# Probability Distribution of the Pearsou X2 of Small Samples

• 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.
•  [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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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.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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## Probability Distribution of the Pearsou X2 of Small Samples

###### Corresponding author: Wu Mei,
• Institute of High Energy Physics,Acadamia Sinica Beijing 100039

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.

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