A stepwise method for determining the number of component distributions in a mixture

Hsu, Yu‐Sheng; Walker, Joseph J.; Ogren, David E.

doi:10.1007/bf00898280

Cited by 15 publications

(6 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, this approach extracts two parameter sets from the sample, directional modes and associated widths [1,17,26], where the widths represent a measure for directional ordering. These parameters will be used in a forthcoming paper to quantify the differences between experimental rod patterns and the expected behavior from theories and simulations.…”

Section: New Model By Means Of Directional Statisticsmentioning

confidence: 99%

Frame theory in directional statistics

Ehler

Galanis

2011

Statistics & Probability Letters

View full text Add to dashboard Cite

Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. By merging directional statistics with frame theory, we find that probabilistic tight frames yield non-uniform distributions that minimize directional potentials, leading to failure of uniformity rejection for the Bingham test. Finally, we apply our results to model patterns found in granular rod experiments.

show abstract

Section: New Model By Means Of Directional Statisticsmentioning

confidence: 99%

Frame theory in directional statistics

Ehler

Galanis

2011

Statistics & Probability Letters

View full text Add to dashboard Cite

show abstract

“…However, it must be stated that Stephen's (1969) comment was made when the available computer power was considerably less than that available today. Hsu et al (1986) tted a mixture of bivariate von Mises distributions; that is, the dip angle and direction were assumed to be distributed independently, each with a von Mises distribution. This assumption does not allow for any correlation between dip direction and dip angle, which can certainly occur.…”

Section: Discussionmentioning

confidence: 99%

“…An important question that needs to be addressed is how many joint sets are present or, in the mixture model framework, the value of g. This question was previously examined for directional data by Hsu, Walker, and Ogren (1986), who looked at a stepwise method for determining the number of components in a mixture with example applications to joint set data. Their stepwise procedure used a bootstrap method to determine the null distribution of Watson's U 2 statistic.…”

Section: Determining the Number Of Joint Setsmentioning

confidence: 99%

Fitting Mixtures of Kent Distributions to Aid in Joint Set Identification

Peel

Whiten

McLachlan

2001

Journal of the American Statistical Association

View full text Add to dashboard Cite

When examining a rock mass, joint sets and their orientations can play a signi cant role with regard to how the rock mass will behave. To identify joint sets present in the rock mass, the orientation of individual fracture planes can be measured on exposed rock faces and the resulting data can be examined for heterogeneity. In this article, the expectation-maximization algorithm is used to t mixtures of Kent component distributions to the fracture data to aid in the identi cation of joint sets. An additional uniform component is also included in the model to accommodate the noise present in the data.

show abstract

“…Jammalamadaka & Sengupta (2001) present the latest developments in circular statistics. Statistical inferences in circular or directional mixture models have been discussed by many authors, e.g., Stephens (1969), Fraser, Hsu &Walker (1981), Hsu, Walker & Ogren (1986), Kim & Koo (2000), and Holzmann, Munk & stratmann (2004).…”

Section: Introductionmentioning

confidence: 99%

Testing homogeneity in a mixture of von mises distributions with a structural parameter

Chen

2008

Can J Statistics

View full text Add to dashboard Cite

MSC 2000: Primary 62F03; secondary 62F05. Abstract: The modified likelihood ratio statistic can be used to test the homogeneity in a variety of mixture models. Here, the authors propose the use of the modified and the iterative modified likelihood ratio for testing homogeneity against a two-component von Mises mixture with a structural parameter. They derive the limiting distributions of the test statistics and propose methods to improve the accuracy of the asymptotic approximation in finite samples. Their simulations show that the tests maintain their nominal level and that they have adequate power. Data on movements of turtles are used as an illustration. Tests d'homogeneite d'un melange de lois de von Mises avec parametre structurelR h m C : La statistique du rapport des vraisemblances modifik permet de tester I'homogbn6it6 dans divers modkles de melanges. Les auteurs proposent ici l'emploi du rapport des vraisemblances modifie ou it& rativement modifie pour tester I'homog6n6it6 d'un mClange de deux lois de von Mises avec parametre structurel. ils dkterminent les lois limites des statistiques de test et proposent des techniques pennettant d'ameliorer I'approximation asymptotique il taille finie. Leurs simulations montrent que les tests maintiennent leur seuil nominal et qu'ils sont assez puissants. Des donnQs de dkplacements de tortues illustrent le propos.

show abstract

A stepwise method for determining the number of component distributions in a mixture

Cited by 15 publications

References 4 publications

Frame theory in directional statistics

Frame theory in directional statistics

Fitting Mixtures of Kent Distributions to Aid in Joint Set Identification

Testing homogeneity in a mixture of von mises distributions with a structural parameter

Contact Info

Product

Resources

About