Unbiased Estimation for Special Exponential Distributions with Partially Missing Data 

Author  ChenChunHua 
Tutor  XieMinYu 
School  Central China Normal University 
Course  Probability Theory and Mathematical Statistics 
Keywords  Partially Missing Data Special Exponential Distribution Progressive unbiased estimate Unbiased estimate Minimum Variance sex 
CLC  O212.1 
Type  Master's thesis 
Year  2008 
Downloads  53 
Quotes  0 
If an overall observation is completely under the control of the observer , when the data has no missing , however, and each observation, when the overall is not entirely under the control of the observer's data is lost to a certain degree of probability , then we said part of data missing. In the case of the missing part of the data , the literature [ 3 ] discussed the estimates of the parameters of twoparameter exponential distribution , [ 4] discussed the estimation and testing of the two parameter exponential distribution , another in [ 5 ] to discuss two of normality the problem of distributed parameter estimation and testing , and for special exponential distribution also no literature on . In the case of missing data , using the observed data and the mean value of the missing data supplemented , respectively, discussed a special exponential distribution parameters gradual unbiased estimator and unbiased estimate , and proved one of the partial subclass has minimum variance unbiased estimate parameters of a no . The main conclusions are as follows : to Theorem 1 missing data , the mean of the observed data is a special exponential distribution in the case of observational data may be lost completely unbiased estimate parameters gradual . Theorem 2 missing data , the mean of the observed data is a special exponential distribution unbiased estimate of the parameters in the case of the observational data is not completely lost . Theorem 3β _{ 1 → βa is . s. And n 1/2 (β 1 β) (?) N (0, β 2 / p), wherein N (0 , β 2 / p) with zero mean and variance β 2 / p of the normal distribution . Where ( ? ) Convergence in distribution . Corollary 1β 2 → βa. s. And n 1/2 (β 2 β) (?) N (0, β 2 / p), wherein N (0 , β 2 / p) with zero mean and variance β 2 / p of the normal distribution . → means convergence in distribution . }