Related papers: On two simple tests for normality with high power
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…
Most normality tests in the literature are performed for scalar and independent samples. Thus, they become unreliable when applied to colored processes, hampering their use in realistic scenarios.We focus on Mardia's multivariate kurtosis,…
Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
We present two new estimators for estimating the entropy of absolutely continuous random variables. Some properties of them are considered, specifically consistency of the first is proved. The introduced estimators are compared with the…
The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…
Central moments and cumulants are often employed to characterize the distribution of data. The skewness and kurtosis are particularly useful for the detection of outliers, the assessment of departures from normally distributed data,…
Over the past decades, various methods for comparing the means of two log-normal have been proposed. Some of them are differing in terms of how the statistic test adjust to accept or to reject the null hypothesis. In this study, a new…
Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…
We consider the problem of testing multivariate normality when the data consists of a random sample of two-step monotone incomplete observations. We define for such data a generalization of Mardia's statistic for measuring kurtosis, derive…
The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…
As the most important tool to provide high-level evidence-based medicine, researchers can statistically summarize and combine data from multiple studies by conducting meta-analysis. In meta-analysis, mean differences are frequently used…
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, a new goodness-of-fit test for a location-scale family based on progressively Type-II censored order statistics is proposed. Using Monte Carlo simulation studies, the present researchers have observed that the proposed test…
Consider testing normality against a one-parameter family of univariate distributions containing the normal distribution as the boundary, e.g., the family of $t$-distributions or an infinitely divisible family with finite variance. We prove…
Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…
Performances of the Multivariate Kurtosis are investigated when applied to colored data, with or without Auto-Regressive pre-whitening, and with or without projection onto a lower-dimensional random subspace. Computer experiments…
This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of weighted $L^2$-statistics. Since weighted…
A smooth test to simultaneously compare $K$ copulas, where $K \geq 2$ is proposed. The $K$ observed populations can be paired, and the test statistic is constructed based on the differences between moment sequences, called copula…