Parameter estimation of three-parameter Weibull distribution based on progressively Type-II censored samples

Abstract

In this paper, the estimation of parameters for a three-parameter Weibull distribution based on progressively Type-II right censored sample is studied. Different estimation procedures for complete sample are generalized to the case with progressively censored data. These methods include the maximum likelihood estimators (MLEs), corrected MLEs, weighted MLEs, maximum product spacing estimators and least squares estimators. We also proposed the use of a censored estimation method with one-step bias-correction to obtain reliable initial estimates for iterative procedures. These methods are compared via a Monte Carlo simulation study in terms of their biases, root mean squared errors and their rates of obtaining reliable estimates. Recommendations are made from the simulation results and a numerical example is presented to illustrate all of the methods of inference developed here.

Keywords:

• lifetime data
• maximum likelihood estimation
• Monte Carlo simulation
• maximum product spacing estimation

Mathematics Subject Classification :

• 62F10
• 62N02
• 62N05

Acknowledgements

We express our sincere thanks to the editor, the associate editor and the reviewer for their comments that greatly improved this article. The first author's research is supported by The Research Grants Council of Hong Kong General Research Fund.