Wrapped distribution

Abstract: Circular data arise in many areas of application. Recently, there has been interest in looking at circular data collected separately over time and over space. Here, we extend some of this work to the spatio-temporal setting, introducing space–time dependence. We accommodate covariates, implement full kriging and forecasting, and also allow for a nugget which can be time dependent. We work within a Bayesian framework, introducing suitable latent variables to facilitate Markov chain Monte Carlo model fitting. The Bayesian framework enables us to implement full inference, obtaining predictive distributions for kriging and forecasting. We offer comparison between the less flexible but more interpretable wrapped Gaussian process and the more flexible but less interpretable projected Gaussian process. We do this illustratively using both simulated data and data from computer model output for wave directions in the Adriatic Sea off the coast of Italy.

Abstract: We introduce a new wrapped exponential distribution named transmuted wrapped exponential (TWE) distribution, for the modeling of circular datasets by using the Transmutation Rank-Map method. This method is employed for the first time for a wrapped distribution with this study. The introduced distribution is more flexible than traditional wrapped exponential distribution. The paper provides the explicit form of important distributional properties of the introduced distribution such as expectation, median, moments, characteristic function, quantile function, hazard rate function and stress-strength reliability. Renyi and Shannon entropies are also obtained. The statistical inference problem for the TWE distribution is investigated using maximum likelihood, least squares and weighted least squares and comparative numerical study results are presented. Furthermore, we present a real dataset analysis.

Abstract: In many scientific fields such as biology (orientation of birds), geology (orientations of feldspar laths) and meteorology (wind direction and ozone concentration), data occur as angular forms. In this paper, a class of wrapped distribution called wrapped generalized Gompertz distributions are introduced (WGG). Characteristic function and fundamental properties of this distribution are described. Some theorems that relate the distribution to some other circular distributions are established. Applications to density estimation and goodness-of-fit tests are used to analyze data on the heading of orientation of the nest of noisy scrub birds, and it is shown that the model fits much better than some other existing circular symmetric and non-symmetric models.