Note on the probability distribution of a small number of vectors

Vincenz, S. A.; Bruckshaw, J. M.

doi:10.1017/s0305004100034253

Cited by 38 publications

(17 citation statements)

References 6 publications

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“…Variations in the magnitude o f f may be expressed in the form of a probability density function p(f), where the proportion of vectors with lengths between f and f+df is given by p(f)df, and similarly for P(F). Then the angular variance of the population of vectors f + F is given by where the integration is over the domains off and F. (Rayleigh 1919;Vincenz & Bruckshaw 1960;Cox 1964) Variations in the magnitude of f may be described by the density function P(f) = (4fZ/n*fR3) exp (-f21fRz)…”

Section: Latitude Dependence Of Secular Variation-field Directionsmentioning

confidence: 99%

Latitude Dependence of the Angular Dispersion of the Geomagnetic Field

Cox

1970

Geophysical Journal International

272

244

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Changes in the direction of the Earth's magnetic field at a given site are produced in part by wobble of the main geomagnetic dipole, in part by fluctuations in the intensity and direction of the non-dipole field, and in part by changes in the intensity of the main dipole field. These three processes combine to produce an angular variance that is strongly latitude dependent. A method is presented for isolating the contribution due to variation with latitude of the average intensity of the non-dipole field.

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Section: Latitude Dependence Of Secular Variation-field Directionsmentioning

confidence: 99%

Latitude Dependence of the Angular Dispersion of the Geomagnetic Field

Cox

1970

Geophysical Journal International

272

244

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“…J'ai donc vCrifi6, pour toutes les localites ayant 3 specimens ou plus, si les directions Ctaient distribukes au hasard. Watson (1956) et Vincenz et Bruckshaw (1960) ont calcul6 des valeurs qui nous permettent d'etablir, au niveau significatif de 5%, si les directions sont distribuees au hasard. Or, d'apr2s ce test, on trouve que ces deux localitks A8 e t A9 ainsi que la localit6 A l l ont des directions distribuees au hasard et n'ont pratiquement aucune valeur dans la determination du champ.…”

Section: Dksaimntation De Spkcimens-guidesunclassified

Désaimantation Thermique Et Analyse Statistique Des Directions De Sédiments Carbonifères Et Permiens De l'EST Du Canada

Roy¹

1966

Can. J. Earth Sci.

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RESUMBUne desaimantation thermique d'dchantillons sddimentajres (109 khantillons, 42 localit&) provenant des maritime9 et de la Gas+sie dCmontre que I'aimantation fossile est composPe d'une aimantation rgdominante qui est thermiquement stable et d'une ou des aimantations pLs petites qui sont instables e t disparaisent A des tempEratures d'environ 400 "C. L)ans le but de desaimanter ces aimantations instables, tous les sp6cimens sont alors sournis B un nettoiement thermique de 450 "C. Ce proc&e change la dCclinaison et I'inclinaison moyennes dc 6" et 7" respectivernent et, de plrrs, change la distribution des directions autour de la moyenne. Une analyse statistique d6montre que les directions rnoyennes (aprPs dk~imantation) des localit& se conforment 2, unc distribution de Fisher (1953) tandis que les directions des spCcimens ne s'adaptent aucunement A une telle distribution. Ce rGsultat est d'intCrGt sous deux rapports: d'abord, il cl&nontt-e que, dans ce cas-ci, I'usage des statistiques de Fisher (1953) pour analywr les rtsultats, n'est pas permis quand le spPcimen est employ6 comme unid de poids mais que leur usage est justifiable quancl h localit6 est employee comrne unite; ensuite, ce rCsultat est compattble avec I'hypothhse que le champ magnetique, quand les tkhantillons sont preleves de cette facon, peut Btre represent6 par le champ d'un dipble axial geocentrique trouble par des cornposantes nlagn6tiques d i s t r i b u h au hazard B la surface terrestre. En cornparant les resultats d~sponibles pour cette pPriode geologique, on remarque une divergence assez marquPe des differents pbles pal6otnagnCtiques pour 11Am4rique d u Nord. I1 est suggtr6 qu'une d&ainiantation partielle de ces collections ant6rieures pourrait reduire cette divergence. ABSTRACTThermal demagnetization of red beds (109 specimens. 42 sites) from the Maritimes and Gasp6 shows that the fossil magnetization consists of a large, thermally stable component and of small, unstable components that disappear a t about 41H, "C. Thermal cleaning of the whole collection was therefore carried out a t 450 "C to demagnetize these soft components. This procedure changes the mean declination and inclination by 6" and 7' respectively and also changes the distribution of directions about the mean. 11 statistical analysis shows that the site mean directions (after demagnetization) obey a Fisher's (1953) distribution whereas the individual s~c i m e n directions do not. This result is of interest in two connections: first, it shows that, in this instance, the use of Fisher's (19.53) statistics to analyse the results is not permissible when unit weight is given to the specimen, but that their use is legitimate when unit weight is given to the site: second, the result is consistent with the hypothesis that the earth's field, when sampled in this way (paleoma~netically), can be represented by a n axial geocentric dipole field perturbed by randomly directed magnetic components a t the earth's surface. Comparison with other results available for this geological pe...

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“…The first calculation is a test to determine whether the observations are distributed randomly on the sphere (Watson, 1956b;Vincenz and Bruckshaw, 1960). The test is made by comparing the calculated value of the vector resultant R with the tabled value of this statistic at the 5-or 10-percent significance level.…”

Section: Program To Compute Basic Statisticsmentioning

confidence: 99%

Computer program to analyze directional data, based on the methods of Fisher and Watson

Schuenemeyer

Koch

Link

1972

Mathematical Geology

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Based on the methods of Fisher and Watson, FORTRAN IV computer programs are presented for the following analyses of directional observations on the sphere: (1) to determine if points are randomly distributed; (2) to estimate the azimuth and inclination of the center (mean direction) of a chtster and to estimate the precision (closeness) with which points are clustered," (3) to determine if two or more clusters have the same mean direction; (4) to determine if two clusters have the same precision of clustering; and (5) to locate the pole of a great-circle girdle of pohzts. Limitations of these analyses for undirected directional observations on the hemi-sphere also are given.

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Note on the probability distribution of a small number of vectors

Cited by 38 publications

References 6 publications

Latitude Dependence of the Angular Dispersion of the Geomagnetic Field

Latitude Dependence of the Angular Dispersion of the Geomagnetic Field

Désaimantation Thermique Et Analyse Statistique Des Directions De Sédiments Carbonifères Et Permiens De l'EST Du Canada

Computer program to analyze directional data, based on the methods of Fisher and Watson

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