基于Metropolis-Hastings算法的α稳定分布参数估计

Parameter estimation of α-stable distribution using Metropolis-Hastings algorithm

针对α稳定分布参数估计问题,提出了一种基于MCMC动态模拟的参数估计方法。该方法根据贝叶斯理论建立在α稳定分布层次模型的基础上,利用Metropolis-Hastings抽样方法生成Mark-ov链,在贝叶斯框架下将所有待估计参数视为随机变量,利用后验分布实现稳定分布参数的同时估计,给出了新方法的迭代更新过程,并推导了接受概率的计算公式。理论分析和仿真结果表明,该方法能准确地估计出α稳定分布的4个参数,实现了任意对称或非对称α稳定分布的参数估计。

To solve the problem of parameter estimation of α-stable distributions, a method based on Markov chain Monte Carlo （MCMC） is proposed in this paper. A hierarchical model in order to make in- ference on the parameters was constructed based on Bayesian theorem, and the Metropolis-Hastings （M- H） sampling algorithm was used to generate Markov Chain. Under Bayesian framework, all the unknown parameters were regarded as random variables that can be simultaneously estimated using posterior distri- bution. The procedure of parameters updating was shown and the formula of acceptance rate was derived. Theoretic analysis and computer simulations indicate that the method performs well in estimating all the four parameters of arbitrary a-stable distributions.