Citation
Oh, Yit Leng
(2024)
Exponentiated-based Burr type X distributions with censored data and covariate.
Doctoral thesis, Universiti Putra Malaysia.
Abstract
In an attempt to create distributions with greater flexibility to accommodate survival
data with various hazard function forms, a number of extended Burr type X
distributions have been developed recently. For instance, the Weibull Burr type X, beta
Burr type X, and gamma Burr type X distributions. Previous studies have demonstrated
that the hazard functions of these distributions can take various forms, such as
increasing, decreasing, and bathtub, but not unimodal, which is frequently observed in
survival analysis. In order to solve this issue, the aim of this study is to propose three
distributions with greater flexibility in fitting hazard functions in various forms,
particularly the unimodal: exponentiated Weibull Burr type X, exponentiated beta Burr
type X, and exponentiated gamma Burr type X distributions. We begin by deriving the
probability density function and cumulative distribution function of the three proposed
distributions as well as their important statistical characteristics, including the quantile
function, moment, moment generating function, order statistics, and Renyi entropy. To
explore the performance of the three proposed distributions, simulation studies with
various sample sizes and censoring rates for data with and without censored data and
covariate are conducted after it. This study considers two types of censoring: random
censoring and type-I censoring. Besides, for the simulation studies, we consider cases
with single covariates. For these simulation studies, the inverse transform approach is
used to simulate the event time. Meanwhile, we estimate the parameters of each of the
three proposed distributions using the maximum likelihood estimation approach.
Lastly, we use three real data sets: two complete data sets and one with censored data
and covariates, to demonstrate the effectiveness and adaptability of the three suggested
distributions. The two complete data sets are Data Set 1, which represents the failure
time of 84 aircraft windshields, and Data Set 2, which represents the remission time of
128 patients with bladder cancer. Data Set 1 has an increasing hazard function, whereas
Data Set 2 has a unimodal hazard function. Data Set 3 contains the recurrence time of
86 bladder cancer patients with censored data and three covariates. The findings of this
study have demonstrated that the hazard functions of the three proposed distributions
can take the forms of increasing, decreasing, bathtub, and unimodal. Additionally, even
with censored data and covariate are present, the parameters of the three proposed
distributions can be estimated using the maximum likelihood estimation approach.
Finally, the three proposed distributions fit the two complete data sets better than
various extended Burr type X distributions and their sub-models, and they are
formidable rivals to all other competing distributions, including the non-nested
distributions used in this study, as demonstrated in the real data applications.
Nevertheless, the three proposed distributions can be used to fit survival data with
unimodal hazard function as demonstrated in applications of Data Set 3.
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Additional Metadata
Item Type: |
Thesis
(Doctoral)
|
Subject: |
Survival analysis (Biometry) |
Subject: |
Hazard functions |
Subject: |
Distribution (Probability theory) |
Call Number: |
FS 2024 12 |
Chairman Supervisor: |
Lim Fong Peng, PhD |
Divisions: |
Faculty of Science |
Keywords: |
Beta-G, Burr Type X, Exponentiated, Gamma-G, Weibull-G |
Depositing User: |
Ms. Rohana Alias
|
Date Deposited: |
02 Sep 2025 07:01 |
Last Modified: |
02 Sep 2025 07:01 |
URI: |
http://psasir.upm.edu.my/id/eprint/119238 |
Statistic Details: |
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