广义Birnbaum-Saunders分布及其统计分析  

The Generalized Birnbaum-Saunders Distribution and Its Statistical Analysis

作　　者：余炳鹏 YU Bingpeng(College of Mathematics and Physics,Wenzhou University,Wenzhou,China 325035)

机构地区：[1]温州大学数理学院,浙江温州325035

出　　处：《温州大学学报（自然科学版）》2022年第2期19-27,共9页Journal of Wenzhou University(Natural Science Edition)

摘　　要：主要探讨了广义Birnbaum-Saunders分布(以下简称GBS分布)及其统计性质.首先,基于Birnbaum-Saunders分布(以下简称BS分布)将裂纹扩展序列建模为一个长期记忆过程从而给出了GBS分布的定义及其相应的概率密度函数和失效率函数的表达式,并研究了概率密度函数和失效率函数的图像特征.然后,根据第三类修正的贝塞尔函数及其性质推导得出GBS分布n阶原点矩和n阶中心矩的数学表达式,由此得GBS分布期望和方差的具体表达式.最后,给出了GBS分布的极大似然估计及其求解方法,并通过实例具体比较了GBS分布与BS分布的AIC值与BIC值的大小,说明GBS分布相较于BS分布在拟合时更加贴近实际数据,因此在研究疲劳寿命分布的数据时更具优势.This paper mainly discusses the generalized Birnbaum-Saunders(GBS) distribution and its statistical properties. Firstly, based on the BS distribution, the crack growth sequence is modeled as a long-term memory process to give the definition of the GBS distribution, the expression of probability density function and failure rate function, and study the image characteristics of probability density function and failure rate function. Next, the mathematical expressions of the n-order origin moment and n-order central moment of the GBS distribution are derived based on the modified Bessel function of the third kind and its properties, and then the specific expressions of the expectation and variance of the GBS distribution are obtained. Finally, this paper gives the maximum likelihood estimation and calculation method of the GBS distribution, compares AIC value and BIC value of the GBS distribution and the BS distribution by case analysis, and shows that the GBS distribution compared with the BS distribution fits more closely to the actual data and therefore is more advantageous in studying the distribution of data in the fatigue life.

关 键 词：广义Birnbaum-Saunders分布 失效率函数 原点矩 极大似然估计 

分 类 号：O211[理学—概率论与数理统计]