habeck.rot

It generates random rotations in three-dimensional space that follow a probability distribution,
matrix Fisher distribution, arising in fitting and matching problem.

Habeck's rotation matrix generation

A collection of functions for directional data (including massive data, with millions of observations) analysis.
Hypothesis testing, discriminant and regression analysis, MLE of distributions and more are included.
The standard textbook for such data is the "Directional Statistics" by Mardia, K. V. and Jupp, P. E. (2000).
Other references include a) Phillip J. Paine, Simon P. Preston Michail Tsagris and Andrew T. A. Wood (2018).
"An elliptically symmetric angular Gaussian distribution". Statistics and Computing 28(3): 689-697. <doi:10.1007/s11222-017-9756-4>.
b) Tsagris M. and Alenazi A. (2019). "Comparison of discriminant analysis methods on the sphere".
Communications in Statistics: Case Studies, Data Analysis and Applications 5(4):467--491. <doi:10.1080/23737484.2019.1684854>.
c) P. J. Paine, S. P. Preston, M. Tsagris and Andrew T. A. Wood (2020).
"Spherical regression models with general covariates and anisotropic errors".
Statistics and Computing 30(1): 153--165. <doi:10.1007/s11222-019-09872-2>.
d) Tsagris M. and Alenazi A. (2024). "An investigation of hypothesis testing procedures for circular and spherical mean vectors".
Communications in Statistics-Simulation and Computation, 53(3): 1387--1408. <doi:10.1080/03610918.2022.2045499>.
e) Tsagris M. and Alzeley O. (2023). "Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling". <doi:10.48550/arXiv.2302.02468>.
f) Zehao Yu and Xianzheng Huang (2024). A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension.
Electronic Journal of Statistics, 18(1): 301--334. <doi:10.1214/23-EJS2210>.
g) Tsagris M. (2024). "Directional data analysis using the spherical Cauchy and the Poisson-kernel based distribution". <doi:10.48550/arXiv.2409.03292>.

Michail Tsagris

Directional

A Collection of Functions for Directional Data Analysis

Giorgos Athineou

Christos Adam

Anamul Sajib

Eli Amson

Zehao Yu

Habeck's rotation matrix generation function

<dl> <dt>F</dt>
<dd>An arbitrary 3 x 3 matrix represents the parameter matrix of this distribution.</dd></dl>

Arguments

Anamul Sajib.
R implementation and documentation: Anamul Sajib &lt;sajibstat@du.ac.bd&gt;.

Author

Generation of three-dimensional random rotations using Habeck's algorithm. — Habeck's rotation matrix generation

<dl>

 <dt>F</dt>
<dd>An arbitrary 3 x 3 matrix represents the parameter matrix of this distribution.</dd>

</dl>

Habeck's rotation matrix generation: Generation of three-dimensional random rotations using Habeck's algorithm.

Description

Usage

Value

Arguments

Author

Details

References

Examples