Statistical inference for the Nadarajah-Haghighi distribution based on ranked set sampling with applications

Haidy A. Newer; Mostafa M. Mohie El-Din; Hend S. Ali; Isra Al-Shbeil; Walid Emam; Haidy A. Newer; Mostafa M. Mohie El-Din; Hend S. Ali; Isra Al-Shbeil; Walid Emam

doi:10.3934/math.20231099

AIMS Mathematics

2023, Volume 8, Issue 9: 21572-21590. doi: 10.3934/math.20231099

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Research article

Statistical inference for the Nadarajah-Haghighi distribution based on ranked set sampling with applications

1.
Department of Mathematics, Faculty of Education, Ain-Shams University, Cairo 11511, Egypt
2.
Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11511, Egypt
3.
Department of Mathematics, Center of Basic Science, Misr University for Science and Technology, Giza 12511, Egypt
4.
Department of Mathematics and Statistics, University of Ottawa, Ottawa ON K1N 6N5, Canada
5.
Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
6.
Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 14 May 2023 Revised: 14 June 2023 Accepted: 25 June 2023 Published: 07 July 2023
MSC : 2E15, 62G30, 62G32, 62M20, 62F25

In this article, the maximum likelihood and Bayes inference methods are discussed for determining the two unknown parameters and specific lifetime parameters of the Nadarajah-Haghighi distribution, such as the survival and hazard rate functions, with the inclusion of ranked set sampling and simple random sampling. The estimated confidence intervals for the two parameters and any function of them are developed based on the Fisher-information matrix. Metropolis-Hastings algorithm and Lindley-approximation are used for generating the Bayes estimates and related highest posterior density credible ranges for the unknown parameters and reliability parameters under the presumption of conjugate gamma priors. A Monte-Carlo simulation study and a real-life data set have been used to assess the efficacy of the proposed methods.
- ranked set sampling,
- Nadarajah-Haghighi distribution,
- maximum likelihood estimation,
- Lindley approximation method,
- Metropolis-Hastings algorithm
Citation: Haidy A. Newer, Mostafa M. Mohie El-Din, Hend S. Ali, Isra Al-Shbeil, Walid Emam. Statistical inference for the Nadarajah-Haghighi distribution based on ranked set sampling with applications[J]. AIMS Mathematics, 2023, 8(9): 21572-21590. doi: 10.3934/math.20231099

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Abstract

In this article, the maximum likelihood and Bayes inference methods are discussed for determining the two unknown parameters and specific lifetime parameters of the Nadarajah-Haghighi distribution, such as the survival and hazard rate functions, with the inclusion of ranked set sampling and simple random sampling. The estimated confidence intervals for the two parameters and any function of them are developed based on the Fisher-information matrix. Metropolis-Hastings algorithm and Lindley-approximation are used for generating the Bayes estimates and related highest posterior density credible ranges for the unknown parameters and reliability parameters under the presumption of conjugate gamma priors. A Monte-Carlo simulation study and a real-life data set have been used to assess the efficacy of the proposed methods.

References

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