Unbiased Estimation for Special Exponential Distributions with Partially Missing Data
|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|
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 two-parameter 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 sub > → βa is . s. And n 1/2 sup> (β 1 -β) (?) N (0, β 2 sup> / p), wherein N (0 , β 2 sup> / p) with zero mean and variance β 2 sup > / p of the normal distribution . Where ( ? ) Convergence in distribution . Corollary 1β 2 → βa. s. And n 1/2 sup> (β 2 -β) (?) N (0, β 2 sup> / p), wherein N (0 , β 2 sup> / p) with zero mean and variance β 2 sup > / p of the normal distribution . → means convergence in distribution .