The Lehmann type II inverse Weibull distribution in the presence of censored data

Abstract

In this article, we investigate the mathematical properties of the Lehmann type II inverse Weibull distribution. We show that this model is a reparameterized version of the Kumaraswamy-inverse Weibull distribution without identifiability problems. Parameter estimation is discussed using maximum likelihood (ML) method under a right-censoring scheme. Furthermore, a bootstrap resampling approach is considered to reduce the bias of the ML estimates. In order to illustrate the proposed methodology, we consider a real data set related to the failure time of devices in an aircraft.

Keywords:

• Bootstrap-based bias correction
• Maximum likelihood estimation
• Reliability data
• Right-censoring
• Unimodal failure rate

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62N02
• 62F10

Additional information

Funding

The research of Francisco Louzada is supported by the Brazilian Governmental Agencies, CNPq and FAPESP. Pedro L. Ramos acknowledges support from the São Paulo State Research Foundation (FAPESP Proc. 2017/25971-0).