Related papers: Parameter Estimation in Astronomy with Poisson-Dis…
We consider distributional limit of the Pearson chi-square statistic when the number of classes m increases with the sample size n in such way that $n/\sqrt{m} \to {\lambda}$. Under mild moment conditions, the limit is Gaussian for…
The Friedman test has been extensively applied as a nonparametric alternative to the conventional F procedure for comparing treatment effects in randomized complete block designs. A chi-square distribution provides a convenient…
We obtain an asymptotic expansion for the null distribution function of thegradient statistic for testing composite null hypotheses in the presence of nuisance parameters. The expansion is derived using a Bayesian route based on the…
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…
Since its introduction in 1950, Fisher's dispersion test has become a standard means of deciding whether or not count data follow the Poisson distribution. The test is based on a characteristic property of the Poisson distribution, and…
In this paper new families of test statistics are introduced and studied for the problem of comparing two treatments in terms of the likelihood ratio order. The considered families are based on phi-divergence measures and arise as natural…
Given N data points drawn from a chi-square distribution, we use Bayesian inference to determine most likely values and N-dependent confidence intervals for the width sigma and the number k of degrees of freedom of that distribution. Using…
An efficient Bayesian technique for estimation problems in fundamental stellar astronomy is tested on simulated data for a binary observed both astrometrically and spectroscopically. Posterior distributions are computed for the components'…
The assumption that a parametric class of functions fits the data structure sufficiently well is common in fitting curves and surfaces to regression data. One then derives a parameter estimate resulting from a least squares fit, say, and in…
The Poisson-Gamma model is a generalization of the Poisson model, which can be used for modelling count data. We show that the $D$-optimality criterion for the Poisson-Gamma model is equivalent to a combined weighted optimality criterion of…
Evolve and resequence studies provide a popular approach to simulate evolution in the lab and explore its genetic basis. In this context, the chi-square test, Fishers exact test, as well as the Cochran-Mantel-Haenszel test are commonly used…
The density matrix in quantum mechanics parameterizes the statistical properties of the system under observation, just like a classical probability distribution does for classical systems. The expectation value of observables cannot be…
Meta-analysis seeks to combine the results of several experiments in order to improve the accuracy of decisions. It is common to use a test for homogeneity to determine if the results of the several experiments are sufficiently similar to…
Probabilistic generative models of graphs are important tools that enable representation and sampling. Many recent works have created probabilistic models of graphs that are capable of representing not only entity interactions but also…
It has been shown that for the analysis of X-ray spectra the C-statistic, contrary to the chi^2-statistic, provides unbiased estimates of the model parameters and their uncertainty ranges. However, it is often stated that the C-statistic…
The analysis of Fermi Large Area Telescope (LAT) gamma-ray data in a given Region Of Interest (RoI) usually consists of performing a binned log-likelihood fit in order to determine the sky model that, after convolution with the instrument…
We consider goodness-of-fit tests with i.i.d. samples generated from a categorical distribution $(p_1,...,p_k)$. For a given $(q_1,...,q_k)$, we test the null hypothesis whether $p_j=q_{\pi(j)}$ for some label permutation $\pi$. The…
We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic $\chi^2$-goodness-of-fit test.…
We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…
We establish a general inequality on the Poisson space, yielding an upper bound for the distance in total variation between the law of a regular random variable with values in the integers and a Poisson distribution. Several applications…