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Sains Malaysiana 52(2)(2023):
http://doi.org/10.17576/jsm-2023-5202-26
Statistical
Properties and Estimation of the Three-Parameter Lindley Distribution with
Application to COVID-19 Data
(Sifat Statistik dan Anggaran Taburan Lindley Tiga Parameter dengan
Aplikasi pada Data COVID-19)
MATHIL
KAMIL THAMER1,2,* & RAOUDHA ZINE1
1Laboratory of Probability and Statistics,
Faculty of Sciences of Sfax, Sfax, Tunisia
2Department of Economics, College of
Administration and Economics, University of Anbar, Iraq
Received: 14 July 2021/Accepted: 9 May
2022
Abstract
In 2017, the
three-parameter Lindley distribution has been studied. The present paper is a
continuation of the investigation of the properties of this distribution
because of its high flexibility for modeling lifetime data. We studied some
statistical properties of this distribution as central tendency measures,
dispersion measures, and shape measures. In addition, the mode and the quantile
function of the distribution were derived by the authors. The three parameters
were estimated by the Maximum Product of
Spacing Method (MPS) due to its fame in estimating parameters. A simulation study is
carried out to examine the consistency of estimators using mean square error
(MSE). The estimators showed that they have the property of consistency because
MSEs decrease with increasing the size of the sample. On the practical side,
the MPS estimates were used to obtain statistical properties, probability
density function (p.d.f), cumulative distribution
function (c.d.f), survival function, and hazard
function for real data which represents COVID-19 Data in Iraq/Al-Anbar
Province. We found the flexibility of the distribution in representing life
data and the possibility of getting the patients' probability of death and
probability of survival for the time.
Keywords:
COVID-19 data; mathematical model; maximum product of spacing method;
three-parameter Lindley distribution
Abstrak
Pada tahun 2017, taburan Lindley tiga parameter telah dikaji. Makalah ini adalah kesinambungan daripada penyelidikan sifat pengedaran ini kerana kefleksibelannya yang tinggi untuk memodelkan data sepanjang hayat. Kami mengkaji beberapa sifat statistik taburan ini sebagai ukuran kecenderungan pusat, ukuran penyebaran
dan ukuran bentuk. Di samping itu, mod dan fungsi kuantil taburan diperoleh oleh penulis. Ketiga-tiga parameter tersebut dianggarkan menggunakan Kaedah Maksimum Jarak Jauh (MPS) kerana kemasyhurannya dalam menganggar parameter. Suatu kajian simulasi dijalankan untuk mengkaji ketekalan penganggar menggunakan min ralat kuasa dua (MSE). Penganggar menunjukkan bahawa mereka memiliki sifat ketekalan kerana MSE menurun dengan peningkatan ukuran sampel. Dari segi praktikal, anggaran MPS digunakan untuk memperoleh sifat statistik, fungsi ketumpatan kebarangkalian (p.d.f), fungsi taburan kumulatif (c.d.f), fungsi kemandirian dan fungsi bahaya untuk data sebenar yang mewakili Data
COVID-19 di Wilayah Iraq/Al-Anbar. Kami mendapati kefleksibelan penyebaran dalam mewakili data kehidupan dan kemungkinan mendapat kebarangkalian kematian pesakit dan kebarangkalian bertahan untuk masa ini.
Kata kunci: Data COVID-19; model matematik; produk maksimum kaedah jarak; taburan Lindley tiga parameter
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*Corresponding author; email: mathil.thamir@uoanbar.edu.iq
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