in a group of common candidate sensor locations. However, the resulting final optimal sensor placement is included in a group of common candidate sensor locations.

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Barraclough, R. W. "The character table of a group of shape (2×2.G):2." LMS Journal of Computation and Mathematics 13 (March 26, 2010): 82–89. http://dx.doi.org/10.1112/s1461157007000575.

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Zheng, Shurong, Zhidong Bai, and Jianfeng Yao. "CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications." Bernoulli 23, no. 2 (May 2017): 1130–78. http://dx.doi.org/10.3150/15-bej772.

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Favennec, Y. "Hessian and Fisher Matrices For Error Analysis in Inverse Heat Conduction Problems." Numerical Heat Transfer, Part B: Fundamentals 52, no. 4 (August 23, 2007): 323–40. http://dx.doi.org/10.1080/10407790701443958.

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Zografos, K. "Measures of multivariate dependence based on a distance between Fisher information matrices." Journal of Statistical Planning and Inference 89, no. 1-2 (August 2000): 91–107. http://dx.doi.org/10.1016/s0378-3758(00)00096-3.

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Klein, André, Guy Mélard, and Abdessamad Saidi. "The asymptotic and exact Fisher information matrices of a vector ARMA process." Statistics & Probability Letters 78, no. 12 (September 2008): 1430–33. http://dx.doi.org/10.1016/j.spl.2007.12.013.

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Movassagh, Ramis, and Leo P. Kadanoff. "Eigenpairs of Toeplitz and Disordered Toeplitz Matrices with a Fisher–Hartwig Symbol." Journal of Statistical Physics 167, no. 3-4 (September 26, 2016): 959–96. http://dx.doi.org/10.1007/s10955-016-1614-9.

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Pinele, Julianna, João E. Strapasson, and Sueli I. R. Costa. "The Fisher-Rao Distance between Multivariate Normal Distributions: Special Cases, Boundsand Applications." Entropy 22, no. 4 (April 1, 2020): 404. http://dx.doi.org/10.3390/e22040404.

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The Fisher–Rao distance is a measure of dissimilarity between probability distributions, which, under certain regularity conditions of the statistical model, is up to a scaling factor the unique Riemannian metric invariant under Markov morphisms. It is related to the Shannon entropy and has been used to enlarge the perspective of analysis in a wide variety of domains such as image processing, radar systems, and morphological classification. Here, we approach this metric considered in the statistical model of normal multivariate probability distributions, for which there is not an explicit expression in general, by gathering known results (closed forms for submanifolds and bounds) and derive expressions for the distance between distributions with the same covariance matrix and between distributions with mirrored covariance matrices. An application of the Fisher–Rao distance to the simplification of Gaussian mixtures using the hierarchical clustering algorithm is also presented.

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Salinas, Hugo S., Guillermo Martínez-Flórez, Artur J. Lemonte, and Heleno Bolfarine. "On log-bimodal alpha-power distributions with application to nickel contents and erosion data." Mathematica Slovaca 71, no. 6 (December 1, 2021): 1565–80. http://dx.doi.org/10.1515/ms-2021-0072.

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Abstract In this paper, we present a new parametric class of distributions based on the log-alpha-power distribution, which contains the well-known log-normal distribution as a special case. This new family is useful to deal with unimodal as well as bimodal data with asymmetry and kurtosis coefficients ranging far from that expected based on the log-normal distribution. The usual approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive the observed and expected Fisher information matrices. As a byproduct of such study, it is shown that the Fisher information matrix is nonsingular throughout the sample space. Empirical applications of the proposed family of distributions to real data are provided for illustrative purposes.

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