Rashad M EL-Sagheer | Al-Azhar University (original) (raw)
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Papers by Rashad M EL-Sagheer
American Journal of Theoretical and Applied Statistics, 2013
In this paper, based on a new type of censoring scheme called a progressive first-failure censore... more In this paper, based on a new type of censoring scheme called a progressive first-failure censored, the maximum likelihood (ML) and the Bayes estimators for the two unknown parameters of the Generalized Pareto (GP) distribution are derived. This type of censoring contains as special cases various types of censoring schemes used in the literature. A Bayesian approach using Markov Chain Monte Carlo (MCMC) method to generate from the posterior distributions and in turn computing the Bayes estimators are developed. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are also proposed. The approximate Bayes estimators have been obtained under the assumptions of informative and non-informative priors. A numerical example is provided to illustrate the proposed methods. Finally, the maximum likelihood and different Bayes estimators are compared via a Monte Carlo simulation study.
International Journal of Computer Applications, Jul 26, 2013
In this paper, the Bayes estimators of the unknown parameters of the Lomax distribution under the... more In this paper, the Bayes estimators of the unknown parameters of the Lomax distribution under the assumptions of gamma priors on both the shape and scale parameters are considered. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are also proposed. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.
Journal of Statistics Applications & Probability, 2016
Journal of Statistics Applications & Probability, 2016
Journal of Statistics Applications & Probability, 2016
Bulletin of the Malaysian Mathematical Sciences Society, 2016
Intelligent Information Management
American Journal of Theoretical and Applied Statistics, 2015
In this paper, we consider the Bayes estimators of the unknown parameters of the exponentiated We... more In this paper, we consider the Bayes estimators of the unknown parameters of the exponentiated Weibull distribution (EWD) under the assumptions of gamma priors on both shape parameters. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are proposed. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. The approximate Bayes estimators obtained under the assumptions of non-informative priors are compared with the maximum likelihood estimators using Monte Carlo simulations. A numerical example is also presented for illustrative purposes.
Arabian Journal of Mathematics, 2015
This paper considers the estimation problem for Burr type-X model, when the lifetimes are collect... more This paper considers the estimation problem for Burr type-X model, when the lifetimes are collected under type-II progressive censoring with random removals, where the number of units removed at each failure time follows a binomial distribution. The methods of maximum likelihood as well as the Bayes procedure to derive both point and interval estimates of the parameters are used. The expected test time to complete the censoring test is computed and analyzed for different censoring schemes. The effect of the binomial distribution parameter p on the expected test time under progressive censoring and the relative expected test time over the complete sample are investigated. Monte Carlo simulations are performed to compare and evaluate the performance of different methods. Furthermore, an example with a real data set is presented for illustrative purposes.
Intelligent Information Management, 2014
Estimation for the parameters of the generalized logistic distribution (GLD) is obtained based on... more Estimation for the parameters of the generalized logistic distribution (GLD) is obtained based on record statistics from a Bayesian and non-Bayesian approach. The Bayes estimators cannot be obtained in explicit forms. So the Markov chain Monte Carlo (MCMC) algorithms are used for computing the Bayes estimates. Point estimation and confidence intervals based on maximum likelihood and the parametric bootstrap methods are proposed for estimating the unknown parameters. A numerical example has been analyzed for illustrative purposes. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.
Journal of Statistics Applications & Probability, 2013
International Journal of Computer Applications, 2013
In this paper, the Bayes estimators of the unknown parameters of the Lomax distribution under the... more In this paper, the Bayes estimators of the unknown parameters of the Lomax distribution under the assumptions of gamma priors on both the shape and scale parameters are considered. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are also proposed. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.
International Journal of Computer Applications, 2013
The coefficient of variation (CV ) of a population is defined as the ratio of the population stan... more The coefficient of variation (CV ) of a population is defined as the ratio of the population standard deviation to the population mean. It is regarded as a measure of stability or uncertainty, and can indicate the relative dispersion of data in the population to the population mean. In this article, based on the upper record values, we study the behavior of the CV of a random variable that follows a Lomax distribution. Specifically, we compute the maximum likelihood estimations (MLEs) and the confidence intervals of CV based on the observed Fisher information matrix using asymptotic distribution of the maximum likelihood estimator and also by using the bootstrapping technique. In addition, we propose to apply Markov Chain Monte Carlo (MCMC) techniques to tackle this problem, which allows us to construct the credible intervals. A numerical example based on a real data is presented to illustrate the implementation of the proposed procedure. Finally, Monte Carlo simulations are performed to observe the behavior of the proposed methods.
