指数截尾q分布：实复杂系统的广义分布
The exponentially truncated q-distribution: A generalized distribution for real complex systems
摘要：
了解变量的统计分布是资源管理中的一个重要问题。在许多实际系统中可以观察到幂律分布。然而，幂律分布具有无穷大的方差，因此不能用作标准分布。通常该领域的专业人士使用具有可变参数的正态分布或其他近似分布，如Gumbel，Wakeby或Pareto，其有效性有限。Tsallis在非广延热力学的框架下提出了一种考虑长程相互作用或长记忆的幂律微观理论。在本工作中，我们考虑了长程相互作用或记忆的软化，并提出了一个广义分布，具有有限的方差，可以用作所有的真实复杂系统的标准分布的幂律行为。我们将这种分布应用于金融系统、降雨和一些地球物理和社会系统。我们发现，在所有情况下的概率密度函数（pdf）以及累积概率的整个范围内的一个很好的协议。这种分布显示了实际系统中尺寸限制的普遍性质。
英文摘要：
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus can not be used as a standard distribution. Normally professionals in the area use normal distribution with variable parameters or some other approximate distribution like Gumbel, Wakeby, or Pareto, which has limited validity. Tsallis presented a microscopic theory of power law in the framework of non-extensive thermodynamics considering long-range interactions or long memory. In the present work, we consider softing of long-range interactions or memory and presented a generalized distribution which have finite variance and can be used as a standard distribution for all real complex systems with power law behaviour. We applied this distribution for a financial system, rain precipitation and some geophysical and social systems. We found a good agreement for entire range in all cases for the probability density function (pdf) as well as the accumulated probability. This distribution shows universal nature of the size limiting in real systems.
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