Related papers: On a test of normality based on the empirical mome…
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…
We generalize a recent class of tests for univariate normality that are based on the empirical moment generating function to the multivariate setting, thus obtaining a class of affine invariant, consistent and easy-to-use goodness-of-fit…
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…
An empirical power comparison is made between two tests based on the empirical characteristic function and some of the best performing tests for normality. A simple normality test based on the empirical characteristic function calculated in…
Motivated by applications to goodness of fit testing, the empirical likelihood approach is generalized to allow for the number of constraints to grow with the sample size and for the constraints to use estimated criteria functions. The…
We develop a test of normality for spatially indexed functions. The assumption of normality is common in spatial statistics, yet no significance tests, or other means of assessment, have been available for functional data. This paper aims…
Consider a random vector $(X,Y)$ and let $m(x)=E(Y|X=x)$. We are interested in testing $H_0:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}$ for some known function $\gamma$, some compact set…
In this article we prove a generalization of the Ejsmont characterization of the multivariate normal distribution. Based on it, we propose a new test for independence and normality. The test uses an integral of the squared modulus of the…
Claims that the standard methodology of scientific testing is inapplicable to Everettian quantum theory, and hence that the theory is untestable, are due to misconceptions about probability and about the logic of experimental testing.…
We provide novel characterizations of multivariate normality that incorporate both the characteristic function and the moment generating function, and we employ these results to construct a class of affine invariant, consistent and…
We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical…
In this article, we propose a new class of consistent tests for $p$-variate normality. These tests are based on the characterization of the standard multivariate normal distribution, that the Hessian of the corresponding cumulant generating…
This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…
This paper re-examines the first normalized incomplete moment, a well-established measure of inequality with wide applications in economic and social sciences. Despite the popularity of the measure itself, existing statistical inference…
We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero…
The present manuscript is about application of It{\^o}'s calculus to the moment-generating function of the lognormal distribution. While Taylor expansion fails when applied to the moments of the lognormal due to divergence, various methods…
In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel's…
In this paper, we develop a simple non-parametric test for testing normal distribution based on the distance between empirical zero-bias transformation and empirical distribution. The asymptotic properties of the test statistic are studied.…
A goodness-of-fit test for one-parameter count distributions with finite second moment is proposed. The test statistic is derived from the $L^1$ distance of a function of the probability generating function of the model under the null…
We extend the fundamental normality test due to Carath\'eodory in the sense of shared functions.