The article is devoted to normality assumption in statistical data analysis. It gives a short historical review of the development of scientific views on the normal law and its applications. It also briefly covers normality tests and analyzes possible consequences of using the normality assumption incorrectly.

We introduce a new class of functions called almost gs-closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost gs-closed continuous surjections.

In this paper, the Maximum Lq-Likelihood Estimator (MLqE), a new parameter estimator based on nonextensive entropy [16], is introduced. The properties of the MLqE are studied via asymptotic analysis and computer simulations. The behavior of the MLqE is characterized by the degree of distortion q applied to the assumed model. When q is properly chosen for small and moderate sample sizes, the MLq...

The uptake of tritiated thymidine by lymphocytes from 100 cancer patients and 31 normal subjects was tested in the presence and absence of phytohaemagglutinin (PHA) in a medium containing autologous or homologous serum. Significant differences were found between normal subjects and cancer patients in both the time course and degree of uptake. Serum from normal individuals restored the response ...

We explore the finite sample performance of adaptive estimators in linear time series regression models. Our results show that for samples of only 50 observations, the 90 percent confidence interval of the adaptive estimator is 20 to 50 percent smaller than the corresponding interval for its GLS counterpart across a range of symmetrical distributions. When the assumption of symmetry is relaxed ...

An ample study of the comparative powers of a number of omnibus multivariate normality tests is main object in this paper. Since testing for multivariate normality tests is considerably more challenging process than for testing of univariate one and therefore, study of testing for multivariate normality tests has its increasing demand. Through this paper, we have explored several techniques for...