Page 92 - programme book

ST-026
Two-Parameter Bathtub Hazard Model with Covariates and Right
Censored Data

Idari Ismail 1,3, a) and Jayanthi Arasan 1,2, b)

1 Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
2 Institute for Mathematical Research, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
3 Universiti Teknologi MARA Cawangan Kelantan, Kampus Machang Bukit Ilmu, 18500 Machang, Kelantan,
Malaysia

a) Corresponding author: idari512@uitm.edu.my
b) jayanthi@upm.edu.my

Abstract. Many lifetime distributions present monotonic or non-monotonic failure rate functions that
are bathtub-shaped or upside-down bathtub-shaped failure rates. This research extended a two-
parameter bathtub increasing (TBI) model that exhibits either bathtub-shaped or increasing failure rate
depending on its parameter. In this research, the model was extended by adding covariates with right
censored data. The parameter estimates were computed based on maximum likelihood estimation
(MLE). A simulation study was then executed to assess the performance of parameter estimates based
on their bias, standard error and root mean square error at various censoring proportions and sample
sizes. The results suggested that the larger the sample size, the lower the standard error and root mean
square error (RMSE). The RMSE values increased when the censoring proportion increased,
demonstrating that the estimations performed well with smaller censoring proportions.

Keywords: Two-parameter bathtub model, covariates, right censored

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