指数分布抽样基本定理及在三参数一般指数分布参数估计中的应用

讨论三参数一般指数分布的参数估计,首先讨论了三参数一般指数分布参数的最大似然估计的求解问题,当其中参数α=1时,应用指数分布抽样基本定理,得到了三参数一般指数分布其它参数的一致最小方差无偏估计;并且由此给出求解三参数一般指数分布参数最大似然估计的迭代方法,得到了三参数一般指数分布参数最大似然估计的近似值,给出了模拟结果以说明迭代方法的收敛性;并以相关文献的观察数据作为样本,得到了三参数一般指数分布的参数估计,从而说明了迭代方法的有效性.

Sampling Fundamental Theorem for Exponential Distribution with Application to Parameter Estimation of Three-Parameter Generalized Exponential Distribution

parameter estimation of Three-parameter generalized exponential distribution is considered in this paper,first we discuss the problem about maximum likelihood estimator of its parameter,when parameterαis one,by apply the sampling fundamental theorem for exponential distribution to parameter estimation,we obtained uniformly minimum-variance unbiased estimator (UMVUE) of parameters of Two-Parameter exponential distribution,hence,iterative method to solve maximum likelihood estimator of parameters of ThreeParameter exponential distribution are provided,the results of approximate value to exact solution of maximum likelihood estimator of parameters of Three-Parameter exponential distribution is derived,finally,simulation result is provided to show the convergence of iterative method,and the real example is taken based on observed data from table 1 of reference 2] to show the valid of iterative method.