Efficient Estimation of the Generalized Quasi-Lindley Distribution Parameters under Ranked Set Sampling and Applications

Amer Ibrahim Al-Omari,Ibrahim M Almanjahie,Sidahmed Benchiha,Ahmed Salem

doi:10.1155/2021/9982397

Amer Ibrahim Al-Omari, Ibrahim M Almanjahie + Show 2 more

Open Access

https://doi.org/10.1155/2021/9982397

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Abstract

Ranked set sampling is a very useful method to collect data when the actual measurement of the units in a population is difficult or expensive. Recently, the generalized quasi-Lindley distribution is suggested as a new continuous lifetime distribution. In this article, the ranked set sampling method is considered to estimate the parameters of the generalized quasi-Lindley distribution. Several estimation methods are used, including the maximum likelihood, the maximum product of spacings, ordinary least squares, weighted least squares, Cramer–von Mises, and Anderson–Darling methods. The performance of the proposed ranked set sampling based estimators is achieved through a simulation study in terms of bias and mean squared errors compared to the simple random sample. Additional results are obtained based on real data for the survival times of 72 guinea pigs and 23 ball bearings. The simulation study results and the real data applications showed the superiority of the proposed ranked set sampling estimators compared to the simple random sample competitors based on the same number of measuring units.

Highlights

One of the significant interesting fields in statistics is the cost-effective sampling methods. e motivation of this field arises from its superiority in facilitating data collection, especially when collecting data of interest consumes a long time or is expensive
In order to evaluate the performance of the estimation methods under ranked set sampling (RSS), a simulation study is conducted by using R software. 1000 samples are generated from the GQLD with different parameters values as (1, 1), (1, 3), (0.5, 1), and (0.8, 1.5) in different sizes for both RSS and simple random sampling (SRS)
RSS-based estimation is presented for the GQLD

Summary

Introduction

One of the significant interesting fields in statistics is the cost-effective sampling methods. e motivation of this field arises from its superiority in facilitating data collection, especially when collecting data of interest consumes a long time or is expensive. Nassar et al [21] considered parameters estimation of the new extension of Weibull distribution. Alfaer et al (2021) considered the extended log-logistic distribution and estimated its parameters. Many studies considered the estimation of parameters based on RSS designs and their extensions using different estimation methods. Chen et al [28] estimated the scale parameter for the scale distribution using moving extreme ranked set sampling, and Abu-Dayyeh et al [29] considered the logistic method for parameter estimation based on both SRS and RSS. Is paper aims to study the performance of using RSS design in estimating the parameters of the generalized quasi-. Applications to real datasets fitted to the GQLD are given in Section 4. e paper is ended in Section 5 with concluding remarks and suggestions for future works

Methods of Estimation

Simulation

Application to Real Datasets

Method

Findings

Conclusion