Some descriptive properties of normal mixtures

Robertson, Craig; Fryer, J. G.

doi:10.1080/03461238.1969.10404590

Cited by 56 publications

(34 citation statements)

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“…Finite mixture theory tells us that the means of two equally represented, equally dispersed subsamples can be sepa-rated by about two subsample standard deviations before their mixture begins to exhibit visible bimodality (Robertson and Fryer, 1969;Titterington et al, 198~51.~ This is graphically represented in Figure 3.…”

Section: Finite Mixture Models For Estimating Embedded Bimodalitymentioning

confidence: 98%

“…Robertson and Fryer (1969) and Titterington et al (1985) document the extension of finite mixture logic t o non-normal, unequally dispersed subsamples with unequal mixing proportions. While such theory is reassuring, I t is also true that for whole sample sizes of 5 to 50, normality or non-normality of either the population represented by the whole sample or of embedded subpopulations represented by subsamples cannot be ascertained with reasonable statistical power.…”

Section: Finite Mixture Models For Estimating Embedded Bimodalitymentioning

confidence: 98%

“…This problem can be solved with exact precision €or any sample with a given range if the actual standard deviations of the male and female subsamples and the relative percentages of each in the sample as a whole are known (Robertson and Fryer, 1969;Titterington et al, 1985). Because they are not, we must model solutions based on alternative sets of simplifying assumptions.…”

Section: Finite Mixture Models For Estimating Embedded Bimodalitymentioning

confidence: 99%

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Sexual dimorphism in large‐bodied primates: The case of the subfossil lemurs

Godfrey

Lyon

Sutherland

1993

American J Phys Anthropol

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Large body size has evolved repeatedly in the order Primates, not merely among anthropoids but also among prosimians. Whereas high degrees of sexual size dimorphism characterize many of the large-bodied anthropoids, this is not the case for extinct large-bodied lemurs. This paper uses finite mixture analysis and other techniques to ascertain just how much skull length dimorphism might be embedded in the generally unimodal distributions of skull lengths of giant extinct lemurs from single localities, and then compares these results with known skull length dimorphisms in extant lemurs and large-bodied catarrhines. We show that low levels of skull length sexual dimorphism (or none at all) characterize subfossil lemurs, and we explore several possible explanations for this phenomenon. Traditional explanations of sexual size dimorphism generally focus on body size or mating systems. These are not sufficient to explain the variation in sexual dimorphism that can be observed in the order Primates.

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Section: Finite Mixture Models For Estimating Embedded Bimodalitymentioning

confidence: 98%

Section: Finite Mixture Models For Estimating Embedded Bimodalitymentioning

confidence: 98%

Section: Finite Mixture Models For Estimating Embedded Bimodalitymentioning

confidence: 99%

See 1 more Smart Citation

Sexual dimorphism in large‐bodied primates: The case of the subfossil lemurs

Godfrey

Lyon

Sutherland

1993

American J Phys Anthropol

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“…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%

A likelihood ratio test for bimodality in two-component mixtures with application to regional income distribution in the EU

Holzmann

Vollmer²

2008

AStA

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“…Specially, the one dimensional case of logistic mixture is in the preprint paper "A Note On The Convex Combination Of Two 1-, 2-, 3-, and 4-Parameter Logistic Item Response Functions", which is according to [8].…”

Section: Lemmamentioning

confidence: 99%

Multivariate Logistic Mixtures

Xiao¹

2015

ujam

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Logistic mixtures, unlike normal mixtures, have not been studied for their topography. In this paper we discuss analogs of some of the multivariate normal mixture results for the multivariate logistic distribution. We focus on graphical techniques that are based on displaying the elevation of the density on the ridgeline. These techniques are quite elementary, and carry full information about the location and relative heights of the modes and saddle points. Moreover, we turn to a technique that names II-Plot which denotes that the first differentiation of the second component density ratios the difference between the first differentiations of the second component density and the first component density.

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Some descriptive properties of normal mixtures

Cited by 56 publications

References 1 publication

Sexual dimorphism in large‐bodied primates: The case of the subfossil lemurs

Sexual dimorphism in large‐bodied primates: The case of the subfossil lemurs

A likelihood ratio test for bimodality in two-component mixtures with application to regional income distribution in the EU

Multivariate Logistic Mixtures

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