Sains Malaysiana 52(1)(2023): 281-294
http://doi.org/10.17576/jsm-2023-5201-23
A New
Exponentiated Beta Burr Type X Distribution: Model, Theory, and Applications
(Taburan Beta Burr Jenis X Baru yang Dipertingkatkan: Model, Teori dan Aplikasi)
YIT
LENG OH1,2, FONG PENG LIM1,*, CHUEI YEE CHEN1, WENDY SHINYIE LING1 & YUE FANG LOH3
1Department
of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia
2Faculty
of Business, Multimedia University, 75450 Melaka, Malaysia
3Faculty of Business and Management, UCSI University, 56000
Kuala Lumpur, Federal Territory, Malaysia
Received:
20 May 2022/Accepted: 10 October 2022
Abstract
In recent years,
many attempts have been carried out to develop the Burr type X distribution,
which is widely used in fitting lifetime data. These extended Burr type X distributions can model the hazard function in decreasing, increasing and bathtub shapes, except for unimodal. Hence, this paper aims to introduce a new
continuous distribution, namely exponentiated beta Burr type X distribution,
which provides greater flexibility in order to overcome the deficiency of the existing extended
Burr type X distributions.
We first present its density and cumulative function expressions. It is then
followed by the mathematical properties of this new distribution, which include
its limit behaviour, quantile function, moment, moment generating function, and
order statistics. We use maximum likelihood approach to estimate the parameters
and their performance is assessed via a simulation study with varying parameter
values and sample sizes. Lastly, we use two real data sets to illustrate the
performance and flexibility of the proposed distribution. The
results show that the proposed distribution gives better fits in modelling
lifetime data compared to its sub-models and some extended Burr type X
distributions. Besides, it is very competitive and can be used as an
alternative model to some nonnested models. In summary, the proposed distribution is very flexible and able to
model various shaped hazard functions, including the increasing, decreasing,
bathtub, and unimodal.
Keywords: Beta
generalized; Burr type X; exponentiated; survival analysis; unimodal
Abstrak
Dalam beberapa tahun kebelakangan ini, banyak percubaan telah dijalankan
untuk membangunkan taburan Burr jenis X yang digunakan secara meluas dalam
model sepanjang hayat yang sesuai. Taburan lanjutan Burr jenis X ini boleh
memodelkan fungsi hazard dalam bentuk menurun, meningkat dan bathtub,
kecuali bagi unimod. Kertas ini bertujuan untuk memperkenalkan taburan
berterusan baharu, iaitu taburan Burr jenis X beta eksponen, yang lebih
keluwesan, bagi mengatasi kekurangan taburan lanjutan Burr jenis X sedia
ada. Kami bermula dengan membentangkan ketumpatan dan ungkapan fungsi
terkumpulnya. Ia kemudiannya diikuti dengan sifat matematik taburan baharu ini,
yang merangkumi kelakuan hadnya, fungsi kuantil, momen, fungsi penjanaan momen
dan statistik pesanan. Kami menggunakan pendekatan
kemungkinan maksimum untuk menganggarkan parameter dan prestasinya dinilai
melalui kajian simulasi dengan nilai parameter dan saiz sampel yang
berbeza-beza. Akhir sekali, kami menggunakan dua set data sebenar untuk
menggambarkan prestasi dan berkefleksibelan taburan yang dicadangkan. Keputusan
menunjukkan bahawa taburan yang dicadangkan memberikan kesesuaian yang lebih
baik dalam pemodelan data sepanjang hayat berbanding dengan sub-modelnya dan beberapa
taburan lanjutan Burr jenis X. Selain itu, ia sangat bersaing dan boleh
digunakan sebagai model alternatif kepada beberapa model tidak bersarang.
Secara ringkasnya, taburan yang dicadangkan adalah sangat fleksibel dan boleh
memodelkan pelbagai bentuk fungsi hazard, termasuk peningkatan,
penurunan, bathtub dan unimod.
Kata kunci: Analisis
kemandirian; beta teritlak; Burr jenis X; eksponen; unimod
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*Corresponding
author; email: fongpeng@upm.edu.my
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