Weighted generalized Quasi Lindley distribution: Different methods of estimation, applications for Covid-19 and engineering data

SidAhmed Benchiha; Amer Ibrahim Al-Omari; Naif Alotaibi; Mansour Shrahili; SidAhmed Benchiha; Amer Ibrahim Al-Omari; Naif Alotaibi; Mansour Shrahili

doi:10.3934/math.2021688

AIMS Mathematics

2021, Volume 6, Issue 11: 11850-11878. doi: 10.3934/math.2021688

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Weighted generalized Quasi Lindley distribution: Different methods of estimation, applications for Covid-19 and engineering data

1.
Department of Mathematics, University of Jordan Amman, Jordan
2.
Department of Mathematics, Faculty of Science, Al al-Bayt University Mafraq, Jordan
3.
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University, Kingdom of Saudi Arabia
4.
Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia

Received: 16 June 2021 Accepted: 25 July 2021 Published: 16 August 2021
MSC : 62E15, 60E05, 62F10

Recently, a new lifetime distribution known as a generalized Quasi Lindley distribution (GQLD) is suggested. In this paper, we modified the GQLD and suggested a two parameters lifetime distribution called as a weighted generalized Quasi Lindley distribution (WGQLD). The main mathematical properties of the WGQLD including the moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, stochastic ordering, median deviation, harmonic mean, and reliability functions are derived. The model parameters are estimated by using the ordinary least squares, weighted least squares, maximum likelihood, maximum product of spacing's, Anderson-Darling and Cramer-von-Mises methods. The performances of the proposed estimators are compared based on numerical calculations for various values of the distribution parameters and sample sizes in terms of the mean squared error (MSE) and estimated values (Es). To demonstrate the applicability of the new model, four applications of various real data sets consist of the infected cases in Covid-19 in Algeria and Saudi Arabia, carbon fibers and rain fall are analyzed for illustration. It turns out that the WGQLD is empirically better than the other competing distributions considered in this study.
- generalized Quasi Lindley distribution,
- weighted distribution,
- methods of least squares,
- maximum likelihood method,
- methods of minimum distances,
- lifetime distribution
Citation: SidAhmed Benchiha, Amer Ibrahim Al-Omari, Naif Alotaibi, Mansour Shrahili. Weighted generalized Quasi Lindley distribution: Different methods of estimation, applications for Covid-19 and engineering data[J]. AIMS Mathematics, 2021, 6(11): 11850-11878. doi: 10.3934/math.2021688

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Abstract

Recently, a new lifetime distribution known as a generalized Quasi Lindley distribution (GQLD) is suggested. In this paper, we modified the GQLD and suggested a two parameters lifetime distribution called as a weighted generalized Quasi Lindley distribution (WGQLD). The main mathematical properties of the WGQLD including the moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, stochastic ordering, median deviation, harmonic mean, and reliability functions are derived. The model parameters are estimated by using the ordinary least squares, weighted least squares, maximum likelihood, maximum product of spacing's, Anderson-Darling and Cramer-von-Mises methods. The performances of the proposed estimators are compared based on numerical calculations for various values of the distribution parameters and sample sizes in terms of the mean squared error (MSE) and estimated values (Es). To demonstrate the applicability of the new model, four applications of various real data sets consist of the infected cases in Covid-19 in Algeria and Saudi Arabia, carbon fibers and rain fall are analyzed for illustration. It turns out that the WGQLD is empirically better than the other competing distributions considered in this study.

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