Stretched exponential distributions in nature and economy: "fat tails" with characteristic scales
Stretched exponential distributions in nature and economy: "fat tails" with characteristic scales
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DOI：
10.1007/s100510050276
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发表时间：
1998-04-01
影响因子：
1.6
通讯作者：
Sornette, D
中科院分区：
文献类型：
--
作者：
Laherrere, J;Sornette, D
为了定量地解释自然和经济中报道的许多“自然”胖尾分布，我们提出了拉伸指数族作为对常用幂律分布的补充。它具有许多优点，其中之一是经济，只有两个可调参数，物理解释清楚。此外，它来自一个简单而通用的机制，在乘法过程。我们表明，拉伸指数很好地描述了星系的无线电和光发射的分布，美国GOM OCS油田储量大小，世界，美国和法国的聚集规模，国家人口规模，每日外汇美国马克和法郎马克价格变化，东方（南极附近）过去40万年的温度变化，Raup-Sepkoski的死亡曲线和世界上被引用最多的物理学家的引文。我们还讨论了它的潜在的地震规模和断层位移的分布。我们建议物理解释的参数，并提供了一个简短的工具包的统计特性的拉伸指数。我们还提供了与其他分布，如移位线性分形，对数正态分布和最近推出的抛物线分形分布的比较。
To account quantitatively for many reported "natural" fat tail distributions in Nature and Economy, we propose the stretched exponential family as a complement to the often used power law distributions. It has many advantages, among which to be economical with only two adjustable parameters with clear physical interpretation. Furthermore, it derives from a simple and generic mechanism in terms of multiplicative processes. We show that stretched exponentials describe very well the distributions of radio and light emissions from galaxies, of US GOM OCS oilfield reserve sizes, of World, US and French agglomeration sizes, of country population sizes, of daily Forex US-Mark and Franc-Mark price variations, of Vostok (near the south pole) temperature variations over the last 400 000 years, of the Raup-Sepkoski's kill curve and of citations of the most cited physicists in the world. We also discuss its potential for the distribution of earthquake sizes and fault displacements. We suggest physical interpretations of the parameters and provide a short toolkit of the statistical properties of the stretched exponentials. We also provide a comparison with other distributions, such as the shifted linear fractal, the log-normal and the recently introduced parabolic fractal distributions.