Mixture of Two One-Parameter Lindley Distributions: Properties and Estimation
- PDF / 1,540,417 Bytes
- 21 Pages / 439.37 x 666.142 pts Page_size
- 3 Downloads / 283 Views
Mixture of Two One‑Parameter Lindley Distributions: Properties and Estimation A. S. Al‑Moisheer1 · A. F. Daghestani2 · K. S. Sultan3 Accepted: 28 September 2020 © Grace Scientific Publishing 2020
Abstract In this paper, we discuss a mixture of two one-parameter Lindley distributions from both practical and theoretical point of view. The aim of this paper is to set the record straight about this mixture model from different sides. First, we present a brief summary of the Lindley distribution with one parameter. Then, we display the probability density and cumulative distribution functions of the mixture model of two one-parameter Lindley distributions. Consequently, we study some statistical properties of the mixture model with some graphs of both density and hazard rate functions. Also, we focus on the identifiable property of the mixture model and prove it. In addition, we estimate the unknown parameters of the mixture model via suitable methods such as the maximum likelihood and the generalized method of moments. However, we estimate the confidence intervals of the estimated parameters and compute the coverage probability and the average length of the estimated intervals. Finally, we evaluate the performance of our results through a simulation study, numerical examples and real data applications. Keywords Two-component mixture · Mode · Median · Reliability and hazard rate functions · MLEs · GMMEs
* A. S. Al‑Moisheer [email protected] 1
Department of Mathematics, College of Science, Jouf University, Sakaka 72351, P.O.Box 848, Saudi Arabia
2
Department of Mathematics, College of Science and Humanities ‑ Jubail, Imam Abdulrahman Bin Faisal University, Dammam 31441, P.O. Box 1982, Saudi Arabia
3
Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, P.O.Box 2455, Saudi Arabia
13
Vol.:(0123456789)
11
Page 2 of 21
Journal of Statistical Theory and Practice
(2021) 15:11
1 Introduction Mixture models or, in particular, finite mixture models were used in the early years of statistics for modeling different phenomena, and they have continued to receive increasing attention over the years. Finite mixture models are important in many applications such as biology, genetics, medicine, economics, engineering, real life, marketing, social sciences and many other fields. The essential idea of mixture models is to mix two or more distributions by mixing proportions in order to get a new distribution with new properties. Therefore, it is important to study the statistical properties of the proposed mixture model and estimate its unknown parameters via suitable methods. Indeed, many authors have examined mixture distributions such as [11, 23, 25–27, 40]. Because of the importance of the family of exponential distributions in many real-life applications, we will study a mixture of two one-parameter Lindley distributions that belongs to this family and that is used in many applications. In this regard, Lindley distribution is important for modeling various
Data Loading...
