Alpha稳定分布序列的数值仿真方法

Alpha稳定分布是对水声混响数据进行非高斯概率密度拟合的最优模型之一,而仿真产生服从标准参数系下的Alpha稳定分布序列是展开相应研究的基础。论述了三种参数系下服从Alpha稳定分布随机变量的变换关系及各种参数系表述的优缺点,实现了标准参数系下任意参数组合Alpha稳定分布序列的数值仿真;同时还利用直接数值积分法完成了无显性概率密度表达式的Alpha稳定分布序列概率密度值计算,以之作为理论值与统计值进行了分析比较,验证了数值仿真方法的正确性。

Numerical simulation method of Alpha stable distribution sequence

Alpha stable distribution is one of the best non-Gaussian probability models for underwater acoustics rever-beration data. Numerical simulation of Alpha Stable Distribution sequence, which obeys the standard parameter system, is the basis of the corresponding research. The transformation relationship among Alpha Stable Distribution random variables under the three parameter systems and the advantages and disadvantages of various parameter system formu-lations are summarized. Under the standard parameter system the numerical simulation of Alpha stable distribution sequence with of arbitrary parameter combination is implemented. Without explicit probability density expression, the probability density values of Alpha Stable Distribution are calculated with direct numerical integration method, which are used as theoretical values to make comparative analysis with statistical ones, and to verify the correctness of the numerical simulation method.