Study on an Extension to Lindley Distribution: Statistical Properties, Estimation and Simulation

Shafq, Shakaiba; Helal, Tamer S.; Elshaarawy, Rasha S.; Nasiru, Suleman

doi:10.21608/cjmss.2022.270895

Study on an Extension to Lindley Distribution: Statistical Properties, Estimation and Simulation

Document Type : Original Article

Authors

¹ Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur-63100, Pakistan

² Department of Mathematical Statistics Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt

³ Department of Statistics, School of Mathematical Sciences, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Ghana

10.21608/cjmss.2022.270895

Abstract

Recently, Nedjar and Zeghdoudi [6] proposed a new lifetime model called gamma Lindley distribution. Roozegar and Nadarajah [8] introduced some notes around gamma Lindley distribution including only some statistical properties and estimations depending on the same probability density function which proposed by Nedjar and Zeghdoudi [6]. In fact, the model proposed by Nedjar and Zeghdoudi [6] is not a probabilistic model. Further, some of its fundamental properties as well as parameter estimations are incorrect. Hence, all corrections which proposed by Roozegar and Nadarajah [8] are also incorrect. On the other hand, Messaadia and Zeghdoudi [5] proposed only one remark around the parameter space of gamma Lindley distribution which proposed by Nedjar and Zeghdoudi [6], but the mathematical properties and estimations are still wrong for both Nedjar and Zeghdoudi [6] and Roozegar and Nadarajah [8]. Because, Messaadia and Zeghdoudi [5] did not discuss any corrections around quantile function, entropies, estimation methods, simulation and data analysis. In this paper, several corrections including probability density function, quantile function, entropies, estimation the model parameters using the maximum likelihood estimation and moment estimation methods and simulation are discussed in-detail because the previous three papers not make a beneft to the readers, especially in practical feld.

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