Probability Distribution of the Pearsou X<SUP>2</SUP> of Small Samples

Wu Mei; Zhang Chunsheng; Li Tipei; Cheng Lingxiang

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1994, Vol. 18> Issue(10) : 879-883

Probability Distribution of the Pearsou X² of Small Samples

Institute of High Energy Physics,Acadamia Sinica Beijing 100039

Abstract
HTML
Reference
Related

PDF

Abstract：
The probability distribution of the Pearson X² of small samples was investigated in detail,by use of the period analysis of high energy astrophysical observations as an example.It is pointed out that the commonly used formula of X² distribution leads to underestimating fluctuation probabilities of large Pearson X² events if one uses that formula as the probability distribution of the Pearson X².A new formula is presented for more precise calculation if the Pearson X² probability distribution and compared with extensive Monte Carlo simulation results.
References

[1] M.Samorski and W.Stamm,Astrophys J.,268（1983）L17.[2]李惕碚，《实验的数学处理》，科学出版社，1980.

[1]	ZHANG Jian-Bo , TANG Ling-Yun , ZHANG Jiang , QIN Zhen-Xing , ZENG Xiao-Jing , LIU Jing , WEN Jin-Sheng , XU Zhi-Jun , GU Genda , CHEN Xiao-Jia . Pressure-induced isostructural phase transition in Bi₂Sr₂CaCu₂O_8+δ. Chinese Physics C, 2013, 37(8): 088003. doi: 10.1088/1674-1137/37/8/088003
[2]	for the . Status of KLOE-2. Chinese Physics C, 2010, 34(6): 918-923. doi: 10.1088/1674-1137/34/6/051
[3]	PING Rong-Gang , MO Xiao-Hu , DU Shu-Xian , LIU Jing , MA Lian-Liang , SHEN Cheng-Ping , WANG Zhi-Yong , YUAN Chang-Zheng . Extract Signals by Fitting χ² Distribution of the Kinematic Fit. Chinese Physics C, 2007, 31(3): 229-231.
[4]	WANG Zhong-Qing , DUAN Chang-Kui . Phase Probability Distributions of Pair q-Coherent States. Chinese Physics C, 2006, 30(3): 273-276.
[5]	WANG Gui-Mei , WU Wen-Zong , Xiangyang LU , ZHANG Bao-Cheng , QUAN Sheng-Wen , ZHU Feng , LIN LIN , JIAO Fei , ZHAO Kui . Study on HOMs in 1+1/2 Cell Superconducting Cavity. Chinese Physics C, 2005, 29(11): 1077-1080.
[6]	ZHANG Yong-Jun , ZOU Bing-Song . Is f₀ Distinguishable from f₂ by One-dimensional Projections of Angular Distributions in J/ψ→f_{J_→ππKK?}. Chinese Physics C, 2004, 28(5): 479-486.
[7]	CHI Shao-Peng , MO Xiao-Hu , ZHU Yong-Sheng . Measurement of the Integrated Luminosity at s(1/2)=3.650,3.686 GeV for the BES Detector. Chinese Physics C, 2004, 28(11): 1135-1140.
[8]	Li Xinhua , Gu Yifan . Comments on the Ratio of Hadronic Decay Rates of ψ(2S)to J/ψ. Chinese Physics C, 1998, 22(4): 293-298.
[9]	Yao Xiaoxia , He Zhenmin , Duan Chungui , Li Guanglie , Peng Hongan . Improved Q²-Rescaling Model and the Nuclear Effect of Parton Distribution Functions. Chinese Physics C, 1997, 21(6): 548-553.
[10]	Pan Zhongcheng , Jiang Shaozhou , Gao Liangjun . Probability Distribution and Entropy of Nonequilibrium State for ²⁰⁸Pb Nuclei Under Different Excited Energies. Chinese Physics C, 1995, 19(8): 757-763.
