English
Related papers

Related papers: Testing normality via a distributional fixed point…

200 papers

The normal distribution has the unique property that the cumulant generating function has only two terms, namely those involving the mean and the variance. This property is used to construct a simple by using the log of the modulus of the…

Methodology · Statistics 2016-05-02 J. Martin van Zyl

Exact null distributions of goodness-of-fit test statistics are generally challenging to obtain in tractable forms. Practitioners are therefore usually obliged to rely on asymptotic null distributions or Monte Carlo methods, either in the…

Methodology · Statistics 2023-09-06 Alberto Fernández-de-Marcos , Eduardo García-Portugués

We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed tests are weighted $L^2$-type tests depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a…

Methodology · Statistics 2022-01-31 J. S. Allison , S. Betsch , B. Ebner , I. J. H. Visagie

The objective of goodness-of-fit testing is to assess whether a dataset of observations is likely to have been drawn from a candidate probability distribution. This paper presents a rank-based family of goodness-of-fit tests that is…

Statistics Theory · Mathematics 2019-04-18 Feras A. Saad , Cameron E. Freer , Nathanael L. Ackerman , Vikash K. Mansinghka

In this paper we extend Stein's method to the distribution of the product of $n$ independent mean zero normal random variables. A Stein equation is obtained for this class of distributions, which reduces to the classical normal Stein…

Probability · Mathematics 2017-05-30 Robert E. Gaunt

The bivariate Poisson distribution is commonly used to model bivariate count data. In this paper we study a goodness-of-fit test for this distribution. We also provide a review of the existing tests for the bivariate Poisson distribution,…

Statistics Theory · Mathematics 2019-02-26 Francisco Novoa-Muñoz

The discrete Pareto (or Zeta, Zipf) distribution, arises naturally in modeling rank-frequency data across diverse fields such as linguistics, demography, biology, and computer science. Despite its widespread applicability, goodness-of-fit…

Methodology · Statistics 2026-05-08 Deepesh Bhati , Bruno Ebner , Sakshi Khandelwal

The Pareto distribution plays a crucial role in various disciplines, necessitating robust goodness-of-fit tests for its validation. This article introduces a novel tests based on Stein's characterization and the Laplace transform, offering…

Statistics Theory · Mathematics 2026-04-27 Deepesh Bhati , Sakshi Khandelwal

We propose tests of fit for classes of distributions that include the Weibull, the Pareto and the Fr\'echet, distributions. The new tests employ the novel tool of the min--characteristic function and are based on an L2--type weighted…

Methodology · Statistics 2023-10-20 S. G. Meintanis , B. Milošević , M. D. Jiménez-Gamero

We use a system of first-order partial differential equations that characterize the moment generating function of the $d$-variate standard normal distribution to construct a class of affine invariant tests for normality in any dimension. We…

Statistics Theory · Mathematics 2019-01-15 Norbert Henze , Jaco Visagie

The paper considers the classical Goodness of Fit test. It suggests to use the Gamma distribution for the approximation of the distribution of the Pearson statistics with unknown parameters estimated from raw data. The parameters of these…

Statistics Theory · Mathematics 2019-05-21 Nikolai Dokuchaev

This paper develops a smooth test of goodness-of-fit for elliptical distributions. The test is adaptively omnibus, invariant to affine-linear transformations and has a convenient expression that can be broken into components. These…

Statistics Theory · Mathematics 2019-02-12 Gilles R. Ducharme , Pierre Lafaye de Micheaux

We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some…

Machine Learning · Statistics 2020-07-01 Wittawat Jitkrittum , Heishiro Kanagawa , Bernhard Schölkopf

We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the…

Machine Learning · Statistics 2017-10-25 Wittawat Jitkrittum , Wenkai Xu , Zoltan Szabo , Kenji Fukumizu , Arthur Gretton

We propose a new omnibus goodness-of-fit test based on trigonometric moments of probability-integral-transformed data. The test builds on the framework of the LK test introduced by Langholz and Kronmal [J. Amer. Statist. Assoc. 86 (1991),…

Methodology · Statistics 2026-03-31 Alain Desgagné , Frédéric Ouimet

Testing to see whether a given data set comes from some specified distribution is among the oldest types of problems in Statistics. Many such tests have been developed and their performance studied. The general result has been that while a…

Applications · Statistics 2020-12-07 Wolfgang Rolke

Using fixed point characterization, we develop a new goodness of fit test for uniform distribution. We also discuss how the right censored observations can be incorporated in the proposed test procedure. We study the asymptotic properties…

Methodology · Statistics 2021-06-14 Sudheesh K. Kattumannil , Sreedevi E. P

This paper proposes new specification tests for conditional models with discrete responses, which are key to apply efficient maximum likelihood methods, to obtain consistent estimates of partial effects and to get appropriate predictions of…

Statistics Theory · Mathematics 2018-02-01 Igor Kheifets , Carlos Velasco

Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…

Machine Learning · Statistics 2025-04-22 Oscar Key , Arthur Gretton , François-Xavier Briol , Tamara Fernandez

Suppose we have an observed path from a point process counting event occurrences in a large population. Based on the observed path, we would like to test the null hypothesis that the conditional intensity of the point process belongs to a…

Statistics Theory · Mathematics 2026-05-18 Sami Umut Can , Estate V. Khmaladze , Roger J. A. Laeven