Parameter Estimation of Lindley Distribution Based on Progressive Type-II Censored Competing Risks Data with Binomial Removals

Nie, Jiaxin; Gui, Wenhao

doi:10.3390/math7070646

Cited by 5 publications

(8 citation statements)

References 18 publications

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“…The algorithm for generating the adaptive Type II hybrid censored data can be found in Reference [8]. We make a basic adaptation of the algorithm just as Reference [17] did in their paper to generate adaptive Type II progressive hybrid censored data with competing risks. The algorithm to generate the simulated data can be found in Algorithm 1.…”

Section: Simulationmentioning

confidence: 99%

Estimating the Parameters of the Two-Parameter Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Data with Competing Risks

Liu

Gui

2020

Mathematics

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This paper attempts to estimate the parameters for the two-parameter Rayleigh distribution based on adaptive Type II progressive hybrid censored data with competing risks. Firstly, the maximum likelihood function and the maximum likelihood estimators are derived before the existence and uniqueness of the latter are proven. Further, Bayesian estimators are considered under symmetric and asymmetric loss functions, that is the squared error loss function, the LINEXloss function, and the general entropy loss function. As the Bayesian estimators cannot be obtained explicitly, the Lindley method is applied to compute the approximate Bayesian estimates. Finally, a simulation study is conducted, and a real dataset is analyzed for illustrative purposes.

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Section: Simulationmentioning

confidence: 99%

Estimating the Parameters of the Two-Parameter Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Data with Competing Risks

Liu

Gui

2020

Mathematics

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“…Therefore, the EB estimator of σ 2 for PL function is shown by (23), as shown at the bottom of the next page where…”

Section: ) Obtain the Eb Estimator Of µ With Respect To The Pl Functionmentioning

confidence: 99%

“…It is applied in quality assurance of production and used to decide for producers and statisticians. The researches of EB method using loss functions, can be seen in [16]- [23]. In addition, the EB method was also applied to estimate the percentage of defective units when the lots were accepted [24].…”

Section: Introductionmentioning

confidence: 99%

Empirical Bayes Based on Squared Error Loss and Precautionary Loss Functions in Sequential Sampling Plan

et al. 2020

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An acceptance sampling plans are statistical tools in quality control which often used for lot inspection in several areas such as industry, engineering and business. It can be applied for preserving the quality of products in industry process and preserving the producer's risk and consumer's risk in the production process of manufactures. The objective of this study is to utilize the Empirical Bayes approach based on squared error loss and precautionary loss functions for parameter estimation in sequential sampling plans. The parameters are estimated using Lindley's approximation technique, and hyper-parameters can be obtained via Gibbs sampling technique. Data are normally distributed under an unknown mean and variance. The proposed plans are compared with traditional approaches including a single sampling plan and sequential sampling plan. The probability of acceptance (P a) and average sample number (ASN) are used as criterion for comparison. Results show that the proposed plans yielded the smaller ASN and higher P a than both classical methods.

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“…However, due to the popularity of the exponential distribution in many fields, the Lindley distribution has yet to be very well explored and has attracted little attention in the literature [6,7]. The Lindley distribution, as first proposed by Lindley [8], is a two-component mixture comprising of an exponential and a gamma distribution [9]. Over the last decade, research for the purpose of proposing a new model related to the family of Lindley distributions has attracted considerable interest by several researchers [10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach

2020

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In the modeling and analysis of reliability data via the Lindley distribution, the maximum likelihood estimator is the most commonly used for parameter estimation. However, the maximum likelihood estimator is highly sensitive to the presence of outliers. In this paper, based on the probability integral transform statistic, a robust and efficient estimator of the parameter of the Lindley distribution is proposed. We investigate the relative efficiency of the new estimator compared to that of the maximum likelihood estimator, as well as its robustness based on the breakdown point and influence function. It is found that this new estimator provides reasonable protection against outliers while also being simple to compute. Using a Monte Carlo simulation, we compare the performance of the new estimator and several well-known methods, including the maximum likelihood, ordinary least-squares and weighted least-squares methods in the absence and presence of outliers. The results reveal that the new estimator is highly competitive with the maximum likelihood estimator in the absence of outliers and outperforms the other methods in the presence of outliers. Finally, we conduct a statistical analysis of four reliability data sets, the results of which support the simulation results.

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Parameter Estimation of Lindley Distribution Based on Progressive Type-II Censored Competing Risks Data with Binomial Removals

Cited by 5 publications

References 18 publications

Estimating the Parameters of the Two-Parameter Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Data with Competing Risks

Estimating the Parameters of the Two-Parameter Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Data with Competing Risks

Empirical Bayes Based on Squared Error Loss and Precautionary Loss Functions in Sequential Sampling Plan

Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach

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