Directional Statistics, I

By S. Jammalamadaka. 2011

2,380 citations recorded by the source corpus.

Subfields: Atmospheric Science, Molecular Biology

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Citations in the corpus

Federated Learning with Autotuned Communication-Efficient Secure Aggregation (2019, methodology): “Instead, we find that the tails of the normal distribution “wrap around,” producing instead a wrapped normal distribution [8], see Figure 1, with the probability density function”
Recurrent Pixel Embedding for Instance Grouping (2017, methodology): “Mean-shift and closely related algorithms [25, 13, 14, 15] use kernel density estimation to approximate the probability density from a set of samples and then perform clustering on the input data by assigning or moving each sample to the nearest mode (local maxima).”
Granular micromechanics based micromorphic model predicts frequency band gaps (2015, background): “For describing materials with general inherent anisotropy, directional density distribution functions may be formulated as described in [13,18,41,42].”
Resting structures and resting habitat of fishers in the southern Sierra Nevada, California (2009, methodology): “We tested for differences in aspect for rest and random sites using a q-sample Uniform Scores test (Mardia and Jupp, 2000).”
Descriptive tools for the analysis of texture projects with large datasets using MTEX: strength, symmetry and components (2014, methodology): “Later Lisle (1985) used a characteristic developed by Mardia (1972) and more recently by Mardia & Jupp (2000): I = (15n/2) (l21 + l22 + l23 − 1/3).”
Communication Through a Large Reflecting Surface With Phase Errors (2019, methodology): “which are also called trigonometric (or circular) moments [12].”
Exploring wind direction and SO2 concentration by circular–linear density estimation (2012, background): “A circular distribution Ψ(·) for Θ assigns a probability to each direction (cos(θ), sin(θ)) in the plane R2, characterized by the angle θ ∈ [0, 2π) (see Mardia and Jupp (2000) for a survey on statistical methods for circular data).”
Local polynomial regression for circular predictors (2009, background): “Recent accounts are given by Jammalamadaka & SenGupta (2001) and Mardia & Jupp (1999).”
Intrinsic means on the circle: uniqueness, locus and asymptotics (2011, background): “It is easy to see that the extrinsic population mean is (essentially) given by arctan(E(cos(X))/E(sin(X))), and it fulfills a law of large numbers as well as a central limit theorem if the extrinsic population mean is unique, see e.g., Mardia and Jupp (2000).”
Contrastive Learning with Hard Negative Samples (2020, methodology): “The exponential term in q β is an unnormalized von Mises–Fisher distribution with mean direction f ( x ) and “concentration parameter” β (Mardia & Jupp, 2000).”
Crystal structures (2004, neutral): “The prior phase probability distribution Ppr( ) is usually represented as a generalized von Mises distribution (Mardia & Jupp, 1999) and is better known in crystallography as a Hendrickson–Lattman distribution (Hendrickson & Lattman, 1970), Pð Þ ¼ N exp½A cosð Þ þ B sinð Þ þ C cosð2 Þ þD sinð2 Þ ;…”
A smeary central limit theorem for manifolds with application to high-dimensional spheres (2018, background): “In many applications, Q is (a) globally a complete smooth Riemannian manifold, e.g. a sphere (cf. Mardia and Jupp (2000) for directional data), a real or complex projective space (cf. Kendall (1984); Mardia and Patrangenaru (2005) for certain shape spaces) or the space of positive definite matrices…”
Affective image classification using features inspired by psychology and art theory (2010, methodology): “However, since Hue is measured in a circular way (in degrees), vector-based, circular statistics [20] must be used to compute measurements like mean, hue spread, etc. Colorfulness is measured using the Earth Mover’s Distance (EMD) between the histogram of an image and the histogram having a uniform…”
Principal component analysis for functional data on Riemannian manifolds and spheres (2017, background): “Examples of data lying on a Euclidean sphere include geographical data (Zheng 2015) on S2, directional data on S1 (Mardia and Jupp 2009), and square-root compositional data (Huckemann and Eltzner 2016), for which we will study longitudinal/functional versions in Section 4.”
A Family of Distributions on the Circle With Links to, and Applications Arising From, Möbius Transformation (2010, methodology): “The full skew wrapped stable distribution was mentioned briefly in books by Mardia (1972), Mardia and Jupp (1999), and Jammalamadaka and SenGupta (2001) and was recently explored in more depth by Pewsey (2008).”
The General Projected Normal Distribution of Arbitrary Dimension: Modeling and Bayesian Inference (2017, methodology): “Many statistical models and methods exist for circular data; see the monographs (Fisher, 1995; Mardia and Jupp, 2000; Jammalamadaka and Sengupta, 2001; Pewsey et al., 2013), and (Wang and Gelfand, 2014) for recent spatio-temporal extensions.”
Hidden Markov Model on a unit hypersphere space for gesture trajectory recognition (2014, background): “A d-dimentional unit random vector x is said to have a d-variate vMF distribution (Mardia and Jupp, 2000) if its PDF is given by vðxjl;jÞ ¼ cdðjÞ expðjlT xÞ: ð1Þ where x;l 2 Rd; jjxjj ¼ jjljj ¼ 1;j P 0, and d P 2.”
Non‐parametric Regression for Circular Responses (2013, methodology): “Left: Periwinkle data showing fitted models for local linear (LL) and kernel (NW) weights, together with parametric fits given by Fisher & Lee (1992) (F & L), Presnell et al. (1998) (SPML), and a direct trigonometric fit (trig). Right: Law of motion data showing fitted models for local linear (LL) a”