Sains Malaysiana 53(6)(2024): 1427-1440

http://doi.org/10.17576/jsm-2024-5306-16

On a New Transmuted Three-Parameter Lindley Distribution and Its Applications

(Taburan Lindley Tiga Parameter Baharu yang Diubahsuai dan Pengaplikasiannya)

YUHANG XI¹, HEZHI LU^1,2,* & FEI LIANG¹

¹School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China

²Lingnan Research Academy of Statistical Science, Guangzhou University, Guangzhou 510006, China

Diserahkan: 6 Februari 2024/Diterima: 7 Mei 2024

Abstract

In this paper, a new transmuted three-parameter Lindley distribution (TTHPLD) is established using the transmutation map method, which includes the Lindley distribution, two-parameter Lindley distribution, transmuted two-parameter Lindley distribution and three-parameter Lindley distribution as special cases. The statistical properties of the TTHPLD model, which are based on moments, order statistics, hazard rate functions, reliability functions, and Renyi entropy, have been studied. Moreover, the maximum likelihood estimators (MLEs) of the TTHPLD are obtained via differential evolution algorithms, and a simulation study is conducted to evaluate the consistency of the MLEs. Finally, the proposed distribution is applied to a real dataset and compared with other well-known models.

Keywords: Differential evolution algorithm; generalized Lindley distribution; hazard rate function; Renyi entropy; maximum likelihood estimation

Abstrak

Dalam kertas ini, sebuah taburan Lindley tiga-parameter terbaharu (TTHPLD) yang ditransmutasikan telah dibangunkan menggunakan kaedah pemetaan transmutasi, yang merangkumi taburan Lindley, taburan Lindley dua-parameter, taburan Lindley dua-parameter tertransmutasi dan taburan Lindley tiga-parameter sebagai kes khas. Sifat-sifat statistik model TTHPLD yang berdasarkan momen, statistik perintah, fungsi kadar bahaya, fungsi kebolehpercayaan, dan entropi Renyi telah dikaji. Selain itu, penganggar kemungkinan maksimum (MLE) bagi TTHPLD diperoleh melalui algoritma evolusi berbeza dan kajian simulasi dijalankan untuk menilai kekonsistenan MLE tersebut. Akhirnya, pengedaran yang dicadangkan ini diaplikasikan kepada set data sebenar dan dibandingkan dengan model terkenal yang lain.

Kata kunci: Algoritma evolusi berbeza; anggaran kebolehjadian maksimum; fungsi kadar bahaya; entropi Renyi; taburan Lindley teritlak

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*Pengarang untuk surat-menyurat; email: luhz@gzhu.edu.cn