Estimation of the Inverse Weibull Distribution Parameters under Type-I Hybrid Censoring

Kazemi, Mohammad; Azizpoor, Mina

doi:10.17713/ajs.v50i5.1134

Cited by 4 publications

(3 citation statements)

References 17 publications

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“…then by substituting eq (14) and (15) in eq (12) and doing some calculus TVaR function of IW distribution will be:…”

Section: Deriving Tvar Functionmentioning

confidence: 99%

“…Kundu and Howlader (2010) had considered the Bayesian inference and forecast difficulties of the inverse Weibull distribution depending on type II censored data, while Kumar (2019) estimated parameters and reliability characteristics IW distribution depending on random censoring model by both Maximum likelihood and Bayesian estimation methods. The case of type 1 hybrid censored data was considered by Kazemi and Azizpoor (2021) where they studied the Bayesian and classical inference of this distribution.…”

Section: Introductionmentioning

confidence: 99%

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Maximum Likelihood Estimation in the Inverse Weibull Distribution with Type II Censored Data

Alshaikh¹,

Baklizi²

2022

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We consider maximum likelihood estimation for the parameters and certain functions of the parameters in the Inverse Weibull (IW) distribution based on type II censored data. The functions under consideration are the Mean Residual Life (MRL), which is very important in reliability studies, and Tail Value at Risk (TVaR), which is an important measure of risk in actuarial studies. We investigated the performance of the MLE of the parameters and derived functions under various experimental conditions using simulation techniques. The performance criteria are the bias and the mean squared error of the estimators. Recommendations on the use of the MLE in this model are given. We found that the parameter estimators are almost unbiased, while the MRL and TVaR estimators are asymptotically unbiased. Moreover, the mean squared error of all estimators decreased for larger sample sizes and it increased when the censoring proportion is increased for a fixed sample size. The conclusion is that the maximum likelihood method of estimation works well for the parameters and the derived functions of the parameter like the MRL and TVaR. Two examples on a real data set are presented to illustrate the application of the methods used in this paper. The first one is on survival time of pigs while the other is on fire losses.

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“…then by substituting eq (14) and (15) in eq (12) and doing some calculus TVaR function of IW distribution will be:…”

Section: Deriving Tvar Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Maximum Likelihood Estimation in the Inverse Weibull Distribution with Type II Censored Data

Alshaikh¹,

Baklizi²

2022

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“…Aefa et al (2021) obtained estimates of the parameters from a mixture of inverse Chen and inverse Rayleigh lifetime models based on Type-I HCS. Kazemi and Azizpoor (2021) studied the inverse Weibull distribution under Type-I HCS. Garg and Kumar (2021) derived the MLE and Bayes estimate of P for a generalized inverted exponential distribution under the HCS.…”

Section: Introductionmentioning

confidence: 99%

Estimation and prediction in generalized half logistic lifetime model using hybrid censored data

Soni

Shukla²,

Kumar

2023

IJQRM

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PurposeThis article aims to develop procedures for estimation and prediction in case of Type-I hybrid censored samples drawn from a two-parameter generalized half-logistic distribution (GHLD).Design/methodology/approachThe GHLD is a versatile model which is useful in lifetime modelling. Also, hybrid censoring is a time and cost-effective censoring scheme which is widely used in the literature. The authors derive the maximum likelihood estimates, the maximum product of spacing estimates and Bayes estimates with squared error loss function for the unknown parameters, reliability function and stress-strength reliability. The Bayesian estimation is performed under an informative prior set-up using the “importance sampling technique”. Afterwards, we discuss the Bayesian prediction problem under one and two-sample frameworks and obtain the predictive estimates and intervals with corresponding average interval lengths. Applications of the developed theory are illustrated with the help of two real data sets.FindingsThe performances of these estimates and prediction methods are examined under Type-I hybrid censoring scheme with different combinations of sample sizes and time points using Monte Carlo simulation techniques. The simulation results show that the developed estimates are quite satisfactory. Bayes estimates and predictive intervals estimate the reliability characteristics efficiently.Originality/valueThe proposed methodology may be used to estimate future observations when the available data are Type-I hybrid censored. This study would help in estimating and predicting the mission time as well as stress-strength reliability when the data are censored.

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Modified Maximum Likelihood Estimation of the Inverse Weibull Model

Kayid,

Alshehri

2023

Axioms

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The inverse Weibull model is a simple and flexible model used for survival analysis, reliability theory, and other scientific fields. The main problem in this context is the estimation of the model parameters. In this study, a modified version of the maximum likelihood estimator is presented. The idea behind it is that the likelihood equation for the shape parameters of the model is biased; therefore, an unbiased version was defined. The new estimator is based on the definition of an unbiased likelihood equation. Simulation results show that the new modified estimator for the shape parameter has a smaller mean square error. Finally, the proposed estimator and the maximum likelihood estimator were compared in the analysis of the three real data sets.

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Estimation of the Inverse Weibull Distribution Parameters under Type-I Hybrid Censoring

Cited by 4 publications

References 17 publications

Maximum Likelihood Estimation in the Inverse Weibull Distribution with Type II Censored Data

Maximum Likelihood Estimation in the Inverse Weibull Distribution with Type II Censored Data

Estimation and prediction in generalized half logistic lifetime model using hybrid censored data

Modified Maximum Likelihood Estimation of the Inverse Weibull Model

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