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Dryden IL, Kume A, Paine PJ, Wood ATA. Regression Modeling for Size-and-Shape Data Based on a Gaussian Model for Landmarks. J Am Stat Assoc 2021. [DOI: 10.1080/01621459.2020.1724115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Ian L. Dryden
- School of Mathematical Sciences, University of Nottingham, Nottingham, UK\
| | - Alfred Kume
- School of Mathematics, Statistics and Actuarial Sciences, University of Kent, Canterbury, UK
| | - Phillip J. Paine
- School of Mathematics and Statistics, University of Sheffield, Sheffield, UK
| | - Andrew T. A. Wood
- Research School of Finance, Actuarial Studies and Statistics, Australian National University, Canberra, ACT, Australia
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Dore LHG, Amaral GJA, Cruz JTM, Wood ATA. Bias-corrected maximum likelihood estimation of the parameters of the complex Bingham distribution. BRAZ J PROBAB STAT 2016. [DOI: 10.1214/15-bjps285] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Bachmann F, Hielscher R, Jupp PE, Pantleon W, Schaeben H, Wegert E. Inferential statistics of electron backscatter diffraction data from within individual crystalline grains. J Appl Crystallogr 2010. [DOI: 10.1107/s002188981003027x] [Citation(s) in RCA: 94] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
Highly concentrated distributed crystallographic orientation measurements within individual crystalline grains are analysed by means of ordinary statistics neglecting their spatial reference. Since crystallographic orientations are modelled as left cosets of a given subgroup of SO(3), the non-spatial statistical analysis adapts ideas borrowed from the Bingham quaternion distribution on {\bb S}^3. Special emphasis is put on the mathematical definition and the numerical determination of a `mean orientation' characterizing the crystallographic grain as well as on distinguishing several types of symmetry of the orientation distribution with respect to the mean orientation, like spherical, prolate or oblate symmetry. Applications to simulated as well as to experimental data are presented. All computations have been done with the free and open-source texture toolboxMTEX.
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