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→Symmetric Pareto distribution
因此，α 的最大似然估计量是:
因此，α 的最大似然估计量是:
===Symmetric Pareto distribution===
===Symmetric Pareto distribution对称帕累托分布===
\widehat \alpha = \frac{n}{\sum _i \ln (x_i/\widehat x_\mathrm{m}) }.
\widehat \alpha = \frac{n}{\sum _i \ln (x_i/\widehat x_\mathrm{m}) }.
The purpose of Symmetric Pareto distribution and Zero Symmetric Pareto distribution is to capture some special statistical distribution with a sharp probability peak and symmetric long probability tails. These two distributions are derived from Pareto distribution. Long probability tail normally means that probability decays slowly. Pareto distribution performs fitting job in many cases. But if the distribution has symmetric structure with two slow decaying tails, Pareto could not do it. Then Symmetric Pareto or Zero Symmetric Pareto distribution is applied instead.<ref name=":0">{{Cite journal|last=Huang|first=Xiao-dong|date=2004|title=A Multiscale Model for MPEG-4 Varied Bit Rate Video Traffic|journal=IEEE Transactions on Broadcasting|volume=50|issue=3|pages=323–334|doi=10.1109/TBC.2004.834013}}</ref>
The purpose of Symmetric Pareto distribution and Zero Symmetric Pareto distribution is to capture some special statistical distribution with a sharp probability peak and symmetric long probability tails. These two distributions are derived from Pareto distribution. Long probability tail normally means that probability decays slowly. Pareto distribution performs fitting job in many cases. But if the distribution has symmetric structure with two slow decaying tails, Pareto could not do it. Then Symmetric Pareto or Zero Symmetric Pareto distribution is applied instead.<ref name=":0">{{Cite journal|last=Huang|first=Xiao-dong|date=2004|title=A Multiscale Model for MPEG-4 Varied Bit Rate Video Traffic|journal=IEEE Transactions on Broadcasting|volume=50|issue=3|pages=323–334|doi=10.1109/TBC.2004.834013}}</ref>
对称Pareto分布和零对称Pareto分布的目的是捕捉具有尖峰和对称长概率尾的特殊统计分布。这两种分布是由帕累托分布导出的。长概率尾通常意味着概率衰减缓慢。帕累托分布在许多情况下执行拟合工作。但是，如果分布具有两个慢衰减尾的对称结构，则Pareto无法做到这一点。然后应用对称帕累托或零对称帕累托分布
The expected statistical error is:
The expected statistical error is:
The Cumulative distribution function (CDF) of Symmetric Pareto distribution is defined as following:<ref name=":0" />
The Cumulative distribution function (CDF) of Symmetric Pareto distribution is defined as following:<ref name=":0" />
对称帕累托分布的累积分布函数（CDF）定义如下：<ref name=":0" />