Statistical inferences for the parameters of weibull distribution based on progressively type-II right censored sample

This thesis aims to investigate in detail the statistical inference of unknown shape and scale parameters of Weibull distribution in the case of the progressively censored sample. For this purpose, the maximum likelihood, approximate maximum likelihood, maximum product spacing, pivot, graphical and least square estimation methods for the point estimation of unknown parameters of Weibull distribution were discussed and the estimators based on these methods were obtained. Asymptotic confidence intervals, confidence intervals, based on the pivot, confidence intervals relied on Bootstrap-p and Bootstrap-t methods for the interval estimation of the unknown shape and scale parameters of the Weibull distribution are explained and the corresponding ınterval estimators obtained. The performances of the point and interval estimates were examined in detail for different parameter values and different censored schemes based on different sample sizes through extensive simulation studies. According to the obtained results, it was seen that the pivot method performed quite well in both point and interval estimation, while the graphical method performed well in point estimation. Finally, an application was analyzed by using a real data set.