A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical pro...A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.展开更多
Accelerated life tests play a vital role in reliability analysis,especially as advanced technologies lead to the production of highly reliable products to meet market demands and competition.Among these tests,progress...Accelerated life tests play a vital role in reliability analysis,especially as advanced technologies lead to the production of highly reliable products to meet market demands and competition.Among these tests,progressive-stress accelerated life tests(PSALT)allow for continuous changes in applied stress.Additionally,the generalized progressive hybrid censoring(GPHC)scheme has attracted significant attention in reliability and survival analysis,particularly for handling censored data in accelerated testing.It has been applied to various failure models,including competing risks and step-stress models.However,despite its growing relevance,a notable gap remains in the literature regarding the application of GPHC in PSALT models.This paper addresses that gap by studying PSALT under a GPHC scheme with binomial removal.Specifically,it considers lifetimes following the quasi-Xgamma distribution.Model parameters are estimated using both maximum likelihood and Bayesian methods under gamma priors.Interval estimation is provided through approximate confidence intervals,bootstrap methods,and Bayesian credible intervals.Bayesian estimators are derived under squared error and entropy loss functions,using informative priors in simulation and non-informative priors in real data applications.A simulation study is conducted to evaluate various censoring schemes,with coverage probabilities and interval widths assessed via Monte Carlo simulations.Additionally,Bayesian predictive estimates and intervals are presented.The proposed methodology is illustrated through the analysis of two real-world accelerated life test datasets.展开更多
In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy di...In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution.These estimates have been obtained using gamma priors based on various loss functions such as squared error,entropy,weighted balance,and minimum expected loss functions.An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators.The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error.Additionally,the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.展开更多
Yu et al. (2012) considered a certain dependent right censorship model. We show that this model is equivalent to the independent right censorship model, extending a result with continuity restriction in Williams and L...Yu et al. (2012) considered a certain dependent right censorship model. We show that this model is equivalent to the independent right censorship model, extending a result with continuity restriction in Williams and Lagakos (1977). Then the asymptotic normality of the product limit estimator under the dependent right censorship model follows from the existing results in the literature under the independent right censorship model, and thus partially solves an open problem in the literature.展开更多
The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximu...The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.展开更多
In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete informat...In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.展开更多
This article proposes a statistical method for working out reliability sampling plans under Type I censored sample for items whose failure times have either normal or lognormal distributions. The quality statistic is ...This article proposes a statistical method for working out reliability sampling plans under Type I censored sample for items whose failure times have either normal or lognormal distributions. The quality statistic is a method of moments estimator of a monotonous function of the unreliability. An approach of choosing a truncation time is recommended. The sample size and acceptability constant are approximately determined by using the Cornish-Fisher expansion for quantiles of distribution. Simulation results show that the method given in this article is feasible.展开更多
A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense t...A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense that the estimators in a certain class have the same expectation as the mean survival time. The estimators have good properties such as strong consistency （with the rate of O（n^-1/1 （log log n）^1/2）） and asymptotic normality. The application to linear regression is considered and the simulation reports are given.展开更多
In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this pap...In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this paper, we also get the interval estimations of the scale parameters.展开更多
Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing d...Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.展开更多
An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical...An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.展开更多
This article deals with the case of the failure-censored constant-stress partially accelerated life test （CSPALT） for highly reliable materials or products assuming the Pareto distribution of the second kind. The ma...This article deals with the case of the failure-censored constant-stress partially accelerated life test （CSPALT） for highly reliable materials or products assuming the Pareto distribution of the second kind. The maximum likelihood （ML） method is used to estimate the parameters of the CSPALT model. The performance of ML estimators is investigated via their mean square error. Also, the average confidence interval length （IL） and the associated co- verage probability （CP） are obtained. Moreover, optimum CSPALT plans that determine the optimal proportion of the test units al- located to each stress are developed. Such optimum test plans minimize the generalized asymptotic variance （GAV） of the ML estimators of the model parameters. For illustration, Monte Carlo simulation studies are given and a real life example is provided.展开更多
Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes,...Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes, the maximum likelihood estimators are established, and the approximate confidence intervals are also constructed via the observed Fisher information matrix.Moreover, Bayes estimates and highest probability density credible intervals are presented and the importance sampling technique is used to compute corresponding results. Finally, the numerical analysis is proposed for illustration.展开更多
This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). ...This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). We consider the maximum likelihood and Bayesian inference of the unknown parameters of the model, as well as the reliability and hazard rate functions. This was done using the conjugate prior for the shape parameter, and discrete prior for the scale parameter. The Bayes estimators hav been obtained relative to both symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Also, based on this new censoring scheme, approximate confidence intervals for the parameters of CRD are developed. A practical example using real data set was used for illustration. Finally, to assess the performance of the proposed estimators, some numerical results using Monte Carlo simulation study were reported.展开更多
This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author als...This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.展开更多
In present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore...In present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore, we get the variance and covariance of the approximate maximum likelihood estimation.展开更多
Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobse...Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).展开更多
Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of ...Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of the new probability distribution function are estimated by the maximum likelihood method under progressive type II censored data via expectation maximization algorithm.展开更多
In this article, a law of iterated logarithm for the maximum likelihood estimator in a random censoring model with incomplete information under certain regular conditions is obtained.
In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially acc...In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.展开更多
文摘A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.
