Product of Spacing Estimation of Stress–Strength Reliability for Alpha Power Exponential Progressively Type-II Censored Data
The present study focuses on estimating the stress–strength parameter when the parent distribution is the alpha power exponential model and the available data are progressively Type-II censored. As a starting point, the usual maximum likelihood approach is applied to obtain point and interval estima...
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MDPI AG
2023-07-01
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| Online Access: | https://www.mdpi.com/2075-1680/12/8/752 |
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| author | Mazen Nassar Refah Alotaibi Chunfang Zhang |
| author_facet | Mazen Nassar Refah Alotaibi Chunfang Zhang |
| author_sort | Mazen Nassar |
| collection | DOAJ |
| description | The present study focuses on estimating the stress–strength parameter when the parent distribution is the alpha power exponential model and the available data are progressively Type-II censored. As a starting point, the usual maximum likelihood approach is applied to obtain point and interval estimates of the model parameters, as well as the stress–strength parameter. Another competing strategy employed in this paper is the maximum product of spacing method, which may be thought of as a rival to the maximum likelihood method. The product of spacing approach is used to obtain point and interval estimates for the various parameters. The asymptotic properties of both methods are used to obtain interval estimates of the model parameter and the stress–strength parameter, and the variance of the stress–strength parameter is approximated using the well-known delta method. Two parametric bootstrap confidence intervals are provided based on the suggested classical estimation procedures. A simulation study is also used to assess the performance of various point and interval estimations. For illustrative purposes, the proposed methods are applied to two real data sets, one for the kidney patients’ recurrence times to infection and the other for breaking the strength of jute fibers. |
| first_indexed | 2024-03-11T00:07:42Z |
| format | Article |
| id | doaj.art-a21d0fea519e4f1a99690f1715ef415b |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T00:07:42Z |
| publishDate | 2023-07-01 |
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| spelling | doaj.art-a21d0fea519e4f1a99690f1715ef415b2023-11-19T00:14:42ZengMDPI AGAxioms2075-16802023-07-0112875210.3390/axioms12080752Product of Spacing Estimation of Stress–Strength Reliability for Alpha Power Exponential Progressively Type-II Censored DataMazen Nassar0Refah Alotaibi1Chunfang Zhang2Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaSchool of Mathematics and Statistics, Xidian University, Xi’an 710126, ChinaThe present study focuses on estimating the stress–strength parameter when the parent distribution is the alpha power exponential model and the available data are progressively Type-II censored. As a starting point, the usual maximum likelihood approach is applied to obtain point and interval estimates of the model parameters, as well as the stress–strength parameter. Another competing strategy employed in this paper is the maximum product of spacing method, which may be thought of as a rival to the maximum likelihood method. The product of spacing approach is used to obtain point and interval estimates for the various parameters. The asymptotic properties of both methods are used to obtain interval estimates of the model parameter and the stress–strength parameter, and the variance of the stress–strength parameter is approximated using the well-known delta method. Two parametric bootstrap confidence intervals are provided based on the suggested classical estimation procedures. A simulation study is also used to assess the performance of various point and interval estimations. For illustrative purposes, the proposed methods are applied to two real data sets, one for the kidney patients’ recurrence times to infection and the other for breaking the strength of jute fibers.https://www.mdpi.com/2075-1680/12/8/752stress–strength reliabilityalpha power exponential distributionmaximum likelihoodmaximum product of spacing estimationstress–strength parameter |
| spellingShingle | Mazen Nassar Refah Alotaibi Chunfang Zhang Product of Spacing Estimation of Stress–Strength Reliability for Alpha Power Exponential Progressively Type-II Censored Data Axioms stress–strength reliability alpha power exponential distribution maximum likelihood maximum product of spacing estimation stress–strength parameter |
| title | Product of Spacing Estimation of Stress–Strength Reliability for Alpha Power Exponential Progressively Type-II Censored Data |
| title_full | Product of Spacing Estimation of Stress–Strength Reliability for Alpha Power Exponential Progressively Type-II Censored Data |
| title_fullStr | Product of Spacing Estimation of Stress–Strength Reliability for Alpha Power Exponential Progressively Type-II Censored Data |
| title_full_unstemmed | Product of Spacing Estimation of Stress–Strength Reliability for Alpha Power Exponential Progressively Type-II Censored Data |
| title_short | Product of Spacing Estimation of Stress–Strength Reliability for Alpha Power Exponential Progressively Type-II Censored Data |
| title_sort | product of spacing estimation of stress strength reliability for alpha power exponential progressively type ii censored data |
| topic | stress–strength reliability alpha power exponential distribution maximum likelihood maximum product of spacing estimation stress–strength parameter |
| url | https://www.mdpi.com/2075-1680/12/8/752 |
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