[11]	Yu Zhaoxian , Liu Yehou , Li Qinglin , Liang Bifang . Study of SU(2)_q,s Coherent State by Using (q,s) Deformed Harmonic Oscillators of SU(2)_q,s Quantum Algebra. Chinese Physics C, 1995, 19(3): 258-263.
[12]	PAN Zhong-Cheng , JIANG Shao-Zhou , GAO Liang-Jun , LONG Sheng-Dong . Instantaneous Probability Distribution and Nonequilibrium Entropy of Nuclear Exciton States. Chinese Physics C, 1993, 17(5): 444-447.
[13]	YU Qing-Chang . THE FLUID THEORY OF SELF-SUSTAINING MAGNETICALLY CONFINED ELECTRON CLOUDSⅡ.DISTRIBUTIONS OF PHYSICAL QUANTITY OF ELECTRON CLOUDS AND NUMERICAL COMPUTATIONAL METHOD. Chinese Physics C, 1990, 14(12): 1067-1072.
[14]	Chen Tianlun , Huang Wuqun , Jin Ke , Suo Cunchuan . β Function tor SU(2)×SU(2) Chiral Model on 2-Dimensional Random Triangle Lattice. Chinese Physics C, 1989, 13(S1): 43-48.
[15]	YAN Wu-Guang , YU Hong . THE ANGULAR DISTRIBUTION FOR THE PROCESS e⁺e^－→J/ψ→γB,B→P₁P₂ AND THE SPIN ANALYSIS OF B. Chinese Physics C, 1989, 13(3): 234-240.
[16]	WU Ji-Min , ZHAO Pei-Ying . ANALYTIC CALCULATION FOR GLUON CONDENSATION IN SU (2) LATTICE GAUGE THEORY. Chinese Physics C, 1987, 11(1): 64-67.
[17]	MA ZHONG-QI , DONG FANG-XIAO , YUE ZONG-WU , ZHOU XIAN-JIAN , XUE PEI-YOU . DISCUSSION OF A SU(2)×U(1)×S₃ MODEL WITH TWO HIGGS DOUBLETS AND CALCULATION OF CABIBBO-LIKE-PARAMETERS. Chinese Physics C, 1981, 5(3): 298-306.
[18]	Lu Jing-xian . 2π→2K SCATTERING AND πK ELASTIC SCATTERING. Chinese Physics C, 1980, 4(1): 28-32.
[19]	Dong Fang-xiao , Zhou Xian-jian , Huang Tao , Xue Pei-you . THE TIME-DEPENDENCES OF THE STATIC SOLUTION OF SU(2) AND SU(3) GAUGE THEORY AT THE PRESENCE OF STATIC EXTENDED SOURCE. Chinese Physics C, 1980, 4(6): 724-734.
[20]	GAO CHUNG-SHOU . ON THE NEW PHENOMENA OF THE INVARIANT MASS DISTRIBUTION IN THE DOUBLE INCLUSIVE REACTION AND THE STRATON MODEL. Chinese Physics C, 1977, 1(1): 92-95.

Access

Get Citation

Wu Mei, Zhang Chunsheng, Li Tipei and Cheng Lingxiang. Probability Distribution of the Pearsou X² of Small Samples[J]. Chinese Physics C, 1994, 18(10): 879-883.

Wu Mei, Zhang Chunsheng, Li Tipei and Cheng Lingxiang. Probability Distribution of the Pearsou X² of Small Samples[J]. Chinese Physics C, 1994, 18(10): 879-883. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(2728)
PDF Downloads(509)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Probability Distribution of the Pearsou X² of Small Samples

Corresponding author: Wu Mei,

Institute of High Energy Physics,Acadamia Sinica Beijing 100039

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1994-10-05

Abstract: The probability distribution of the Pearson X² of small samples was investigated in detail,by use of the period analysis of high energy astrophysical observations as an example.It is pointed out that the commonly used formula of X² distribution leads to underestimating fluctuation probabilities of large Pearson X² events if one uses that formula as the probability distribution of the Pearson X².A new formula is presented for more precise calculation if the Pearson X² probability distribution and compared with extensive Monte Carlo simulation results.