The wrapped stable family of distributions as a flexible model for circular data

Integration of facial features under memory load

Simple visual items and complex real-world objects are stored into visual working memory as a collection of independent features, not as whole or integrated objects. Storing faces into memory might differ, however, since previous studies have reported perceptual and memory advantage for whole faces compared to other objects. We investigated whether facial features can be integrated in a statistically optimal fashion and whether memory maintenance disrupts this integration. The observers adjusted a probe – either a whole face or isolated features (eyes or mouth region) – to match the identity of a target while viewing both stimuli simultaneously or after a 1.5 second retention period. Precision was better for the whole face compared to the isolated features. Perceptual precision was higher than memory precision, as expected, and memory precision further declined as the number of memorized items was increased from one to four. Interestingly, the whole-face precision was better predicted by models assuming injection of memory noise followed by integration of features than by models assuming integration of features followed by the memory noise. The results suggest equally weighted or optimal integration of facial features and indicate that feature information is preserved in visual working memory while remembering faces.

Wrapped: An R package for circular data

The Wrapped package computes the probability density function, cumulative distribution function, quantile function and also generates random samples for many univariate wrapped distributions. It also computes maximum likelihood estimates, standard errors, confidence intervals and measures of goodness of fit for nearly fifty univariate wrapped distributions. Numerical illustrations of the package are given.

Inverse Batschelet distributions for circular data

We provide four-parameter families of distributions on the circle which are unimodal and display the widest ranges of both skewness and peakedness yet available. Our approach is to transform the scale of a generating distribution, such as the von Mises, using various nontrivial extensions of an approach first used in Batschelet's (1981, Circular Statistics in Biology) book. The key is to employ inverses of Batschelet-type transformations in certain ways; these exhibit considerable advantages over direct Batschelet transformations. The skewness transformation is especially appealing as it has no effect on the normalizing constant. As well as a variety of interesting theoretical properties, when likelihood inference is explored these distributions display orthogonality between elements of a pairing of parameters into (location, skewness) and (concentration, peakedness). Further, the location parameter can sometimes be made approximately orthogonal to all the other parameters. Profile likelihoods come to the fore in practice. Two illustrative applications, one concerning the locomotion of a Drosophila fly larva, the other analyzing a large set of sudden infant death syndrome data, are investigated.