Related papers: Transmuted Geometric Distribution and its Prpoerti…
We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on…
In this paper, four parameters Wright function is considered. Certain geometric properties such as starlikeness, convexity, uniform convexity and close-to-convexity are discussed for this function. Further, certain geometric properties of…
One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this…
We introduce the univariate two--piece sinh-arcsinh distribution, which contains two shape parameters that separately control skewness and kurtosis. We show that this new model can capture higher levels of asymmetry than the original…
The hypergeometric distribution is a popular distribution, whose properties have been extensively investigated. Generating functions of this distribution, such as the probability-generating function, the moment-generating function, and the…
The Landau potential in the general Ginzburg-Landau theory with two order parameters and all possible quadratic and quartic terms cannot be minimized with the straightforward algebra. Here, a geometric approach is presented that circumvents…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
The hyperbolic secant distribution has several generalizations with applications in finance. In this study, we explore the dual geometric structure of one such generalization, namely the beta-logistic distribution. Recent findings also…
Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the covariance matrix and its inverse. We study the semi-algebraic geometry of these models, in particular…
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…
This paper presents likelihood-based inference methods for the family of univariate gamma-normal distributions GN({\alpha}, r, {\mu}, {\sigma}^2 ) that result from summing independent gamma({\alpha}, r) and N({\mu}, {\sigma}^2 ) random…
The properties of the square bias transformation are studied, in particular, the precise moment-type estimate for the $L_1$-metric between the transformed and the original distributions is proved, a relation between their characteristic…
In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the $D=10$ ungauged maximal and…
A field theory is constructed in the context of parameterized absolute parallelism geometry. The theory is shown to be a pure gravity one. It is capable of describing the gravitational field and a material distribution in terms of the…
The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena generate data that follow asymmetric distributions, and consequently bivariate normal model is inappropriate in…
A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They…
Algorithms for generating random numbers that follow a gamma distribution with shape parameter less than unity are proposed. Acceptance-rejection algorithms are developed, based on the generalized exponential distribution. The squeeze…
In this paper we propose a bimodal gamma distribution using a quadratic transformation based on the alpha-skew-normal model. We discuss several properties of this distribution such as mean, variance, moments, hazard rate and entropy…