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Keywords = beta inverted exponential distribution

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26 pages, 527 KB  
Article
Order-Restricted Inference for Generalized Inverted Exponential Distribution under Balanced Joint Progressive Type-II Censored Data and Its Application on the Breaking Strength of Jute Fibers
by Chunmei Zhang, Tao Cong and Wenhao Gui
Mathematics 2023, 11(2), 329; https://doi.org/10.3390/math11020329 - 8 Jan 2023
Cited by 4 | Viewed by 1519
Abstract
This article considers a new improved balanced joint progressive type-II censoring scheme based on two different populations, where the lifetime distributions of two populations follow the generalized inverted exponential distribution with different shape parameters but a common scale parameter. The maximum likelihood estimates [...] Read more.
This article considers a new improved balanced joint progressive type-II censoring scheme based on two different populations, where the lifetime distributions of two populations follow the generalized inverted exponential distribution with different shape parameters but a common scale parameter. The maximum likelihood estimates of all unknown parameters are obtained and their asymptotic confidence intervals are constructed by the observed Fisher information matrix. Furthermore, the existence and uniqueness of solutions are proved. In the Bayesian framework, the common scale parameter follows an independent Gamma prior and the different shape parameters jointly follow a Beta-Gamma prior. Based on whether the order restriction is imposed on the shape parameters, the Bayesian estimates of all parameters concerning the squared error loss function along with the associated highest posterior density credible intervals are derived by using the importance sampling technique. Then, we use Monte Carlo simulations to study the performance of the various estimators and a real dataset is discussed to illustrate all of the estimation techniques. Finally, we seek an optimum censoring scheme through different optimality criteria. Full article
(This article belongs to the Section D1: Probability and Statistics)
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11 pages, 429 KB  
Technical Note
A New Probability Distribution for SAR Image Modeling
by Murilo Sagrillo, Renata R. Guerra, Fábio M. Bayer and Renato Machado
Remote Sens. 2022, 14(12), 2853; https://doi.org/10.3390/rs14122853 - 14 Jun 2022
Cited by 6 | Viewed by 3087
Abstract
This article introduces exponentiated transmuted-inverted beta (ET-IB) distribution, supported by a continuous positive real line, as a synthetic aperture radar (SAR) imagery descriptor. It is an extension of the inverted beta distribution, an important texture model for SAR imagery. The considered distribution extension [...] Read more.
This article introduces exponentiated transmuted-inverted beta (ET-IB) distribution, supported by a continuous positive real line, as a synthetic aperture radar (SAR) imagery descriptor. It is an extension of the inverted beta distribution, an important texture model for SAR imagery. The considered distribution extension approach increases the flexibility of the baseline distribution, and is a new probabilistic model useful in SAR image applications. Besides introducing the new model, the maximum likelihood method is discussed for parameter estimation. Numerical experiments are performed to validate the use of the ET-IB distribution as a SAR amplitude image descriptor. Finally, three measured SAR images referring to forest, ocean, and urban regions are considered, and the performance of the proposed distribution is compared to distributions usually considered in this field. The proposed distribution outperforms the competitor models for modeling SAR images in terms of some selected goodness-of-fit measures. The results show that the ET-IB distribution is suitable as a SAR descriptor and can be used to develop image-processing tools in remote sensing applications. Full article
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37 pages, 638 KB  
Article
On Estimating the Parameters of the Beta Inverted Exponential Distribution under Type-II Censored Samples
by Maha A. Aldahlan, Rana A. Bakoban and Leena S. Alzahrani
Mathematics 2022, 10(3), 506; https://doi.org/10.3390/math10030506 - 5 Feb 2022
Cited by 4 | Viewed by 1894
Abstract
This article aims to consider estimating the unknown parameters, survival, and hazard functions of the beta inverted exponential distribution. Two methods of estimation were used based on type-II censored samples: maximum likelihood and Bayes estimators. The Bayes estimators were derived using an informative [...] Read more.
This article aims to consider estimating the unknown parameters, survival, and hazard functions of the beta inverted exponential distribution. Two methods of estimation were used based on type-II censored samples: maximum likelihood and Bayes estimators. The Bayes estimators were derived using an informative gamma prior distribution under three loss functions: squared error, linear exponential, and general entropy. Furthermore, a Monte Carlo simulation study was carried out to compare the performance of different methods. The potentiality of this distribution is illustrated using two real-life datasets from difference fields. Further, a comparison between this model and some other models was conducted via information criteria. Our model performs the best fit for the real data. Full article
(This article belongs to the Section D1: Probability and Statistics)
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