scholarly journals Estimation of the Parameters of Type-II Discrete Weibull Distribution Under Type-I Censoring

2021 ◽  
Vol 10 (5) ◽  
pp. 1
Author(s):  
Mohamed S. A. Muiftah ◽  
Samir K. Ashour
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Simulation Study ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Type Ii ◽  
Comparison Study ◽  
Numerical Examples ◽  
Mean Squared Errors ◽  
Type I Censoring

Maximum likelihood and proportion estimators of the parameters of the discrete Weibull type II distribution with type I censored data are discussed. A simulation study is performed to generate data from this distribution for suggested values of its parameters and to get the Maximum likelihood estimates of the parameters numerically. The method of proportions suggested by Khan et al. (1989) is also used to estimate the model's parameters. Numerical examples are used to perform a comparison study between the two method results according the values of the estimates and their corresponding mean squared errors.

scholarly journals Optimal Plan and Estimation for Bivariate Step-Stress Accelerated Life Test under Progressive Type-I Censoring

2021 ◽  
pp. 683-694
Author(s):  
Mashroor Ahmad Khan ◽  
Navin Chandra
Keyword(s):  
Maximum Likelihood ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Cumulative Exposure ◽  
Type I ◽  
Life Test ◽  
Type I Censoring ◽  
Accelerated Life ◽  
Progressive Type ◽  
Stress Levels

 In this paper, a step-stress accelerated life test with two stress variables for Weibull distribution under progressive type-I censoring is considered. The stress-life relationship as a log-linear function of stress levels, and for each combination of stress levels, a cumulative exposure model is assumed. The maximum likelihood and Bayes estimates of the model parameters are obtained. The optimum test plan is developed using variance-optimality criterion, which consists in finding out the optimal stress change time by minimizing asymptotic variance of the maximum likelihood estimates of the log of the scale parameter at the design stress. The proposed study illustrated by using simulated data.

The odd Nadarajah-Haghighi family of distributions: properties and applications

2019 ◽  
Vol 56 (2) ◽  
pp. 185-210 ◽  
Author(s):  
Abraão D. C. Nascimento ◽  
Kássio F. Silva ◽  
Gauss M. Cordeiro ◽  
Morad Alizadeh ◽  
Haitham M. Yousof ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Simulation Study ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
New Family ◽  
Mathematical Properties ◽  
The Family ◽  
Family Of Distributions

Abstract We study some mathematical properties of a new generator of continuous distributions called the Odd Nadarajah-Haghighi (ONH) family. In particular, three special models in this family are investigated, namely the ONH gamma, beta and Weibull distributions. The family density function is given as a linear combination of exponentiated densities. Further, we propose a bivariate extension and various characterization results of the new family. We determine the maximum likelihood estimates of ONH parameters for complete and censored data. We provide a simulation study to verify the precision of these estimates. We illustrate the performance of the new family by means of a real data set.

Estimation of P(X

2017 ◽  
Vol 34 (7) ◽  
pp. 1111-1122 ◽  
Author(s):  
Soumya Roy ◽  
Biswabrata Pradhan ◽  
E.V. Gijo
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Quality Characteristic ◽  
Logistic Distribution ◽  
Type Ii ◽  
Finite Sample ◽  
Data Set ◽  
Content Type ◽  
Type Ii Censored Data ◽  
Interval Estimators

Purpose The purpose of this paper is to compare various methods of estimation of P(X<Y) based on Type-II censored data, where X and Y represent a quality characteristic of interest for two groups. Design/methodology/approach This paper assumes that both X and Y are independently distributed generalized half logistic random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator of R are obtained based on Type-II censored data. An exact 95 percent maximum likelihood estimate-based confidence interval for R is also provided. Next, various Bayesian point and interval estimators are obtained using both the subjective and non-informative priors. A real life data set is analyzed for illustration. Findings The performance of various point and interval estimators is judged through a detailed simulation study. The finite sample properties of the estimators are found to be satisfactory. It is observed that the posterior mean marginally outperform other estimators with respect to the mean squared error even under the non-informative prior. Originality/value The proposed methodology can be used for comparing two groups with respect to a suitable quality characteristic of interest. It can also be applied for estimation of the stress-strength reliability, which is of particular interest to the reliability engineers.

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 Estimating the Gumbel-Barnett copula parameter of dependence

2018 ◽  
Vol 41 (1) ◽  
pp. 53-73 ◽  
Author(s):  
Jennyfer Portilla Yela ◽  
José Rafael Tovar Cuevas
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Empirical Evaluation ◽  
Bayesian Estimator ◽  
Dependence Structure ◽  
Type I ◽  
Copula Parameter

In this paper, we developed an empirical evaluation of four estimation procedures for the dependence parameter of the Gumbel-Barnett copula obtained from a Gumbel type I distribution. We used the maximum likelihood, moments and Bayesian methods and studied the performance of the estimates, assuming three dependence levels and 20 different sample sizes. For each method and scenario, a simulation study was conducted with 1000 runs and the quality of the estimator was evaluated using four different criteria. A Bayesian estimator assuming a Beta(a,b) as prior distribution, showed the best performance regardless the sample size and the dependence structure.

scholarly journals Comparing Four Methods for Estimating Tree-Based Treatment Regimes

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Aniek Sies ◽  
Iven Van Mechelen
Keyword(s):  
Simulation Study ◽  
Optimal Treatment ◽  
Treatment Regime ◽  
Type I ◽  
Type Ii ◽  
Type Ii Error ◽  
Treatment Alternative ◽  
Treatment Regimes ◽  
Qualitative Interaction ◽  
Error Probabilities

AbstractWhen multiple treatment alternatives are available for a certain psychological or medical problem, an important challenge is to find an optimal treatment regime, which specifies for each patient the most effective treatment alternative given his or her pattern of pretreatment characteristics. The focus of this paper is on tree-based treatment regimes, which link an optimal treatment alternative to each leaf of a tree; as such they provide an insightful representation of the decision structure underlying the regime. This paper compares the absolute and relative performance of four methods for estimating regimes of that sort (viz., Interaction Trees, Model-based Recursive Partitioning, an approach developed by Zhang et al. and Qualitative Interaction Trees) in an extensive simulation study. The evaluation criteria were, on the one hand, the expected outcome if the entire population would be subjected to the treatment regime resulting from each method under study and the proportion of clients assigned to the truly best treatment alternative, and, on the other hand, the Type I and Type II error probabilities of each method. The method of Zhang et al. was superior regarding the first two outcome measures and the Type II error probabilities, but performed worst in some conditions of the simulation study regarding Type I error probabilities.

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