The kappa distribution has been used for decades as a numerical fitting function to represent the energetic particle distributions measured with satellite instruments. The distributions are generally either a three dimensional distribution in the particle velocity or the one dimensional distribution in a velocity component in a particular direction. The theoretical basis for the origin of the kappa functional form is incomplete. The current paper considers published data for one dimensional distributions and provides a unique method of analysis to determine whether the measured distributions are well represented by the kappa distribution. The analysis is based on the Pearson differential equation which arises from the steady distribution of a Fokker-Planck equation.

数十年来，kappa 分布一直用作数值拟合函数来表示用卫星仪器测量的高能粒子分布。分布通常是粒子速度的三维分布或特定方向的速度分量的一维分布。kappa函数形式起源的理论基础是不完整的。当前论文考虑了已发表的一维分布数据，并提供了一种独特的分析方法来确定测量的分布是否能很好地由 kappa 分布表示。该分析基于 Pearson 微分方程，该方程源自 Fokker-Planck 方程的稳定分布。