Reliability estimation and parameter estimation for inverse Weibull distribution under different loss functions

Yılmaz, Asuman; Kara, Mahmut

doi:10.48129/kjs.v49i1.9967

Cited by 4 publications

(2 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…That is why the two-parameter IWD has attracted the attention of more and more researchers and has caused discussion among them in recent years [17,18]. For example, Asuman and Mahmut [19] considered the classical and Bayesian estimation of parameters and the reliability function of the IWD. In classical estimation, they derived the ML estimators and modified ML estimators.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution

Ren

Han

2023

Mathematics

View full text Add to dashboard Cite

In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve the likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real dataset are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation.

show abstract

Section: Introductionmentioning

confidence: 99%

Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution

Ren

Han

2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…Therefore, it is appropriate to use IWD for data fitting in many cases. Yilmaz and Kara [1] investigated the classical and Bayesian estimation methods for estimating the reliability of IWD. The classical approach involved obtaining the maximum likelihood estimation and the modified maximum likelihood estimation.…”

Section: Introductionmentioning

confidence: 99%

Reliability Estimation of Inverse Weibull Distribution Based on Intuitionistic Fuzzy Lifetime Data

Hu,

Ren

2023

Axioms

View full text Add to dashboard Cite

As a commonly used model in reliability analysis, the inverse Weibull distribution (IWD) is widely applied in various scientific fields. This paper considers the reliability estimation of the IWD based on intuitionistic fuzzy lifetime data. Firstly, the related concepts of the fuzzy set theory are reviewed, and the concepts of the intuitionistic fuzzy conditional density, intuitionistic fuzzy likelihood function, and intuitionistic fuzzy conditional expectation are obtained by extension. In classical estimations, the maximum likelihood estimators of parameters and reliability are derived. Due to the nonlinearity, the EM algorithm is used to obtain the maximum likelihood estimates. In the Bayesian estimation, the gamma prior is selected, and the Bayesian estimation of the parameters and reliability is conducted under the symmetric entropy and the scale square error loss function, respectively. Since the integrals are complicated, the Lindley approximation is used to approximate the Bayesian estimates. Then, the performance of these estimators is evaluated by the Monte Carlo simulation. The simulation results show that the Bayesian estimation is more suitable than the maximum likelihood estimation for the reliability estimation. Finally, a set of real data is used to prove the effectiveness of these proposed methods. Through these methods, the reliability of the intuitive fuzzy life data is accurately estimated, which provides an important reference for the reliability analysis in the scientific field.

show abstract

Bayesian Modeling for a Shape Parameter of Weibull-Lomax Distribution with an Application to Health Data

Irfan,

Sharma

2024

Communications in Computer and Information Science

View full text Add to dashboard Cite

Reliability estimation and parameter estimation for inverse Weibull distribution under different loss functions

Cited by 4 publications

References 32 publications

Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution

Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution

Reliability Estimation of Inverse Weibull Distribution Based on Intuitionistic Fuzzy Lifetime Data

Bayesian Modeling for a Shape Parameter of Weibull-Lomax Distribution with an Application to Health Data

Contact Info

Product

Resources

About