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This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
Compound distributions allow construction of a rich set of distributions. Typically they involve an intractable integral. Here we use a quadrature approximation to that integral to define the quadrature compound family. Special care is…
A new class of distributions, called as normal power series (NPS), which contains the normal one as a particular case, is introduced in this paper. This new class which is obtained by compounding the normal and power series distributions,…
A nonparametric family of conditional distributions is introduced, which generalizes conditional exponential families using functional parameters in a suitable RKHS. An algorithm is provided for learning the generalized natural parameter,…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of…
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…
The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…
In this paper we present an alternative representation of the Negative Binomial--Lindley distribution recently proposed by Zamani and Ismail (2010) which shows some advantages over the latter model. This new formulation provides a tractable…
Recent theoretical developments revived the interest in charged particle multiplicities and their wide-spread parametrization, the negative binomial distribution (NBD). The central observable of the studies is the Shannon entropy of the…
The sum of independent, but not necessary identically distributed, exponential random variables follows hypoexponential distribution. We focus on a particular case when all, but one rate parameters of the exponential variables are…
This paper proposes a novel method to estimate the rate parameter of the Poisson distribution. The proposed method employs the Cramer-von Mises type optimization which has been commonly used in estimating parameters of continuous…
One-parameter natural exponential family (NEF) plays fundamental roles in probability and statistics. This article contains two independent results: (a) A conjecture of Bar-Lev, Bshouty and Enis states that a polynomial with a simple root…
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…
We develop a Nonparametric Empirical Bayes (NEB) framework for compound estimation in the discrete linear exponential family, which includes a wide class of discrete distributions frequently arising from modern big data applications. We…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
Recently, Lee and Cha (2015, `On two generalized classes of discrete bivariate distributions', {\it American Statistician}, 221 - 230) proposed two general classes of discrete bivariate distributions. They have discussed some general…
We introduce a broadly applicable statistical procedure for testing which parametric distribution family generated a random sample of data. The method, termed the Difference in Differential Entropy (DDE) test, provides a unified framework…
In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…