【摘要】：本文基于置信帶的構(gòu)建理論及方法,關(guān)注當(dāng)隨機(jī)變量的分布函數(shù)受區(qū)間限制時(shí),正態(tài)性檢驗(yàn)的效果如何變化。在給定的限制區(qū)間下,通過(guò)對(duì)不同類型的十二個(gè)非正態(tài)分布進(jìn)行模擬勢(shì)函數(shù)的計(jì)算,從而對(duì)正態(tài)檢驗(yàn)進(jìn)行全面比較。本文討論了七個(gè)正態(tài)性檢驗(yàn)統(tǒng)計(jì)量,其中包括五個(gè)圖像檢驗(yàn)統(tǒng)計(jì)量:D、Dm、De、D_(bi)、D_(be)和兩個(gè)非圖像檢驗(yàn)統(tǒng)計(jì)量:AD檢驗(yàn)、SW檢驗(yàn),根據(jù)上述檢驗(yàn)統(tǒng)計(jì)量的特點(diǎn)分別設(shè)計(jì)了對(duì)稱受限區(qū)間和非對(duì)稱受限區(qū)間,并在三個(gè)置信水平下對(duì)于這七種正態(tài)檢驗(yàn)進(jìn)行效果比較。最后得出:區(qū)間的限制對(duì)于正態(tài)性檢驗(yàn)有影響,隨著隨機(jī)變量的區(qū)間變小,正態(tài)性檢驗(yàn)效果變差;對(duì)于七個(gè)正態(tài)檢驗(yàn),與其余四個(gè)圖像檢驗(yàn)相比,D檢驗(yàn)在大多數(shù)情況下效果最差,而對(duì)于隨機(jī)變量在非對(duì)稱區(qū)間的分布,D_(bi)的檢驗(yàn)效果最好,但是對(duì)于隨機(jī)變量在(-∞,+∞)上的對(duì)稱分布,De檢驗(yàn)效果更好;隨著置信水平α的增大,正態(tài)檢驗(yàn)效果變好。
[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，

本文編號(hào)：2305587