二参数广义Rayleigh分布

Two-Parameter Generalized Rayleigh Distribution

为了研究某些工程过程的寿命,需要一个能够适应这些过程性质的寿命模型.与简单模型相比,基于寿命分布的广义模型在建模过程中更具有直观的适用性和吸引力.本文介绍一个二参数广义Rayleigh分布,推导出了其矩生成函数和k阶矩的表达式,通过对样本点进行归一化,得到了它的近似分布函数、概率密度函数、生存函数、风险率函数等.在此基础上,利用EM算法计算了二参数广义Rayleigh分布中未知参数的最大似然估计,并且得到了观测Fisher信息矩阵.最后根据参数的最大似然估计渐进服从正态分布,从而构造未知参数的渐近置信区间.

In order to study the life of some engineering processes, we need a life model which can adapt to the nature of these processes. Compared with the simple model, the generalized model based on life distribution has more intuitive applicability and attraction in the process of modeling. In this paper, a two parameter generalized Rayleigh distribution is introduced, and its moment generating function and k-order moment expressions are derived. By normalizing the sample points, its approximate distribution function, probability density function, survival function and risk rate function are obtained.On this basis, EM algorithm is used to calculate the maximum likelihood estimation of unknown parameters in two parameter generalized Rayleigh distribution, and the observed Fisher information matrix is obtained. Finally, the asymptotic confidence interval of unknown parameters is constructed according to the asymptotic normal distribution of maximum likelihood estimation.