Parameter Estimation Based On Likelihood Depth With Research And Application

Exponential family distribution(such as exponential distribution, Weibull distribution and Gamma distribution) is a very important distributions of the family in the statistical, and is the theoretical basis of reliability analysis and life test, whose application is very extensive in scientific research and engineering practice. How to scientific and precise estimate the value of exponential distribution model is related to the application value of the model which is an important researched direction of scientific analysis and machine studies workers. This paper on basis of estimating exponential family distribution’s parameters, and adopts likelihood depth estimation for them. Likelihood depth estimation is a new method which is basis of likelihood function and data depth.Because most of the actual work data obtained are missing or contaminated, using the classic model parameter estimation method such data cannot be correctly estimated, but likelihood depth estimation can resovle this problem. The paper select complete data,contaminated data and truncated data to compare with the contaminated and truncated data,and also adopts moment estimation and maximum likelihood estimation to estimate through conducting an random simulation experiment. The result shows that the effect of likelihood depth is not good for complete data, contaminated data and truncated data, and is very good for contaminated censored data, and is better than moment estimation and maximum likelihood estimation, which indicates likelihood depth estimation is an effective method for estimating the parameters.