The stress-strength S-S method employs a variety of estimation techniques, including maximum like... more The stress-strength S-S method employs a variety of estimation techniques, including maximum likelihood, shrinkage and least square, to determine and estimate the reliability of a particular system R = P (Y 1 < X < Y 2 ) while the system contains a single component with strength X subject to two stresses, Y 1 and Y 2 . With the consumption of Monte Carlo simulation and the statistical measurement Mean Squared Error (MSE), the various estimation methods have been evaluated according to the Restricted Generalized Weibull Distribution (RGWD), the stresses Y 1 and Y 2 and the strength X constitute independent, non-identical random variables in our S-S model.
The stress-strength S-S method employs a variety of estimation techniques, including maximum like... more The stress-strength S-S method employs a variety of estimation techniques, including maximum likelihood, shrinkage and least square, to determine and estimate the reliability of a particular system R = P (Y 1 < X < Y 2) while the system contains a single component with strength X subject to two stresses, Y 1 and Y 2. With the consumption of Monte Carlo simulation and the statistical measurement Mean Squared Error (MSE), the various estimation methods have been evaluated according to the Restricted Generalized Weibull Distribution (RGWD), the stresses Y 1 and Y 2 and the strength X constitute independent, non-identical random variables in our S-S model.
In this paper, we use a variety of nonparametric estimation techniques, based on a sample from co... more In this paper, we use a variety of nonparametric estimation techniques, based on a sample from complete real data, to estimate the survival function of lung cancer patients. This function describes the time a patient with lung cancer is expected to live after receiving a diagnosis of the disease or entering a hospital. The mean squared error was used to compare the aforementioned estimation techniques, and it was found that the shrinkage approach produced the best survival function for lung cancer.
This paper deal with estimate the reliability system which contains one component for the strengt... more This paper deal with estimate the reliability system which contains one component for the strength random variable x subject to the stress random y; R=p(y&lt;x) when the two random variable x and y follow the inverted exponential distribution (IED), using different estimation methods like; maximum likelihood method, least square method, weighted least square method, rank set sampling method, Modified Thompson type shrinkage estimation method. A comparison of the proposed estimation methods by using Monte-carle simulation depend on the mean square error indicator.
The purpose of this article to find and derive the formula of the system reliability in stress-st... more The purpose of this article to find and derive the formula of the system reliability in stress-strength model when the strength x and stress y are independent and follows Chen distribution (GD) with two shapes parameters. After this we concern with estimation the system reliability via different estimation methods namely; Maximum likelihood method (MLE), Least square method (LS), Weighted least square (WLS), Rank regression method (RR), Rank set sampling method (RS) and Percentile estimation method. Finally, the comparisons among the proposed estimation methods through Mote Carle simulation based on mean square error criteria will be made to obtain the best method.
In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The p... more In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The paper has estimated the parameters (shape and scale) using (Maximum likelihood, Modified moment, Lindley (1980) Bayesian approximation technique and Shrinkage Bayesian) methods, and then computing the value of the above-mentioned. We consider the Bayesian estimators for the unknown parameters of the Birnbaum_Saunders distribution under the reference prior. The Bayesian estimators cannot be obtained in closed forms. An approximate Bayesian approach is proposed using the idea of Lindley to obtain the Bayesian estimators. We then calculated and estimated all previous parameters, and compared the numerical estimation using statistical indicators mean absolute percentage error among the four considered estimation methods. Results are compared using Monte Carlo simulations studies carried out showed that the Shrinkage method gave us the best estimator.
This paper deal with estimate the reliability system which contains one component for the strengt... more This paper deal with estimate the reliability system which contains one component for the strength random variable x subject to the stress random y; R=p(y<x) when the two random variable x and y follow the inverted exponential distribution (IED), using different estimation methods like; maximum likelihood method, least square method, weighted least square method, rank set sampling method, Modified Thompson type shrinkage estimation method. A comparison of the proposed estimation methods by using Monte-carle simulation depend on the mean square error indicator.
The purpose of this article to find and derive the formula of the system reliability in stress-st... more The purpose of this article to find and derive the formula of the system reliability in stress-strength model when the strength x and stress y are independent and follows Chen distribution (GD) with two shapes parameters. After this we concern with estimation the system reliability via different estimation methods namely; Maximum likelihood method (MLE), Least square method (LS), Weighted least square (WLS), Rank regression method (RR), Rank set sampling method (RS) and Percentile estimation method. Finally, the comparisons among the proposed estimation methods through Mote Carle simulation based on mean square error criteria will be made to obtain the best method.
In this article, we introduce a new model that extends the inverse Gaussian distribution. This mo... more In this article, we introduce a new model that extends the inverse Gaussian distribution. This model is obtained when a parameter is incorporated into the logarithmic inverse Gaussian distribution producing great flexibility for fitting non-negative data. We present a comprehensive ...
In this study, we present different methods of estimating fuzzy reliability of a two-paramete... more In this study, we present different methods of estimating fuzzy reliability of a two-parameter Rayleigh distribution via the maximum likelihood estimator, median first-order statistics estimator, quartile estimator, L-moment estimator, and mixed Thompson-type estimator. The mean-square error MSE as a measurement for comparing the considered methods using simulation through different values for the parameters and unalike sample sizes is used. The results of simulation show that the fuzziness values are better than the real values for all sample sizes, as well as the fuzzy reliability at the estimation of the Maximum likelihood Method, and Mixed Thompson Method perform better than the other methods in the sense of MSE, so that we recommend to use this type of estimation.
