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Gradients have been exploited in proposal distributions to accelerate the convergence of Markov chain Monte Carlo algorithms on discrete distributions. However, these methods require a natural differentiable extension of the target discrete…
In this paper, we explore the modified Greenwood statistic, which, in contrast to the classical Greenwood statistic, is properly defined for random samples from any distribution. The classical Greenwood statistic, extensively examined in…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
In this paper, we proposed a new lifetime distribution namely generalized weighted Lindley (GLW) distribution. The GLW distribution is a useful generalization of the weighted Lindley distribution, which accommodates increasing, decreasing,…
The upsilon distribution, the sum of independent chi random variates and a normal, is introduced. As a special case, the upsilon distribution includes Lecoutre's lambda-prime distribution. The upsilon distribution finds application in…
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…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…
Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since…
This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects,…
We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
We propose new goodness-of-fit tests for the Poisson distribution. The testing procedure entails fitting a weighted Poisson distribution, which has the Poisson as a special case, to observed data. Based on sample data, we calculate an…
In a recent development in the literature, a new temporal rainfall model, based on the Bartlett-Lewis clustering mechanism and intended for sub-hourly application, was introduced. That model replaced the rectangular rain cells of the…
Compound Poisson distributions and signed compound Poisson measures are used for approximation of the Markov binomial distribution. The upper and lower bound estimates are obtained for the total variation, local and Wasserstein norms. In a…
Methods have been developed to identify the probability distribution of a random vector $Z$ from information consisting of its bounded range and the probability density function or moments of a quantity of interest, $Q(Z)$. The mapping from…
The collective risk model differentiates usually between claims frequencies (and their distribution) and claim sizes (and their distribution). For the claims frequencies typically classical discrete distributions are considered, such as…
We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration…