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首页> 外文会议>Proceedings of the 6th Asian-Pacific symposium on structural reliability and its applications >Sample Size Effect on the Probability Distribution Fitting Accuracy of Random Variable by Using Normal Diffusion Estimation Method-Compared with Normal Distribution
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Sample Size Effect on the Probability Distribution Fitting Accuracy of Random Variable by Using Normal Diffusion Estimation Method-Compared with Normal Distribution

机译：正态扩散估计方法与正态分布相比，样本量对随机变量概率分布拟合精度的影响

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摘要

In the case of general normal distribution, eight groups' simulated samples with size 15, 20, 30, 50,100, 200, 500 and 1000 were produced by the Monte-Carlo method.To analyze the sample size effect on the probability distribution fitting accuracy of random variable, the Normal Diffusion Estimation Method (NDE method) and Typical Distribution Fitting method (TDF method) were used to infer the corresponding probability distribution functions of eight groups' samples above and the Kolmogorov-Smirnov method was applied to test the result.It shows that the fitting distributions obtained by two methods can all pass the critical test and the test value will decrease with the increasing of the sample size.However, for any group of samples,the test value of NDE distribution is always smaller than that of TDF distribution, furthermore, the probability cumulative value of NDE distribution in the integral interval is always equal to 1 while that of the TDF distribution is less than 1.The curves of PDF (probability density fuction) and CDF (cumulative probability fuction) obtained with two methods are also compared with the histogram and cumulative probability curve of samples respectively, and the results also show that the NDE distribution is more approximate to that of the actual sample.From the above comparison, it is can be concluded that the NDE method is more suitable to deduce the probability distribution of random variable and its fitting accuracy is higher than that of TDF method, which can reflect the actual distribution of random variables more better.
机译：在一般正态分布的情况下，通过蒙特卡洛方法制作了15组，15组，20组，30组，50,100组，200组，500组和1000组的模拟样本，以分析样本大小对概率分布拟合精度的影响。使用随机变量，正态扩散估计法（NDE方法）和典型分布拟合法（TDF方法）推断上述八组样本的相应概率分布函数，并使用Kolmogorov-Smirnov方法检验结果。结果表明，两种方法得到的拟合分布都可以通过关键测试，并且随着样本数量的增加，测试值将减小。但是，对于任何一组样本，NDE分布的测试值始终小于TDF的测试值此外，积分区间中NDE分布的概率累积值始终等于1而TDF分布的概率累积值始终小于1。还将两种方法获得的PDF（概率密度函数）和CDF（累积概率函数）分别与样本的直方图和累积概率曲线进行比较，结果还表明，NDE分布更接近于实际样本。从以上比较可以得出结论，NDE方法更适合于推导随机变量的概率分布，其拟合精度高于TDF方法，可以更好地反映随机变量的实际分布。

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