基于置信带理论的正态检验统计量的评价与比较
发布时间：2018-11-02 09:09
【摘要】：本文基于置信带的构建理论及方法,关注当随机变量的分布函数受区间限制时,正态性检验的效果如何变化。在给定的限制区间下,通过对不同类型的十二个非正态分布进行模拟势函数的计算,从而对正态检验进行全面比较。本文讨论了七个正态性检验统计量,其中包括五个图像检验统计量:D、Dm、De、D_(bi)、D_(be)和两个非图像检验统计量:AD检验、SW检验,根据上述检验统计量的特点分别设计了对称受限区间和非对称受限区间,并在三个置信水平下对于这七种正态检验进行效果比较。最后得出:区间的限制对于正态性检验有影响,随着随机变量的区间变小,正态性检验效果变差;对于七个正态检验,与其余四个图像检验相比,D检验在大多数情况下效果最差,而对于随机变量在非对称区间的分布,D_(bi)的检验效果最好,但是对于随机变量在(-∞,+∞)上的对称分布,De检验效果更好;随着置信水平α的增大,正态检验效果变好。
[Abstract]:Based on the theory and method of constructing confidence band, this paper focuses on how the effect of normality test changes when the distribution function of random variables is restricted by interval. Under a given restricted interval, the normal test is compared comprehensively by calculating the simulated potential function of twelve different types of non-normal distributions. In this paper, seven normality test statistics are discussed, which include five image test statistics: DX DMD _ (bi), D _ (be) and two non-image test statistics: AD test, SW test. According to the characteristics of the above test statistics, the symmetric restricted interval and the asymmetric restricted interval are designed, and the results of the seven normal tests are compared at three confidence levels. Finally, it is concluded that: the limitation of interval has an effect on the test of normality, and with the interval of random variables becoming smaller, the effect of normality test becomes worse; For the seven normal tests, compared with the other four image tests, the D test is the worst in most cases, while the D _ (bi) test is the best for the distribution of random variables in the asymmetric interval. But for the symmetric distribution of random variables on (- 鈭，
本文编号：2305587
[Abstract]:Based on the theory and method of constructing confidence band, this paper focuses on how the effect of normality test changes when the distribution function of random variables is restricted by interval. Under a given restricted interval, the normal test is compared comprehensively by calculating the simulated potential function of twelve different types of non-normal distributions. In this paper, seven normality test statistics are discussed, which include five image test statistics: DX DMD _ (bi), D _ (be) and two non-image test statistics: AD test, SW test. According to the characteristics of the above test statistics, the symmetric restricted interval and the asymmetric restricted interval are designed, and the results of the seven normal tests are compared at three confidence levels. Finally, it is concluded that: the limitation of interval has an effect on the test of normality, and with the interval of random variables becoming smaller, the effect of normality test becomes worse; For the seven normal tests, compared with the other four image tests, the D test is the worst in most cases, while the D _ (bi) test is the best for the distribution of random variables in the asymmetric interval. But for the symmetric distribution of random variables on (- 鈭，
本文编号：2305587
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