Estimation For The Pareto Distribution Under Progressive Type Ⅰ Interval Censored Data

Pareto distribution is taking more and more interest recent years due to its good quality. In this thesis we studied the parameter estimate for Pareto distribution under progressive type Ⅰ interval censoring data.In the first chapter we show the definition of progressive type Ⅰ interval censoring data and the existing works for Pareto distribution and its properties. In the second chapter we show the MLE for Pareto distribution under progressive type Ⅰ interval censoring data and use Newton-Raphson, EM algorithm for the approximate estimation. A simulation work is conducted also. In the third chapter we discussed the asymptotic properties of maximum likelihood estimators based on progressive Type-Ⅱ censoring for Pareto distribution and show the consistency and normality of MLE. At last we discussed the estimate for two parameter Pareto distribution.