Intelligent Information Management, 2013
Estimation for the parameters of the generalized logistic distribution (GLD) is obtained based on... more Estimation for the parameters of the generalized logistic distribution (GLD) is obtained based on record statistics from a Bayesian and non-Bayesian approach. The Bayes estimators cannot be obtained in explicit forms. So the Markov chain Monte Carlo (MCMC) algorithms are used for computing the Bayes estimates. Point estimation and confidence intervals based on maximum likelihood and the parametric bootstrap methods are proposed for estimating the unknown parameters. A numerical example has been analyzed for illustrative purposes. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.
Intelligent Information Management, 2013
In this article, we study the problem of predicting future records and order statistics (two-samp... more In this article, we study the problem of predicting future records and order statistics (two-sample prediction) based on progressive type-II censored with random removals, where the number of units removed at each failure time has a discrete binomial distribution. We use the Bayes procedure to derive both point and interval bounds prediction. Bayesian point prediction under symmetric and symmetric loss functions is discussed. The maximum likelihood (ML) prediction intervals using "plug-in" procedure for future records and order statistics are derived. An example is discussed to illustrate the application of the results under this censoring scheme. A. A. SOLIMAN ET AL. 163 random removals. In Section 4, the ML prediction both point and interval prediction using "plug-in" procedure are derived. In Section 5, Bayesian predictive distribution for the future order statistics based on progressive type-II censored with random removals. In Section 6, the ML prediction both point and interval prediction using "plugin" procedure for the future order statistics are derived. A practical example using generating data set Progressively type-II censored random sample from Burr-X distribution, and a simulation study has been carried out in order to compare the performance of different methods of prediction are presented in Section 8. Finally we conclude the paper in Section 8.
Economic Quality Control, 2014
Intelligent Information Management, 2013
In this paper, the inference for the Burr-X model under progressively first-failure censoring sch... more In this paper, the inference for the Burr-X model under progressively first-failure censoring scheme is discussed. Based on this new censoring were the number of units removed at each failure time has a discrete binomial distribution. The maximum likelihood, Bootstrap and Bayes estimates for the Burr-X distribution are obtained. The Bayes estimators are obtained using both the symmetric and asymmetric loss functions. Approximate confidence interval and highest posterior density interval (HPDI) are discussed. A numerical example is provided to illustrate the proposed estimation methods developed here. The maximum likelihood and the different Bayes estimates are compared via a Monte Carlo simulation study.
American Journal of Theoretical and Applied Statistics, 2013
In this paper, based on a new type of censoring scheme called a progressive first-failure censore... more In this paper, based on a new type of censoring scheme called a progressive first-failure censored, the maximum likelihood (ML) and the Bayes estimators for the two unknown parameters of the Generalized Pareto (GP) distribution are derived. This type of censoring contains as special cases various types of censoring schemes used in the literature. A Bayesian approach using Markov Chain Monte Carlo (MCMC) method to generate from the posterior distributions and in turn computing the Bayes estimators are developed. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are also proposed. The approximate Bayes estimators have been obtained under the assumptions of informative and non-informative priors. A numerical example is provided to illustrate the proposed methods. Finally, the maximum likelihood and different Bayes estimators are compared via a Monte Carlo simulation study.
International Journal of Computer Applications, Jul 26, 2013
In this paper, the Bayes estimators of the unknown parameters of the Lomax distribution under the... more In this paper, the Bayes estimators of the unknown parameters of the Lomax distribution under the assumptions of gamma priors on both the shape and scale parameters are considered. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are also proposed. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.
Journal of Statistics Applications & Probability, 2016
Journal of Statistics Applications & Probability, 2016
Journal of Statistics Applications & Probability, 2016
Bulletin of the Malaysian Mathematical Sciences Society, 2016
Intelligent Information Management
American Journal of Theoretical and Applied Statistics, 2015
In this paper, we consider the Bayes estimators of the unknown parameters of the exponentiated We... more In this paper, we consider the Bayes estimators of the unknown parameters of the exponentiated Weibull distribution (EWD) under the assumptions of gamma priors on both shape parameters. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are proposed. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. The approximate Bayes estimators obtained under the assumptions of non-informative priors are compared with the maximum likelihood estimators using Monte Carlo simulations. A numerical example is also presented for illustrative purposes.
Arabian Journal of Mathematics, 2015
This paper considers the estimation problem for Burr type-X model, when the lifetimes are collect... more This paper considers the estimation problem for Burr type-X model, when the lifetimes are collected under type-II progressive censoring with random removals, where the number of units removed at each failure time follows a binomial distribution. The methods of maximum likelihood as well as the Bayes procedure to derive both point and interval estimates of the parameters are used. The expected test time to complete the censoring test is computed and analyzed for different censoring schemes. The effect of the binomial distribution parameter p on the expected test time under progressive censoring and the relative expected test time over the complete sample are investigated. Monte Carlo simulations are performed to compare and evaluate the performance of different methods. Furthermore, an example with a real data set is presented for illustrative purposes.
