中文摘要：

本文利用Kaminskiy和Vasiliy提出的简单贝叶斯估计过程，研究线性指数分布的参数的简单贝叶斯估计．本文的创新之处是利用了核密度估计法和缺一交叉验证法构造概率密度函数．在估计过程中，先验信息可以通过可靠度函数估计的区间形式表示．基于这种先验信息，可以构造线性指数分布参数的连续联合先验分布，并可以给出在任意给定时刻可靠度函数的均值及标准差的后验估计．通过一个数值例子说明这种估计方法．Rayleigh分布是线性指数分布的特殊情况，通过简单贝叶斯估计过程，给出TRayleigh分布的尺度参数的一种新的先验分布，这个模型的均值可由一个级数逼近．

英文摘要：

In this paper, with a simple Bayesian estimation procedure proposed by Kaminskiy and Vasiliy, a simple Bayesian estimation of linear exponential distribution is obtained. The novelty of this paper is that the methods of kernel density estimator and leave-one-out Cross-Validation are introduced to construct the density function . The prior information can be presented in the form of the interval assessment of the reliability function. Based on this prior information, the procedure allows constructing the continuous joint prior distribution of the two parameters, and the posterior estimates of the mean and standard deviation of the estimated reliability function at any given value of the exposure variable are constructed. We study a numeric example as an illustration. And for the scale parameter of the Rayleigh distribution, we additionally elaborate on a new parametric form of the prior distribution; The mean of the mode is obtained through a series approximation.