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This paper discusses new approaches to parameter estimation of gamma distribution based on representative points. In the first part, the existence and uniqueness of gamma mean squared error representative points (MSE-RPs) are discussed theoretically. In the second part, by comparing three types of representative points, we show that gamma MSE-RPs perform well in parameter estimation and simulation. The last part proposes a new Harrel–Davis sample standardization technique. Simulation studies reveal that the standardized samples can be used to improve estimation performance or generate MSE-RPs. In addition, a real data analysis illustrates that the proposed technique yields efficient estimates for gamma parameters. [ABSTRACT FROM AUTHOR]

The multivariate normal is a common assumption in many statistical models and methodologies for high-dimensional data analysis. The exploration of approaches to testing multivariate normality never stops. Due to the characteristics of the multivariate normal distribution, most approaches to testing multivariate normality show more or less advantages in their power performance. These approaches can be classified into two types: multivariate and univariate. Using the multivariate normal characteristic by the Mahalanobis distance, we propose an approach to testing multivariate normality based on representative points of the simple univariate F-distribution and the traditional chi-square statistic. This approach provides a new way of improving the traditional chi-square test for goodness-of-fit. A limited Monte Carlo study shows a considerable power improvement of the representative-point-based chi-square test over the traditional one. An illustration of testing goodness-of-fit for three well-known datasets gives consistent results with those from classical methods. [ABSTRACT FROM AUTHOR]

AbstractHypothesis testing for the Weibull distribution always raises attention in the literature. It is challenging especially in small-sample scenarios. In this paper, we propose a new Kolmogorov-Smirnov type test based on the distance between two empirical functions, one from the data and another from the representative points of the underlying distribution. A bias correction technique is used to estimate unknown parameters in the Weibull distribution. We also discuss how to choose a suitable number of representative points based on the proposed loss function, which is recommended for constructing the empirical function from the Weibull distribution. To compare with tailor-made tests in the literature, a simulation study of the empirical type I error and testing power is conducted. It shows that our proposed test statistic is more powerful in most alternative scenarios, and it significantly improves the power of testing in small-sample scenarios. Finally, two real-world datasets are conducted to further demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]