Related papers: Bivariate distributions with equi-dispersed normal…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
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…
Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…
This study is motivated by a series of recent papers that show that, if a given deterministic sequence in the unit interval has a Poisson pair correlation function, then the sequence is uniformly distributed. Analogous results have been…
Birnbaum-Saunders models have been widely used to model positively skewed data. In this paper, we introduce a bivariate Birnbaum-Saunders distribution which has the means as parameters. We present some properties of the univariate and…
In this paper, we introduce a new class of bivariate distributions called the bivariate exponentiated extended Weibull distributions. The model introduced here is of Marshall-Olkin type. This new class of bivariate distributions contains…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. Its mean and variance are known, but results for its median and mode are difficult to obtain, although a few cases have been solved and upper/lower…
Data analyses typically rely upon assumptions about missingness mechanisms that lead to observed versus missing data. When the data are missing not at random, direct assumptions about the missingness mechanism, and indirect assumptions…
In this note we discuss additional properties of mixed Poisson distributions. We discuss the convergence of mixed Poisson distributions to its mixing distribution for the scaling parameter tending to infinity. Moreover, we obtain a central…
We study sums of independent random variables that take values $0$, $1/2$, or $1$. We show that the probability mass function of the sum splits into two interleaved parts: one supported on the integers and the other supported on the…
In this present work, we discuss the Bayesian inference for the bivariate pseudo-exponential distribution. Initially, we assume independent gamma priors and then pseudo-gamma priors for the pseudo-exponential parameters. We are primarily…
The proliferation of science and technology has led to the prevalence of voluminous data sets that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the…
In this paper, we introduce a new approach to generate flexible parametric families of distributions. These models arise on competitive and complementary risks scenario, in which the lifetime associated with a particular risk is not…
This article provides some characterizations of extended COM-Poisson distribution: conditional distribution given the sum, functional operator characterization (Stein identity). We also give some conditions such that the extended…
Bayesian models that can handle both over and under dispersed counts are rare in the literature, perhaps because full probability distributions for dispersed counts are rather difficult to construct. This note takes a first look at Bayesian…
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…
The article is devoted to the study of exponential statistical structures of type B, which constitute a subclass of exponential families of probability distributions. This class is characterized by a number of analytical and probabilistic…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
It is known that if X is uniformly distributed modulo 1 and Y is an arbitrary random variable independent of X then Y+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable Y (or a reasonable…
I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first…