dwood

Density of the Wood bimodal distribution on the sphere.

 Wood distribution 

 Bimodal distribution on the sphere 

Density of the Wood bimodal distribution on the sphere

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) Paine J.P., Preston S.P., Tsagris M. and Wood A.T.A. (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) Paine J.P., Preston S.P., Tsagris M. and Wood A.T.A. (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) Yu Z. and Huang X. (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>.
f) Tsagris M. and Alzeley O. (2024). "Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling". Australian & New Zealand Journal of Statistics (Accepted for publication). <doi:10.48550/arXiv.2302.02468>.
g) Tsagris M., Papastamoulis P. and Kato S. (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

Zehao Yu

Anamul Sajib

Eli Amson

Panagiotis Papastamoulis

Density of the Wood bimodal distribution on the sphere function

<dl><dt>y</dt>
<dd>A matrix containing two columns. The first one is the latitude and the second is the longitude, both expressed in degrees.</dd><dt>param</dt>
<dd>A vector with the 5 parameters, in the order they are returned by the <code>wood.mle</code> function.
That is, \((\gamma, \delta, \alpha, \beta, \kappa)\).</dd><dt>logden</dt>
<dd>If you the logarithm of the density values set this to TRUE.</dd></dl>

Arguments

Michail Tsagris.
R implementation and documentation: Michail Tsagris <a href="/link/mtsagris%40uoc.gr?package=Directional&version=7.0" data-mini-rdoc="Directional::mtsagris@uoc.gr">mtsagris@uoc.gr</a>.

Author

Density of the Wood bimodal distribution on the sphere — Density of the Wood bimodal distribution on the sphere

<dl>

<dt>y</dt>
<dd>A matrix containing two columns. The first one is the latitude and the second is the longitude, both expressed in degrees.</dd>

<dt>param</dt>
<dd>A vector with the 5 parameters, in the order they are returned by the <code>wood.mle</code> function.
That is, \((\gamma, \delta, \alpha, \beta, \kappa)\).</dd>

<dt>logden</dt>
<dd>If you the logarithm of the density values set this to TRUE.</dd>

</dl>

Michail Tsagris.
R implementation and documentation: Michail Tsagris <a href='mailto:mtsagris@uoc.gr'>mtsagris@uoc.gr</a>.

Density of the Wood bimodal distribution on the sphere: Density of the Wood bimodal distribution on the sphere

Description

Usage

Value

Arguments

Author

Details

References

See Also

Examples