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

Received: 6 February 2024/Accepted: 7 May 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

REFERENCES

Abouammoh, A.M., Alshangiti, A.M. & Ragab, I.E. 2015. A new generalized two parameter Lindley distribution. Journal of Statistical Computation and Simulation 85(18): 3662-3678.

Al-Khazaleh, M., Al-Omari, A.I. & Al-Khazaleh, A.M.H. 2016. Transmuted two-parameter Lindley distribution. Journal of Statistics Applications & Probability 5(3): 421-432.

Al-Omari, A.I., Ciavolino, E. & Al-Nasser, A.D. 2020. Economic design of acceptance sampling plans for truncated life tests using three-parameter Lindley distribution. Journal of Modern Applied Statistical Methods 18(2): 2-15.

Aryal, G. & Tsokos, C. 2011. Transmuted Weibull distribution: A generalization of the Weibull probability distribution. European Journal of Pure and Applied Mathematics 4(2): 89-102.

Chakraborty, S. 2015. Transmuted Geometric distribution and its properties. https://arxiv.org/abs/1502.04203

Ekhosuehi, N., Opone, F. & Odobaire, F. 2018. A new generalized two parameter Lindley distribution. Journal of Data Science 16(3): 549-566.

Ghitany, M.E., Atieh, B. & Nadarajah, S. 2008. Lindley distribution and its application. Mathematics and Computers in Simulation 78(4): 493-506.

Ieren, T.G. & Abdullahi, J.A. 2020. Transmuted normal distribution: Properties and applications. Equity Journal of Science and Technology 7(1): 16-35.

Lindley, D.V. 1958. Fiducial distributions and Bayes theorem. Journal of the Royal Statistical Society Series B 20: 102-107.

Merovci, F. 2013a. Transmuted Lindley distribution. International Journal of Open Problems in Computer Science and Mathematics 6(2): 63-72.

Merovci, F. 2013b. Transmuted Rayleigh distribution. Austrian Journal of Statistics 42(1): 21-32.

Merovci, F. & Puka, L. 2014. Transmuted Pareto distribution. ProbStat Forum 7: 1-11.

Moniem, A.I.B. & Seham, M. 2015. Transmuted Gompertz distribution. Computational and Applied Mathematics 1(3): 88-96.

Shanker, R. & Rahman, U.H. 2020. A new two-parameter Lindley distribution. Nepal Journal of Mathematical Sciences 1: 33-42.

Shanker, R. & Sharma, S. 2013. A two-parameter Lindley distribution for modeling waiting and survival times data. Applied Mathematics 4(2): 363-368.

Shanker, R., Shukla, K.K. & Mishra, A. 2017. A three-parameter weighted Lindley distribution and its applications to model survival time. Statistics in Transition New Series 18(2): 291-310.

Shanker, R., Shukla, K.K., Shanker, R. & Leonida, T.A. 2017. A three-parameter Lindley distribution. American Journal of Mathematics and Statistics 7(1): 15-26.

Shaw, W.T. & Buckley, I.R.C. 2009. The alchemy of probability distributions: Beyond Gram-Charlier expansions, and a skew-kurtotic normal distribution from a rank transmutation map. https://arxiv.org/abs/0901.0434

Thamer, M.K. & Zine R. 2023. Statistical properties and estimation of the three-parameter Lindley distribution with application to COVID-19 data. Sains Malaysiana 52(2): 669-682.

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