Moments of von mises and fisher distributions and applications
The von Mises and Fisher distributions are spherical analogues to theNormal distribution on the unit circle and unit sphere, respectively. The computation of their moments, and in particular the second moment, usually involves solving tedious trigonometric integrals. Here we present a new method to...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2017-05-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017038 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590092237012992 |
|---|---|
| author | Thomas Hillen Kevin J. Painter Amanda C. Swan Albert D. Murtha |
| author_facet | Thomas Hillen Kevin J. Painter Amanda C. Swan Albert D. Murtha |
| author_sort | Thomas Hillen |
| collection | DOAJ |
| description | The von Mises and Fisher distributions are spherical analogues to theNormal distribution on the unit circle and unit sphere, respectively. The computation of their moments, and in particular the second moment, usually involves solving tedious trigonometric integrals. Here we present a new method to compute the moments of spherical distributions, based on the divergence theorem. This method allows a clear derivation of the second moments and can be easily generalized to higher dimensions. In particular we note that, to our knowledge, the variance-covariance matrix of the three dimensional Fisher distribution has not previously been explicitly computed. While the emphasis of this paper lies in calculating the moments of spherical distributions, their usefulness is motivated by their relationship to population statistics in animal/cell movement models and demonstrated in applications to the modelling of sea turtle navigation, wolf movement and brain tumour growth. |
| format | Article |
| id | doaj-art-ff1a903a1aaf437ebb516d670a276186 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-ff1a903a1aaf437ebb516d670a2761862025-01-24T02:39:47ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-05-0114367369410.3934/mbe.2017038Moments of von mises and fisher distributions and applicationsThomas Hillen0Kevin J. Painter1Amanda C. Swan2Albert D. Murtha3University of Alberta, Centre for Mathematical Biology, Edmonton, Alberta, T6G2G1, CanadaDepartment of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, UKUniversity of Alberta, Centre for Mathematical Biology, Edmonton, Alberta, T6G2G1, CanadaCross Cancer Institute, 11560-University Ave NW, Edmonton, Alberta, T6G 1Z2, CanadaThe von Mises and Fisher distributions are spherical analogues to theNormal distribution on the unit circle and unit sphere, respectively. The computation of their moments, and in particular the second moment, usually involves solving tedious trigonometric integrals. Here we present a new method to compute the moments of spherical distributions, based on the divergence theorem. This method allows a clear derivation of the second moments and can be easily generalized to higher dimensions. In particular we note that, to our knowledge, the variance-covariance matrix of the three dimensional Fisher distribution has not previously been explicitly computed. While the emphasis of this paper lies in calculating the moments of spherical distributions, their usefulness is motivated by their relationship to population statistics in animal/cell movement models and demonstrated in applications to the modelling of sea turtle navigation, wolf movement and brain tumour growth.https://www.aimspress.com/article/doi/10.3934/mbe.2017038von mises distributionfisher distributionspherical distributionsmomentsbiological applications |
| spellingShingle | Thomas Hillen Kevin J. Painter Amanda C. Swan Albert D. Murtha Moments of von mises and fisher distributions and applications Mathematical Biosciences and Engineering von mises distribution fisher distribution spherical distributions moments biological applications |
| title | Moments of von mises and fisher distributions and applications |
| title_full | Moments of von mises and fisher distributions and applications |
| title_fullStr | Moments of von mises and fisher distributions and applications |
| title_full_unstemmed | Moments of von mises and fisher distributions and applications |
| title_short | Moments of von mises and fisher distributions and applications |
| title_sort | moments of von mises and fisher distributions and applications |
| topic | von mises distribution fisher distribution spherical distributions moments biological applications |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017038 |
| work_keys_str_mv | AT thomashillen momentsofvonmisesandfisherdistributionsandapplications AT kevinjpainter momentsofvonmisesandfisherdistributionsandapplications AT amandacswan momentsofvonmisesandfisherdistributionsandapplications AT albertdmurtha momentsofvonmisesandfisherdistributionsandapplications |