Related papers: Sequential two-fold Pearson chi-squared test and t…
Fitting mixture distributions is needed in applications where data belongs to inhomogeneous populations comprising homogeneous sub-populations. The mixing proportions of the sub populations are in general unknown and need to be estimated as…
We show how one can obtain an asymptotic expression for some special functions satisfying a second order differential equation with a very explicit error term starting from appropriate upper bounds. We will work out the details for the…
We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
Two-sample tests are important areas aiming to determine whether two collections of observations follow the same distribution or not. We propose two-sample tests based on integral probability metric (IPM) for high-dimensional samples…
The Bessel process models the local eigenvalue statistics near $0$ of certain large positive definite matrices. In this work, we consider the probability \begin{align*} \mathbb{P}\Big( \mbox{there are no points in the Bessel process on }…
We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial distribution with unknown parameter p, when we reinforce data with an independent sample of a negative-binomial experiment having the same p.
Despite a substantial literature on nonparametric two-sample goodness-of-fit testing in arbitrary dimensions spanning decades, there is no mention there of any curse of dimensionality. Only more recently Ramdas et al. (2015) have discussed…
The concept of splitting tessellations and splitting tessellation processes in spherical spaces of dimension $d\geq 2$ is introduced. Expectations, variances and covariances of spherical curvature measures induced by a splitting…
I investigate the use of Pearson's chi-square statistic, the Maximum Likelihood Ratio statistic for Poisson distributions, and the chi-square-gamma statistic (Mighell 1999, ApJ, 518, 380) for the determination of the goodness-of-fit between…
Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws. Given a sequence of $n$ observations, we are interested…
The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the…
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…
The main purpose of this paper is to investigate the strong approximation of the $p$-fold integrated empirical process, $p$ being a fixed positive integer. More precisely, we obtain the exact rate of the approximations by a sequence of…
The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…
In this paper, we address the problem of testing goodness-of-fit for discrete distributions, where we focus on the geometric distribution. We define new likelihood-based goodness-of-fit tests using the beta-geometric distribution and the…
Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…
We use a Stein identity to define a new class of parametric distributions which we call ``independent additive weighted bias distributions.'' We investigate related $L^2$-type discrepancy measures, empirical versions of which not only…
We calculate the chiral and thermal susceptibilities for two confining Dyson-Schwinger equation models of QCD with two light flavours, a quantitative analysis of which yields the critical exponents, beta and delta, that characterise the…