Related papers: On the Spherical Dirichlet Distribution: Correctio…
In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…
Mixture models are commonly used when data show signs of heterogeneity and, often, it is important to estimate the distribution of the latent variable responsible for that heterogeneity. This is a common problem for data taking values in a…
We use Stein characterizations to obtain new moment-type estimators for the parameters of three classical spherical distributions (namely the Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the i.i.d. case. This leads…
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA).…
Sine-skewed circular distributions are identifiable and have easily-computable trigonometric moments and a simple random number generation algorithm, whereas they are known to have relatively low levels of asymmetry. This study proposes a…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
Pyrosequencing is emerging as one of the important next-generation sequencing technologies. We derive the statistical distributions of this technique in terms of nucleotide probabilities of the target sequences. We give exact distributions…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its…
For an observed response that is composed by a set - or vector - of positive values that sum up to 1, the Dirichlet distribution (Bol'shev, 2018) is a helpful mathematical construction for the quantification of the data-generating mechanics…
This article presents a novel method to sampling on manifolds based on the Dirichlet distribution. The proposed strategy allows to completely respect the underlying manifold around which data is observed, and to do massive samplings with…
This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a…
Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…
There exist several endeavors proposing a new family of extended distributions using the beta-generating technique. This is a well-known mechanism in developing flexible distributions, by embedding the cumulative distribution function (cdf)…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
The shortcomings of the traditional univariate distributions in the past greatly encouraged mathematical statisticians to develop new generalizations of distributions. The New Generalized Fisk distribution, a unique distribution presented…
The directional precision of the sample mean estimator was calculated analytically for the offset exponential and normal distributions in three-dimensional space both for a finite sample and for limiting cases. It was shown that the…
Traditional topic models do not account for semantic regularities in language. Recent distributional representations of words exhibit semantic consistency over directional metrics such as cosine similarity. However, neither categorical nor…
Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…