相关论文: High moments Jarque-Bera tests for arbitrary distr…
The skew normal law has been introduced in Azzalin (1985) as an alternative to adjusting asymmetric data that share important patterns with the normal law. It has been extensively studied. However, there is so much to do in order to catch…
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…
In this paper we introduce an efficient fat-tail measurement framework that is based on the conditional second moments. We construct a goodness-of-fit statistic that has a direct interpretation and can be used to assess the impact of…
In this paper, I present the calculation of the third and fourth moments of both the distribution function of the large--scale density and the large--scale divergence of the velocity field, $\theta$. These calculations are made by the mean…
In this paper the testing of normality for unconditionally heteroscedastic macroeconomic time series is studied. It is underlined that the classical Jarque-Bera test (JB hereafter) for normality is inadequate in our framework. On the other…
Magnetic moment measurements in odd nuclei directly probe the distribution of fermion states and hence provide one of the most critical tests for multi-$j$ supersymmetries in collective nuclei. Due to complexity of calculations and lack of…
The assumption of normality has underlain much of the development of statistics, including spatial statistics, and many tests have been proposed. In this work, we focus on the multivariate setting and first review the recent advances in…
Results of extensive computations of moments of the Riemann zeta function on the critical line are presented. Calculated values are compared with predictions motivated by random matrix theory. The results can help in deciding between those…
It is numerically well known that moment-based tests for Gaussianity and estimators become increasingly unreliable at higher moment orders; however, this phenomenon has lacked rigorous mathematical justification. In this work, we establish…
We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet integral includes weighted arithmetic means,…
We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the…
For many probability laws, in parametric models, the estimation of the parameters can be done in the frame of the maximum likelihood method, or in the frame of moment estimation methods, or by using the plug-in method, etc. Usually, for…
This article presents an important theorem, which shows that from the moments of the standard normal distribution one can generate density functions originating a family of models. Additionally, we discussed that different random variable…
We extend a general result showing that the asymptotic behavior of high moments, factorial or standard, of random variables, determines the asymptotically normality, from the one dimensional to the multidimensional setting. This approach…
We consider univariate distributions with finite moments of all positive orders. The moment problem is to determine whether or not a given distribution is uniquely determined by the sequence of its moments. There is a huge literature on…
The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…
In this paper, we are interested in the free Jacobi process starting at the unit of the compressed probability space where it takes values and associated with the parameter values $\lambda=1, \theta =1/2$. Firstly, we derive a…
We propose new affine invariant tests for multivariate normality, based on independence characterizations of the sample moments of the normal distribution. The test statistics are obtained using canonical correlations between sets of sample…
Pearson's chi-squared test is widely used to test the goodness of fit between categorical data and a given discrete distribution function. When the number of sets of the categorical data, say $k$, is a fixed integer, Pearson's chi-squared…
It is well known that the finite-sample null distribution of the Jarque-Bera Lagrange Multiplier (LM) test for normality and its adjusted version (ALM) introduced by Urzua differ considerably from their asymptotic chi^2(2) limit. Here, we…