论文标题
单侧重尾分布的参数估计
Parameter estimation for one-sided heavy-tailed distributions
论文作者
论文摘要
稳定的下属以及具有功率定律概率尾巴的更通用的下属，已被广泛用于分区的背景下，其中粒子在许多时间段内被捕获或不动，称为恒定周期。恒定周期的长度遵循单方面的分布，该分布涉及0到1之间的参数，并且不存在其第一矩。本文构造了参数的估计器，将矩的方法应用于固定时间间隔的观察到的恒定周期的数量。最终的估计量是渐近公正和一致的，并且非常适合对同一次扩散过程进行多个观察结果的情况。我们提供了支持数值示例，并提出了低量股票的市场价格数据的应用。
Stable subordinators, and more general subordinators possessing power law probability tails, have been widely used in the context of subdiffusions, where particles get trapped or immobile in a number of time periods, called constant periods. The lengths of the constant periods follow a one-sided distribution which involves a parameter between 0 and 1 and whose first moment does not exist. This paper constructs an estimator for the parameter, applying the method of moments to the number of observed constant periods in a fixed time interval. The resulting estimator is asymptotically unbiased and consistent, and it is well-suited for situations where multiple observations of the same subdiffusion process are available. We present supporting numerical examples and an application to market price data for a low-volume stock.