Intelligent Information Management, 2014
Estimation for the parameters of the generalized logistic distribution (GLD) is obtained based on... more Estimation for the parameters of the generalized logistic distribution (GLD) is obtained based on record statistics from a Bayesian and non-Bayesian approach. The Bayes estimators cannot be obtained in explicit forms. So the Markov chain Monte Carlo (MCMC) algorithms are used for computing the Bayes estimates. Point estimation and confidence intervals based on maximum likelihood and the parametric bootstrap methods are proposed for estimating the unknown parameters. A numerical example has been analyzed for illustrative purposes. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.
Journal of Statistics Applications & Probability, 2013
International Journal of Computer Applications, 2013
In this paper, the Bayes estimators of the unknown parameters of the Lomax distribution under the... more In this paper, the Bayes estimators of the unknown parameters of the Lomax distribution under the assumptions of gamma priors on both the shape and scale parameters are considered. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are also proposed. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.
International Journal of Computer Applications, 2013
The coefficient of variation (CV ) of a population is defined as the ratio of the population stan... more The coefficient of variation (CV ) of a population is defined as the ratio of the population standard deviation to the population mean. It is regarded as a measure of stability or uncertainty, and can indicate the relative dispersion of data in the population to the population mean. In this article, based on the upper record values, we study the behavior of the CV of a random variable that follows a Lomax distribution. Specifically, we compute the maximum likelihood estimations (MLEs) and the confidence intervals of CV based on the observed Fisher information matrix using asymptotic distribution of the maximum likelihood estimator and also by using the bootstrapping technique. In addition, we propose to apply Markov Chain Monte Carlo (MCMC) techniques to tackle this problem, which allows us to construct the credible intervals. A numerical example based on a real data is presented to illustrate the implementation of the proposed procedure. Finally, Monte Carlo simulations are performed to observe the behavior of the proposed methods.
Intelligent Information Management, 2013
Estimation for the parameters of the generalized logistic distribution (GLD) is obtained based on... more Estimation for the parameters of the generalized logistic distribution (GLD) is obtained based on record statistics from a Bayesian and non-Bayesian approach. The Bayes estimators cannot be obtained in explicit forms. So the Markov chain Monte Carlo (MCMC) algorithms are used for computing the Bayes estimates. Point estimation and confidence intervals based on maximum likelihood and the parametric bootstrap methods are proposed for estimating the unknown parameters. A numerical example has been analyzed for illustrative purposes. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.
Intelligent Information Management, 2013
In this article, we study the problem of predicting future records and order statistics (two-samp... more In this article, we study the problem of predicting future records and order statistics (two-sample prediction) based on progressive type-II censored with random removals, where the number of units removed at each failure time has a discrete binomial distribution. We use the Bayes procedure to derive both point and interval bounds prediction. Bayesian point prediction under symmetric and symmetric loss functions is discussed. The maximum likelihood (ML) prediction intervals using "plug-in" procedure for future records and order statistics are derived. An example is discussed to illustrate the application of the results under this censoring scheme. A. A. SOLIMAN ET AL. 163 random removals. In Section 4, the ML prediction both point and interval prediction using "plug-in" procedure are derived. In Section 5, Bayesian predictive distribution for the future order statistics based on progressive type-II censored with random removals. In Section 6, the ML prediction both point and interval prediction using "plugin" procedure for the future order statistics are derived. A practical example using generating data set Progressively type-II censored random sample from Burr-X distribution, and a simulation study has been carried out in order to compare the performance of different methods of prediction are presented in Section 8. Finally we conclude the paper in Section 8.
Economic Quality Control, 2014
Intelligent Information Management, 2013
In this paper, the inference for the Burr-X model under progressively first-failure censoring sch... more In this paper, the inference for the Burr-X model under progressively first-failure censoring scheme is discussed. Based on this new censoring were the number of units removed at each failure time has a discrete binomial distribution. The maximum likelihood, Bootstrap and Bayes estimates for the Burr-X distribution are obtained. The Bayes estimators are obtained using both the symmetric and asymmetric loss functions. Approximate confidence interval and highest posterior density interval (HPDI) are discussed. A numerical example is provided to illustrate the proposed estimation methods developed here. The maximum likelihood and the different Bayes estimates are compared via a Monte Carlo simulation study.