On the modes of a mixture of two von Mises distributions

Mardia, K. V.; Sutton, Terence W.

doi:10.1093/biomet/62.3.699

Cited by 43 publications

(18 citation statements)

References 9 publications

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“…We therefore propose that bidirectional orientation is a normal feature of D. diseoideum slug phototaxis usually obscured because the preferred directions are too close together. Following the methods of Mardia and Sutton [10] we calculated that even with an accuracy of orientation (K) as high as 120 (X22 slugs on charcoal agar [2]), D. discoideum slugs would need to aim at directions more than 5 ° either side of the light source before a bimodal distribution would result. Lower accuracies of orientation, slugs switching from one preferred direction to the other, and sampling error all increase this minimum separation of directions required to reliably observe bimodality.…”

Section: Resultsmentioning

confidence: 99%

Bidirectional phototaxis by Dictyostelium discoideum slugs

Fisher

1981

FEMS Microbiology Letters

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Section: Resultsmentioning

confidence: 99%

Bidirectional phototaxis by Dictyostelium discoideum slugs

Fisher

1981

FEMS Microbiology Letters

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“…Thus, the corrected numbers of SIDS cases for the year 1998 are shown in Table 11 (also see Table 1 in Mooney et al 2003). In general, the number of cases in a year can be converted to angles for fitting von Misses distribution (see Mardia and Jupp 2000). Hence, we convert the corrected numbers of SIDS cases for the year 1998 in Table 11 to circular data by dividing 360°into 12, i.e.…”

Section: â100%mentioning

confidence: 99%

“…directional data on the plane) and Watson and Williams (1956) first investigated inference problems for the von Mises distribution and gave the construction of statistical methods on circular data., the researches on circular data got increasing concerns. Mardia (1972), Fisher (1993) and Mardia and Jupp (2000) are good reference books for the analysis of circular data with applications to biology, geology, medicine, meteorology, oceanography, etc. Furthermore, Mooney et al (2003) considered circular data for a case study involving sudden infant death syndrome (SIDS).…”

Section: Introductionmentioning

confidence: 99%

On mean shift-based clustering for circular data

2012

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Cluster analysis is a useful tool for data analysis. Clustering methods are used to partition a data set into clusters such that the data points in the same cluster are the most similar to each other and the data points in the different clusters are the most dissimilar. The mean shift was originally used as a kernel-type weighted mean procedure that had been proposed as a clustering algorithm. However, most mean shift-based clustering (MSBC) algorithms are used for numeric data. The circular data that are the directional data on the plane have been widely used in data analysis. In this paper, we propose a MSBC algorithm for circular data. Three types of mean shift implementation procedures with nonblurring, blurring and general methods are furthermore compared in which the blurring mean shift procedure is the best and recommended. The proposed MSBC for circular data is not necessary to give the number of cluster. It can automatically find a final cluster number with good clustering centers. Several numerical examples and comparisons with some existing clustering methods are used to demonstrate its effectiveness and superiority of the proposed method.

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“…μ 2 − μ 1 =: d ∈ [0, π] (since the maximal distance on the circle of two points along the arc is π ). Mardia and Sutton (1975) gave precise conditions for bimodality for general parameters constellations. Here we review only their results for the case of equal concentration parameters, i.e.…”

Section: Example 2 (Von Mises Distribution) the Von Mises Distributiomentioning

confidence: 99%

“…Therefore, there is no immediate connection between the number of components in a mixture and the number of modes of the resulting density. Nevertheless, the modal structure of two-component mixtures of certain parametric families, notably the normal distribution (Robertson and Fryer 1969) and the von Mises distribution (Mardia and Sutton 1975), is completely known in terms of the parameters of the mixture. For two-component mixtures, for which such an explicit characterization of the modal structure is available, we construct a likelihood ratio (LR) test for unimodality against bimodality.…”

Section: Introductionmentioning

confidence: 99%