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

Wu Mei; Zhang Chunsheng; Li Tipei; Cheng Lingxiang

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

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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.

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[19]	Lu Jing-xian . 2π→2K SCATTERING AND πK ELASTIC SCATTERING. Chinese Physics C, 1980, 4(1): 28-32.
[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.

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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

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

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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.