Maximum likelihood estimators under progressive Type-I interval censoring

2017 ◽  
Vol 123 ◽  
pp. 202-209 ◽  
Author(s):  
Sonal Budhiraja ◽  
Biswabrata Pradhan ◽  
Debasis Sengupta
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Interval Censoring ◽  
Type I ◽  
Progressive Type

scholarly journals Bayesian estimation for Dagum distribution based on progressive type I interval censoring

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0252556
Author(s):  
Refah Alotaibi ◽  
Hoda Rezk ◽  
Sanku Dey ◽  
Hassan Okasha
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Interval Censoring ◽  
Type I ◽  
Bayes Estimators ◽  
Squared Error Loss ◽  
Squared Error ◽  
Dagum Distribution ◽  
Credible Intervals ◽  
Better Than

In this paper, we consider Dagum distribution which is capable of modeling various shapes of failure rates and aging criteria. Based on progressively type-I interval censoring data, we first obtain the maximum likelihood estimators and the approximate confidence intervals of the unknown parameters of the Dagum distribution. Next, we obtain the Bayes estimators of the parameters of Dagum distribution under the squared error loss (SEL) and balanced squared error loss (BSEL) functions using independent informative gamma and non informative uniform priors for both scale and two shape parameters. A Monte Carlo simulation study is performed to assess the performance of the proposed Bayes estimators with the maximum likelihood estimators. We also compute credible intervals and symmetric 100(1 − τ)% two-sided Bayes probability intervals under the respective approaches. Besides, based on observed samples, Bayes predictive estimates and intervals are obtained using one-and two-sample schemes. Simulation results reveal that the Bayes estimates based on SEL and BSEL performs better than maximum likelihood estimates in terms of bias and MSEs. Besides, credible intervals have smaller interval lengths than confidence interval. Further, predictive estimates based on SEL with informative prior performs better than non-informative prior for both one and two sample schemes. Further, the optimal censoring scheme has been suggested using a optimality criteria. Finally, we analyze a data set to illustrate the results derived.

On inference and design under progressive type-I interval censoring scheme for inverse Gaussian lifetime model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Soumya Roy ◽  
Biswabrata Pradhan ◽  
Annesha Purakayastha
Keyword(s):  
Maximum Likelihood ◽  
Interval Censoring ◽  
Budget Constraints ◽  
Type I ◽  
Inverse Gaussian ◽  
Content Type ◽  
Progressive Type ◽  
Interval Censored ◽  
Optimal Censoring ◽  
Lifetime Model

PurposeThis article considers Inverse Gaussian distribution as the basic lifetime model for the test units. The unknown model parameters are estimated using the method of moments, the method of maximum likelihood and Bayesian methods. As part of maximum likelihood analysis, this article employs an expectation-maximization algorithm to simplify numerical computation. Subsequently, Bayesian estimates are obtained using the Metropolis–Hastings algorithm. This article then presents the design of optimal censoring schemes using a design criterion that deals with the precision of a particular system lifetime quantile. The optimal censoring schemes are obtained after taking into account budget constraints.Design/methodology/approachThis article first presents classical and Bayesian statistical inference for Progressive Type-I Interval censored data. Subsequently, this article considers the design of optimal Progressive Type-I Interval censoring schemes after incorporating budget constraints.FindingsA real dataset is analyzed to demonstrate the methods developed in this article. The adequacy of the lifetime model is ensured using a simulation-based goodness-of-fit test. Furthermore, the performance of various estimators is studied using a detailed simulation experiment. It is observed that the maximum likelihood estimator relatively outperforms the method of moment estimator. Furthermore, the posterior median fares better among Bayesian estimators even in the absence of any subjective information. Furthermore, it is observed that the budget constraints have real implications on the optimal design of censoring schemes.Originality/valueThe proposed methodology may be used for analyzing any Progressive Type-I Interval Censored data for any lifetime model. The methodology adopted to obtain the optimal censoring schemes may be particularly useful for reliability engineers in real-life applications.

scholarly journals A Progressive Interval Type-I Censored Life Test Plan for Rayleigh Distribution

2019 ◽  
Vol 48 (3) ◽  
pp. 76-86
Author(s):  
Arun Kaushik
Keyword(s):  
Rayleigh Distribution ◽  
Interval Censoring ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Test Plan ◽  
Type I Censoring ◽  
Progressive Type ◽  
Interval Type ◽  
Censoring Scheme ◽  
Two Parameter

In this paper, we have considered the problem of optimal inspection times for the progressive interval type-I censoring scheme where uncertainty in the process is governed by the two-parameter Rayleigh distribution. Here, we also introduced some optimality criterion and determined the optimum inspection times, accordingly. The effect of the number of inspections and choice of optimally spaced inspection times based on the asymptotic relative efficiencies of the maximum likelihood estimates of the parameters are also investigated. Further, we have discussed the optimal progressive type-I interval censoring plan when the inspection times and the expected proportions of total failures in the experiment are under control.

scholarly journals On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Jin Xia ◽  
Jie Mi ◽  
YanYan Zhou
Keyword(s):  
Maximum Likelihood ◽  
Lognormal Distribution ◽  
Existence And Uniqueness ◽  
Maximum Likelihood Estimators ◽  
Invariance Property ◽  
Type I ◽  
Grouped Data ◽  
Sample Data ◽  
Censored Sample ◽  
Two Parameters

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

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