Related papers: An Extension of the Cardioid Distributions on Circ…
In this paper, we study the spherical cardioid distribution, a higher-dimensional and higher-order generalization of the circular cardioid distribution. This distribution is rotationally symmetric and generates unimodal, multimodal, axial,…
We propose a flexible family of distributions, generalized $t$-distributions, on the cylinder which is obtained as a conditional distribution of a trivariate $t$ distribution. The new distribution has unimodality or bimodality, symmetry or…
We introduce a four-parameter extended family of distributions related to the wrapped Cauchy distribution on the circle. The proposed family can be derived by altering the settings of a problem in Brownian motion which generates the wrapped…
The Cardioid distribution is a relevant model for circular data. However, this model is not suitable for scenarios were there is asymmetry or multimodality. In order to overcome this gap, an extended Cardioid model is proposed, which is…
A new family of integer-valued Cauchy-type distributions is introduced, the {\it Cauchy-Cacoullos family}. The characteristic function is evaluated, showing some interesting distributional properties, similar to the ordinary (continuous)…
We introduce a novel family of projected distributions on the circle and the sphere, namely the circular and spherical projected Cauchy distributions, as promising alternatives for modelling circular and spherical data. The circular…
Two specific families of distributions in harmonic and Clifford analysis are further studied through a spherical co-ordinates approach. In particular actions involving spherical co-ordinates, such as the radial derivative and the…
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…
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…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
In this paper, we prove some value distribution results which lead to some normality criteria for a family of analytic functions. These results improve some recent results.
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
This paper introduces two families of probability distributions for Bayesian analysis of hypertoroidal data. The first family consists of symmetric distributions derived from the projection of multivariate normal distributions under…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
The new Sine Skewed Cardioid (ssc) distribution been just introduced and characterized by Ahsanullah (2018). Here, we study the asymptotic properties of its tails by determining its extreme value domain, the characteristic function, the…
We introduce families of jointly symmetric, binary distributions that are generated over directed star graphs whose nodes represent variables and whose edges indicate positive dependences. The families are parametrized in terms of a single…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…