Interval Estimations for Parameters of Bathtub Hazard Model with Fixed Covariate in the Presence of Right- Censored Data
Idari Ismail(a*,b), Assoc. Prof. Dr Jayanthi Arasan(a), Dr Mohd Shafie Mustafa(a), Dr Muhammad Aslam Mohd Safari(a)

a) Department of Mathematics and Statistics, Faculty of Science
Universiti Putra Malaysia (UPM)
43400 UPM Serdang
Selangor Darul Ehsan
MALAYSIA
*idari512[at]uitm.edu.my
b) Mathematical Sciences Studies,
College of Computing, Informatics and Media,
Universiti Teknologi MARA (UiTM) Cawangan Kelantan,
18500 Machang, Kelantan Darul Naim
MALAYSIA

Abstract

In this study, a two-parameter lifetime model has been extended to incorporate covariate in the presence of right-censored data. The model has bathtub-shaped or increasing failure rate function which enables it to fit real lifetime data sets. The method of maximum likelihood was used to estimate the parameters in the model and a simulation study was then conducted to evaluate the performance of parameter estimates at various sample sizes and censoring proportion levels. The results from simulation study show that larger sample sizes and smaller censoring proportion give better estimates. Further, three interval estimation methods: Wald, likelihood ratio and bootstrap-t (B-t) were constructed, and the performance of these methods was evaluated based on a coverage probability study. Both Wald and likelihood ratio techniques appear to have better performance when the sample size is larger. On the other hand, B-t method performs better than those two techniques at smaller sample sizes. Finally, an application to a real medical data is presented for illustrative purposes.

Keywords: bathtub-shaped- right-censored- interval estimation method

Topic: MATHEMATICS AND STATISTICS