Estimation of the Bingham distribution function on nearly two-dimensional data sets

Gillett, Stephen L.

doi:10.1111/j.1365-246x.1986.tb04375.x

Cited by 3 publications

(1 citation statement)

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“…Mardia and Zemroch (1977) suggest using (6) when both I"1 I and I"21 are large. Gillett (1986) suggests using (5) when I"1 I alone is large. However, more accurate results can be obtained by using higher order terms in a suitable asymptotic series expansion.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Expansions for the Bingham Distribution

Kent¹

1987

Applied Statistics

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SUMMARY Statistical estimation for the Bingham distribution on the sphere requires the calculation of the normalization constant and its derivatives. The usual Taylor series expansion in two variables is useful only if the parameter values are not too large. The asymptotic series developed here enable the normalization constant to be easily and accurately evaluated when one or both of the parameter values is large.

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Section: Introductionmentioning

confidence: 99%

Asymptotic Expansions for the Bingham Distribution

Kent¹

1987

Applied Statistics

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User-driven integrated software lives: “Paleomag” paleomagnetics analysis on the Macintosh

Jones

2002

Computers & Geosciences

178

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Paleomagnetism and age determinations of the Deccan Traps (India): Results of a Nagpur‐Bombay Traverse and review of earlier work

Vandamme¹,

Courtillot²,

Besse³

et al. 1991

Reviews of Geophysics

209

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Review of available radiometric age determinations of the Deccan traps (India) shows a spectrum of K-Ar ages that is highly polluted by argon loss. Stepwise 40 Ar_39 Ar age determinations include estimates of data quality and thus avoid contaminated results. The absolute age of the Deccan traps determined using 22 40 Ar_39 Ar plateau age spectra is 65.5 _+ 2.5 Ma. Paleontological data on infratrappean and intertrappean sediments constrain Deccan age to between the A. mayaroensis zone, in the Upper Maestrichtian (about 67 Ma), and the P2 foraminifer zone, in the Lower Paleocene (about 60.5 Ma). Paleomagnetic study of a Nagpur-Bombay traverse (preliminary results of which were used by Courtillot et al. (1986a, b) for a general discussion about Deccan volcanism and the Cretaceous-Tertiary boundary) is presented in detail. All available paleomagnetic results from the Deccan traps (563 flows) are then compiled. Results considered to be transitional or to come from suspicious sites are removed leaving 485 flow results. This extensive data set from a single geological unit allowed us to look in some detail at its statistical distribution. The virtual geomagnetic poles (VGP) are approximately Fisher distributext but present a complex asymmetry. No regional variation can be seen (to within paleomagnetic uncertainties). Although the 3.5 ø angular difference between the separate normal (pole) and reversed (antipole) data is not statistically significant, it can be explained by either a 2.1 m.y. drift along the apparent polar wander path (APWP) of the Indian plate assuming a normal-reverse-normal (N-R-N) magnetostratigraphy, or a 3.5% contamination by a present field overprint, or a slight nondipole field component. A quality coefficient has been assigned to each result on the basis of existence and value of published 95% confidence angle. Because the normal and reversed mean poles become more precisely antipodal with higher-quality data and with more recent publication date (as a consequence of the evolution of paleomagnetic techniques), we favor the overprint hypothesis. The angular standard deviation of our VGP set is 20% larger than the value predicted by the paleoSeCular variation model of McFadden and McElhinny (1984). Finally, our best estimate of the overall mean pole is located at 281.3øE, 36.9øN, A95 = 2.4 ø (calculated from the 163 highest-quality flow VGPs). It is in remarkable agreement with the reference APWP of Besse and Courtillot (1991), leading to an independent estimate of the age of Deccan volcanism at 67.2 _+ 6.6 Ma. The same comparison following Acton and Gordon (1989) provides an estimated age at 67 _+ 5 Ma. These estimates which are based on paleomagnetic data only are in perfect agreement with both radiometric and paleontological ages. et al., 1986a, b; Courtillot and Cisowski, 1987; Courtillot and Besse, 1987]. The aim of this review is to present an up-to-date compilation of available age constraints and paleomagnetic data from a formation that may have resulted from the most significant volcanic e...

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Estimation of the Bingham distribution function on nearly two-dimensional data sets

Cited by 3 publications

References 10 publications

Asymptotic Expansions for the Bingham Distribution

Asymptotic Expansions for the Bingham Distribution

User-driven integrated software lives: “Paleomag” paleomagnetics analysis on the Macintosh

Paleomagnetism and age determinations of the Deccan Traps (India): Results of a Nagpur‐Bombay Traverse and review of earlier work

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