基金supported and funded by the Deanship of Scientifc Research at ImamMohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2503).
文摘Accelerated life tests play a vital role in reliability analysis,especially as advanced technologies lead to the production of highly reliable products to meet market demands and competition.Among these tests,progressive-stress accelerated life tests(PSALT)allow for continuous changes in applied stress.Additionally,the generalized progressive hybrid censoring(GPHC)scheme has attracted significant attention in reliability and survival analysis,particularly for handling censored data in accelerated testing.It has been applied to various failure models,including competing risks and step-stress models.However,despite its growing relevance,a notable gap remains in the literature regarding the application of GPHC in PSALT models.This paper addresses that gap by studying PSALT under a GPHC scheme with binomial removal.Specifically,it considers lifetimes following the quasi-Xgamma distribution.Model parameters are estimated using both maximum likelihood and Bayesian methods under gamma priors.Interval estimation is provided through approximate confidence intervals,bootstrap methods,and Bayesian credible intervals.Bayesian estimators are derived under squared error and entropy loss functions,using informative priors in simulation and non-informative priors in real data applications.A simulation study is conducted to evaluate various censoring schemes,with coverage probabilities and interval widths assessed via Monte Carlo simulations.Additionally,Bayesian predictive estimates and intervals are presented.The proposed methodology is illustrated through the analysis of two real-world accelerated life test datasets.
基金funded by Researchers Supporting Project number(RSPD2025R969),King Saud University,Riyadh,Saudi Arabia.
文摘In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution.These estimates have been obtained using gamma priors based on various loss functions such as squared error,entropy,weighted balance,and minimum expected loss functions.An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators.The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error.Additionally,the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.
文摘Yu et al. (2012) considered a certain dependent right censorship model. We show that this model is equivalent to the independent right censorship model, extending a result with continuity restriction in Williams and Lagakos (1977). Then the asymptotic normality of the product limit estimator under the dependent right censorship model follows from the existing results in the literature under the independent right censorship model, and thus partially solves an open problem in the literature.
基金supported by the National Natural Science Foundation of China(70471057)
文摘The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.
文摘In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.
基金This work is partially supported by National Natural Science Foundation of China (10071090 and 10271013).
文摘This article proposes a statistical method for working out reliability sampling plans under Type I censored sample for items whose failure times have either normal or lognormal distributions. The quality statistic is a method of moments estimator of a monotonous function of the unreliability. An approach of choosing a truncation time is recommended. The sample size and acceptability constant are approximately determined by using the Cornish-Fisher expansion for quantiles of distribution. Simulation results show that the method given in this article is feasible.
基金Supported by the National Natural Science Foundation of China (70171008)
文摘A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense that the estimators in a certain class have the same expectation as the mean survival time. The estimators have good properties such as strong consistency （with the rate of O（n^-1/1 （log log n）^1/2）） and asymptotic normality. The application to linear regression is considered and the simulation reports are given.
基金Supported by the NSF of China(69971016) Supported by the Shanghai Higher Learning Science Supported by the Technology Development Foundation(00JC14507)
文摘In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this paper, we also get the interval estimations of the scale parameters.
文摘Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.
文摘An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.
基金supported by the King Saud University,Deanship of Scientific Research and College of Science Research Center
文摘This article deals with the case of the failure-censored constant-stress partially accelerated life test （CSPALT） for highly reliable materials or products assuming the Pareto distribution of the second kind. The maximum likelihood （ML） method is used to estimate the parameters of the CSPALT model. The performance of ML estimators is investigated via their mean square error. Also, the average confidence interval length （IL） and the associated co- verage probability （CP） are obtained. Moreover, optimum CSPALT plans that determine the optimal proportion of the test units al- located to each stress are developed. Such optimum test plans minimize the generalized asymptotic variance （GAV） of the ML estimators of the model parameters. For illustration, Monte Carlo simulation studies are given and a real life example is provided.
基金supported by the National Natural Science Foundation of China(11501433)the Fundamental Research Funds for the Central Universities(JB180711)
文摘Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes, the maximum likelihood estimators are established, and the approximate confidence intervals are also constructed via the observed Fisher information matrix.Moreover, Bayes estimates and highest probability density credible intervals are presented and the importance sampling technique is used to compute corresponding results. Finally, the numerical analysis is proposed for illustration.
文摘This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). We consider the maximum likelihood and Bayesian inference of the unknown parameters of the model, as well as the reliability and hazard rate functions. This was done using the conjugate prior for the shape parameter, and discrete prior for the scale parameter. The Bayes estimators hav been obtained relative to both symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Also, based on this new censoring scheme, approximate confidence intervals for the parameters of CRD are developed. A practical example using real data set was used for illustration. Finally, to assess the performance of the proposed estimators, some numerical results using Monte Carlo simulation study were reported.
文摘This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.
基金Supported by the NSF of China(69971016)Supported by the Shanghai Higher Learning Science and Technology Development Foundation(04DB24)
文摘In present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore, we get the variance and covariance of the approximate maximum likelihood estimation.
文摘Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).
文摘Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of the new probability distribution function are estimated by the maximum likelihood method under progressive type II censored data via expectation maximization algorithm.
文摘In this article, a law of iterated logarithm for the maximum likelihood estimator in a random censoring model with incomplete information under certain regular conditions is obtained.
基金Supported by National Natural Science Foundation of China(11271039)
文摘In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.
