| In many research areas, such as medicine, biology, reliability engineering, public hygiene, insurance actuarial science, population statistics, economics and so on,the data we encountered is a class of incomplete data-interval censored data. For example, the available information about the true failure time X is whether it before or after a random monitoring time T, but the exact value of X can not be observed. Such data are called case I interval censored data. This kind of data often occur on the reliability analysis, there are important theoretical and practical value in studying this type of problem. In recent years, the case I interval censored data gradually get the attention of statisticians and are applied widely in other subject areas. There are two directions in the research of this data. One case is the nonparametric inference about the lifetime distribution, and the other is assuming the distribution form is known and estimating the unknown parameter.Success-failure life test is widely used in reliability engineering test to estimate the storage time. Observational data obtained in the test is case I interval censored data, often summarized as a form of group data. The paper focuses on parameter estimation of the life distributions whose cumulative distribution functions cannot be linearized with this data. According to the characteristics of this data, we propose the two-step iterative algorithm to get parameter estimator. There are five chapters in this paper. In the chapter1, we describe briefly the background and current research about case I interval censored data. Chapter2presents some preparatory knowledge. Chapter3introduces the two-stage iteration algorithm and the uniformly-distributed-points algorithm, which is a method used to maximize the log-likelihood without solving the score equation. Chapter4verifies the reasonable and computational efficiency of the proposed method through the simulation. Chapter5gives some remarks and discussions. |
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