Discrete Weibull-Rayleigh distribution properties and parameter estimations

Ma, Hai-Jing; Yan, Zaizai

doi:10.2298/tsci2203627m

Cited by 3 publications

(5 citation statements)

References 20 publications

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“…The joint MLEs are, therefore, (â, β, λ) = (0.0001, 1.2552, 565.8382). At this point the value −25.7299 is declared as the maximum of the log-likelihood function (10). For a detailed overview, it is noteworthy to illustrate the behavior of log-likelihood function (19) on the area [0, 2] × [100, 900].…”

Section: Data Setmentioning

confidence: 99%

“…• Case I Constraint optimization on Θ 0 yields the MLEs ( β, λ) = (0, 5.1259) with −3.6131 as the attained maximum value of (10). However, in this setting the system (17) becomes ill-defined.…”

Section: Simulated Datamentioning

confidence: 99%

“…However, in this setting the system (17) becomes ill-defined. So, in order to overcome this issue, we expand the parameter space Θ 0 to Θ * 0 and obtain the point ( β0 , λ0 ) = (−0.3016, 6.0042) with −3.6036 as the achieved maximum value of (10). But, by this we may notice that the fitted P Y EW model becomes an ill-suitable model choice.…”

Section: Simulated Datamentioning

confidence: 99%

“…[7,8], and provide a better choice, having the principle of parsimony in mind, than mixtures of distributions, see e.g. [9,10].…”

Section: Introductionmentioning

confidence: 99%

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On maximum likelihood estimates of a proportional hazard rate model parameters based on record values

Vidović

2023

THERM SCI

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The proportional hazard rate models have wide acceptance in modeling complex data from different engineering, reliability and survival applications. The hazard rate function of such models is able to model data with a monotonic or a bathtubshape hazard rate. In this paper, we propose a subclass of proportional hazard rate models with three-parameters for which we have proved the existence and uniqueness of the maximum likelihood estimators based on upper kth record values. The proposed inference is found especially useful in some real illustrations within mechanical and medical analysis. Finally, several remarks are presented in the final stage of this paper.

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Section: Data Setmentioning

confidence: 99%

Section: Simulated Datamentioning

confidence: 99%

Section: Simulated Datamentioning

confidence: 99%

“…[7,8], and provide a better choice, having the principle of parsimony in mind, than mixtures of distributions, see e.g. [9,10].…”

Section: Introductionmentioning

confidence: 99%

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On maximum likelihood estimates of a proportional hazard rate model parameters based on record values

Vidović

2023

THERM SCI

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“…The Rayleigh distribution is a special case of the Weibull distribution. The Whipple distribution depends on two degrees of freedom, which corresponds to the Kay distribution, while the Rayleigh distribution can be used using one degree of freedom, which makes the Rayleigh distribution simpler [25].…”

Section: Feasibility Studiesmentioning

confidence: 99%

Rayleigh-Monte Carlo Method for Image Noise Detection and Elimination

Abbas,

Ruhaima,

Hayder

et al. 2023

Preprint

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The issue of identifying areas of distortion in images is a common problem encountered in digital media processing. Traditional filtering methods often rely on setting thresholds that are dependent on the specific image being processed, leading to imprecise results. Adaptive filters have been proposed as a solution, but they are not without their technical difficulties. This paper presents a study on the effectiveness of the Rayleigh distribution method in identifying distortion areas in images. Monte Carlo estimation was used to estimate the distribution of image content, and the results showed that the Rayleigh distribution is highly efficient at identifying areas of distortion. The filtering process was then applied only to the regions with deformation, while ensuring that all other features of the image were preserved. The novelty of this study lies in the use of the Rayleigh distribution method to identify areas of distortion in images. The purpose of this study was to improve the quality of images by using a more precise filtering method that only targets distorted areas. The theoretical framework of this study is based on the application of the Rayleigh distribution method in digital media processing. The approach used in this study involved the use of Monte Carlo estimation to determine the effectiveness of the Rayleigh distribution method. The findings of this study show that the Rayleigh distribution method is highly effective in identifying areas of distortion in images, leading to higher quality images than traditional filtering methods. The research findings have practical implications for digital media processing industries, where the quality of images is paramount. By using the Rayleigh distribution method, images can be processed more efficiently, leading to improved quality and reduced processing time. Socially, improved image quality can have a positive impact on areas such as medical imaging, where accurate and high-quality images are crucial for diagnosis and treatment. Overall, this study offers an original and effective solution to the problem of identifying areas of distortion in images. By using the Rayleigh distribution method, images can be processed more precisely, leading to higher quality results. The use of Monte Carlo estimation provides a solid foundation for future research in this area.

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Bivariate and two-phase degradation modeling and reliability analysis with random effects

Sun,

Li,

Yuan

et al. 2024

THERM SCI

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The paper aims at predicting the remaining useful life of highly reliable and long-life products with multiple and multi-stage characteristics in the degradation process. Considering the unit-to-unit variability among the product units, a new bivariate and two-phase Wiener process model with random effects is established. Schwarz Information Criterion is used to identify the change points of the degradation model, and the analytical expressions of life and remaining useful life are given by the concept of first hitting time. Furthermore, the appropriate Copula function is selected to describe the correlation between the two quality characteristics based on Akaike Information Criterion. A bivariate degradation model is established and the unknown parameters of the model are estimated by Markov Chain Monte Carlo method. Finally, the applicability and effectiveness of the proposed method are verified by the comparative analysis of turbine engine.

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Discrete Weibull-Rayleigh distribution properties and parameter estimations

Cited by 3 publications

References 20 publications

On maximum likelihood estimates of a proportional hazard rate model parameters based on record values

On maximum likelihood estimates of a proportional hazard rate model parameters based on record values

Rayleigh-Monte Carlo Method for Image Noise Detection and Elimination

Bivariate and two-phase degradation modeling and reliability analysis with random effects

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