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We introduce the first analytical model of asymmetric community dynamics to yield Hubbell's neutral theory in the limit of functional equivalence among all species. Our focus centers on an asymmetric extension of Hubbell's local community…
In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed…
By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameter n and k. The…
We introduce a theory of probability in $\lambda$-rings designed to efficiently describe random variables valued in multisets of complex numbers, varieties over a field, or other similar enriched settings. A key role is played by the…
The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the…
Semicontinuous outcomes occur frequently in health services, insurance, and cost studies. Standard nonparametric density estimators are not well suited to such data because they do not naturally accommodate the mixed structure, the…
In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape…
We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…
Let $a(1) >0$, $a(n) \ge 0$ for $n \ge 2$ and $a(n) = O(n^\varepsilon)$ for any $\varepsilon >0$, and put $Z(\sigma + it):= \sum_{n=1}^\infty a(n) n^{-\sigma - it}$ where $\sigma , t \in {\mathbb{R}}$. In the present paper, we show that any…
We introduce a new family of multivariate distributions by taking the component-wise Tukey-h transformation of a random vector following a skew-normal distribution. The proposed distribution is named the skew-normal-Tukey-h distribution and…
In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
In this paper, we consider a coherent theory about the asymptotic representations for a family of inequality indices called Theil-Like Inequality Measures (TLIM), within a Gaussian field. The theory uses the functional empirical process…
The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear…
We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…
The proportional odds model gives a method of generating new family of distributions by adding a parameter, called tilt parameter, to expand an existing family of distributions. The new family of distributions so obtained is known as…
We establish a good lambda inequality relating to the distribution function of Riesz potential and fractional maximal function on $\left(\mathbb{R}^n, d\mu\right)$ where $\mu$ is a positive Radon measure which doesn't necessarily satisfy a…