Sains Malaysiana 54(3)(2025): 927-941

http://doi.org/10.17576/jsm-2025-5403-23

A New Gompertz-Three-Parameter-Lindley Distribution for Modeling Survival Time Data

(Taburan Gompertz-Tiga-Parameter-Lindley Baharu untuk Memodelkan Data Masa Kemandirian)

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

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

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

Received: 20 May 2024/Accepted: 2 December 2024

Abstract

In this paper, a new survival distribution is introduced. It is a mixture of the Gompertz distribution and three-parameter-Lindley distribution. The statistical properties of the proposed distribution including the shape properties, cumulative distribution, quantile functions, moment generating function, failure rate function, mean residual function, and stochastic orders are studied. Moreover, a new regression model based on the proposed distribution is presented. Maximum likelihood estimators (MLEs) of unknown parameters are obtained via differential evolution algorithms, and simulation studies are conducted to evaluate the consistency of the MLEs. Finally, the proposed model and its regression model are applied to a real dataset and compared with other well-known models, demonstrating their superior performance, particularly for heavy-tailed data.

Keywords: Differential evolution algorithm; Gompertz-Lindley distribution; maximum likelihood estimation; regression model; structural property

Abstrak

Dalam kertas ini, suatu taburan survival baharu diperkenalkan. Ia adalah campuran taburan Gompertz dan taburan tiga parameter-Lindley. Sifat statistik bagi taburan yang dicadangkan termasuk sifat bentuk, taburan kumulatif, fungsi kuantil, fungsi penjanaan momen, fungsi kadar kegagalan, fungsi baki min dan susunan stokastik dikaji. Selain itu, model regresi baharu berdasarkan pengedaran yang dicadangkan dibentangkan. Anggaran kebolehjadian maksimum (MLE) bagi parameter yang tidak diketahui diperoleh melalui algoritma evolusi pembezaan, dan kajian simulasi dijalankan untuk menilai ketekalan MLE. Akhir sekali, model yang dicadangkan dan model regresinya digunakan pada set data sebenar dan dibandingkan dengan model terkenal lain, menunjukkan prestasi unggul mereka, terutamanya untuk data berat.

Kata kunci: Algoritma evolusi berbeza; anggaran kebolehjadian maksimum; model regresi; sifat struktur; taburan Gompertz-Lindley

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*Corresponding author; email: luhz@gzhu.edu.cn