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The Statistical Analysis of Zero-Failure Data

Author: LiFanQun
Tutor: GuoDaWei
School: Anhui Normal University
Course: Basic mathematics
Keywords: Zero-failure data quasi-likelihood MLE quasi-moment estimation Bayes estimation Exponential distribution Weibull distribution Extreme distribution Pareto dis-trbution entropy loss function
CLC: O212
Type: Master's thesis
Year: 2006
Downloads: 228
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Abstract


In this thesis .point estimations and Bayes estimations of parameters are given under Zero-failure data . Several numerical examples illustrate that the estimations are progressive comparing with the results in the past .This thesis is divided into five parts .In the first chapter ,we obtain the Bayes estimations and hierarchical Bayes estimations about p, at the time ti（i = 1,…,k） and estimations of β and η by using the convex and concave properties of extreme distribution function .see Theorem 2.1,3.1,3.2. Meanwhile caculations are performed regarding to a practical problems .In the second chapter ,the method of quasi likelihood function is proposed to deal with zero-failure data .We have obtained quasi-MLE of parameters for the exponential distribution ,Weibull distribution ,see （3.1）,（4.1）,（4.2）.In the third chapter ,the quasi-moment estimations of the parameters are proposed based on the zero-failure data in double-parameters exponential distribution according to the concept " mean residual lifetime ", see （5.7）,（5.8）.In the forth chapter,hierarchical baysian method is obtained when we can not give the values of a and b the super-parameters in [l].The estimation of all time is given by （3.6）.In the fifth chapter .basing on the estimation of Pareto distribution parameter under Entropy Loss function,we obtain confidence intervals of 6 and discuss the admissibility of estimator with the form of [cT（x） + d]-1.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics
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