We fit the exponent of the Pareto distribution, that is equivalent or can approximate the continuous power law distribution given a cutoff point, using linear regression (LR). We use LR on the logged variables of the empirical tail (one minus the empirical cumulative distribution function). We find the distribution of the consistent LR estimator and an approximate sigmoid relationship of the mean that underestimates the exponent. By factoring out a sigmoid function used to approximate the mean we transform the LR estimator so it is approximately unbiased with variance comparable to the minimum variance unbiased transformed MLE estimator.

翻译：我们使用线性回归拟合帕累托分布的指数，该分布在给定截断点的情况下等同于或可近似连续幂律分布。我们对经验尾部（即一减去经验累积分布函数）的对数变量应用线性回归。我们发现了线性回归一致估计量的分布，以及均值低估指数的一种近似S形关系。通过分解出用于近似均值的S形函数，我们对线性回归估计量进行变换，使其近似无偏，且方差与最小方差无偏变换极大似然估计量相当。