Related papers: A proposal for a different chi-square function for…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
This paper derives the exact transition density and cumulative distribution function of a linear combination of two independent Cox-Ingersoll-Ross (CIR) processes. By combining the Poisson Gamma mixture representation of the noncentral…
In 2020, two novel distributions for the analysis of directional data were introduced: the spherical Cauchy distribution and the Poisson kernel-based distribution. This paper provides a detailed exploration of both distributions within…
In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the…
For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are…
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…
In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its…
[ABRIDGED] The Cash statistic, also known as the C stat, is commonly used for the analysis of low-count Poisson data, including data with null counts for certain values of the independent variable. The use of this statistic is especially…
We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the {\chi}^2 is well suited both for the classical applications of the {\chi}^2 for the analysis of…
Reconstruction of one-dimensional kinematic distributions from calculations based on high-dimensional Monte-Carlo integration is a standard problem in high-energy physics. Traditionally, this is done by collecting randomly-generated events…
We propose a new method, called MonteCarlo Posterior Fit, to boost the MonteCarlo sampling of likelihood (posterior) functions. The idea is to approximate the posterior function by an analytical multidimensional non-Gaussian fit. The many…
In this paper we apply the newly born choice theory of the shape parameters contained in the smooth radial basis functions to solve Poisson equations. Some people complain that Luh's choice theory, based on harmonic analysis, is…
In this paper we propose a new approach to least squares approximation problems. This approach is based on partitioning and Schur function. The nature of this approach is combinatorial, while most existing approaches are based on algebra…
We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…
Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any…
Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the…
Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…
Motivated by contemporary and rich applications of anomalous diffusion processes we propose a new statistical test for fractional Brownian motion, which is one of the most popular models for anomalous diffusion systems. The test is based on…
In this paper, we develop simple, yet efficient, procedures for sampling approximations of the two-Parameter Poisson-Dirichlet Process and the normalized inverse-Gaussian process. We compare the efficiency of the new approximations to the…
In this paper, we have developed a new class of sampling schemes for estimating parameters of binomial and Poisson distributions. Without any information of the unknown parameters, our sampling schemes rigorously guarantee prescribed levels…