• Corpus ID: 86856047

On initial direction, orientation and discreteness in the analysis of circular variables

@article{Mastrantonio2015OnID,
  title={On initial direction, orientation and discreteness in the analysis of circular variables},
  author={Gianluca Mastrantonio and Giovanna Jona Lasinio and Antonello Maruotti and Gianfranco Calise},
  journal={arXiv: Methodology},
  year={2015}
}
In this paper, we propose a discrete circular distribution obtained by extending the wrapped Poisson distribution. This new distribution, the Invariant Wrapped Poisson (IWP), enjoys numerous advantages: simple tractable density, parameter-parsimony and interpretability, good circular dependence structure and easy random number generation thanks to known marginal/conditional distributions. Existing discrete circular distributions strongly depend on the initial direction and orientation, i.e. a… 

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References

SHOWING 1-10 OF 30 REFERENCES
Spatio-temporal circular models with non-separable covariance structure
TLDR
This work accommodates covariates, implements full kriging and forecasting, and also allows for a nugget which can be time dependent, within a Bayesian framework, to facilitate Markov chain Monte Carlo model fitting.
A hidden Markov approach to the analysis of space–time environmental data with linear and circular components
TLDR
A multivariate hidden Markov model that includes features of the data within a single framework, associated with easily interpretable components of large-scale and small-scale spatial variation, and provides a parsimonious representation of the sea surface in terms of alternating environmental states.
Bayesian hidden Markov modelling using circular‐linear general projected normal distribution
We introduce a multivariate hidden Markov model to jointly cluster time‐series observations with different support, that is, circular and linear. Relying on the general projected normal distribution,
Directional Statistics, I
In many natural and physical sciences the measurements are directions—either in two- or three-dimensions. This chapter briefly introduces this novel area of statistics, and provides a good starting
Inference for circular distributions and processes
  • S. Coles
  • Computer Science, Mathematics
    Stat. Comput.
  • 1998
TLDR
The power and flexibility of Markov chain Monte Carlo methods to fit such classes of models to circular data and applications are given to multivariate and time series data of wind directions.
Wrapped Skew Laplace Distribution on Integers:A New Probability Model for Circular Data
In this paper we propose a new family of circular distributions, obtained by wrapping discrete skew Laplace distribution on Z = 0, ±1, ±2, around a unit circle. In contrast with many wrapped
New Families of Wrapped Distributions for Modeling Skew Circular Data
Abstract We discuss circular distributions obtained by wrapping the classical exponential and Laplace distributions on the real line around the circle. We present explicit forms for their densities
Spatial analysis of wave direction data using wrapped Gaussian processes
TLDR
A model-based approach to handle periodic data in the case of measurements taken at spatial locations, anticipating structured dependence between these measurements, and formulates a wrapped Gaussian spatial process model for this setting.
A hidden Markov model for the analysis of cylindrical time series
A new hidden Markov model is proposed for the analysis of cylindrical time series, that is, bivariate time series of intensities and angles. It allows us to segment cylindrical time series according
Modeling Space and Space-Time Directional Data Using Projected Gaussian Processes
TLDR
The contribution is to develop a fully model-based approach to capture structured spatial dependence for modeling directional data at different spatial locations, and builds a projected Gaussian spatial process, induced from an inline bivariate Gaussia spatial process.
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