This Research deals with estimation the reliability function of two-parameters Rayleigh distribut... more This Research deals with estimation the reliability function of two-parameters Rayleigh distribution, using different estimation methods like, Maximum likelihood, Median-First Order Statistics, Ridge Regression, Modified Thompson-Type Shrinkage and Single Stage Shrinkage methods. Comparisons among the suggestion estimators were made using Monte Carlo Simulation based on statistical indicter mean squared error (MSE).
In this study, we present different methods of estimating fuzzy reliability of a two-parameter Ra... more In this study, we present different methods of estimating fuzzy reliability of a two-parameter Rayleigh distribution via the maximum likelihood estimator, median first-order statistics estimator, quartile estimator, L-moment estimator, and mixed Thompson-type estimator. The mean-square error MSE as a measurement for comparing the considered methods using simulation through different values for the parameters and unalike sample sizes is used. The results of simulation show that the fuzziness values are better than the real values for all sample sizes, as well as the fuzzy reliability at the estimation of the Maximum likelihood Method, and Mixed Thompson Method perform better than the other methods in the sense of MSE, so that we recommend to use this type of estimation.
Ibn Al-Haitham Journal For Pure And Applied Science, Apr 24, 2017
In this paper we estimate the parameters and related probability functions, survival function, cu... more In this paper we estimate the parameters and related probability functions, survival function, cumulative distribution function , hazard function(failure rate) and failure (death) probability function(pdf) for two parameters Birnbaum-Saunders distribution which is fitting the complete data for the patients of lymph glands cancer. Estimating the parameters (shape and scale) using (maximum likelihood , regression quantile and shrinkage) methods and then compute the value of mentioned related probability functions depending on sample from real data which describe the duration of survivor for patients who suffer from the lymph glands cancer based on diagnosis of disease or the inter of patients in a hospital for period of three years ( start with 2010 to the end of 2012) .Calculating and estimating all previous probability functions , then comparing the numerical estimation by using statistical indicators mean squares error and mean absolute percentage error between the three considered estimation methods with respect to survival function. Concluding that, the survival function for the lymph glands cancer by using shrinkage method is the best.
Ibn AL- Haitham Journal For Pure and Applied Science, 2018
This Research deals with estimation the reliability function for two-parameters Exponenti... more This Research deals with estimation the reliability function for two-parameters Exponential distribution, using different estimation methods ; Maximum likelihood, Median-First Order Statistics, Ridge Regression, Modified Thompson-Type Shrinkage and Single Stage Shrinkage methods. Comparisons among the estimators were made using Monte Carlo Simulation based on statistical indicter mean squared error (MSE) conclude that the shrinkage method perform better than the other methods
This paper focuses on the use of censored data in survival analysis. Survival analysis is used mo... more This paper focuses on the use of censored data in survival analysis. Survival analysis is used most frequently in the case of cancer patients when the study is fi nished and a number of individuals are still alive. The original article cited 2 was declared recently to be the most cited statistical study in the biomedical area. The goal of this paper is to explain the basic principles and methods involved. The way survival analysis processes data and interprets outputs is presented using the clinical data of oncological patients. Methods and Results: Survival analysis is used to estimate survivor function from survival data, to compare survivor functions and to assess the relationship of explanatory variables to survival time. These methods were applied to the data of 176 patients with heamato-oncological diagnoses who had undergone bone marrow blood transplant. It is very important to use appropriate methods when processing statistical data. Standard statistical procedures used for incomplete data could not provide the correct estimation.
In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The p... more In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The paper has estimated the parameters (shape and scale) using (Maximum likelihood, Modified moment, Lindley (1980) Bayesian approximation technique and Shrinkage Bayesian) methods, and then computing the value of the above-mentioned. We consider the Bayesian estimators for the unknown parameters of the Birnbaum_Saunders distribution under the reference prior. The Bayesian estimators cannot be obtained in closed forms. An approximate Bayesian approach is proposed using the idea of Lindley to obtain the Bayesian estimators. We then calculated and estimated all previous parameters, and compared the numerical estimation using statistical indicators mean absolute percentage error among the four considered estimation methods. Results are compared using Monte Carlo simulations studies carried out showed that the Shrinkage method gave us the best estimator.
This Research deals with estimation the reliability function for two-parameters Exponential distr... more This Research deals with estimation the reliability function for two-parameters Exponential distribution, using different estimation methods ; Maximum likelihood, Median-First Order Statistics, Ridge Regression, Modified Thompson-Type Shrinkage and Single Stage Shrinkage methods. Comparisons among the estimators were made using Monte Carlo Simulation based on statistical indicter mean squared error (MSE) conclude that the shrinkage method perform better than the other methods .
This Research deals with estimation the reliability function of two-parameters Rayleigh distribut... more This Research deals with estimation the reliability function of two-parameters Rayleigh distribution, using different estimation methods like, Maximum likelihood, Median-First Order Statistics, Ridge Regression, Modified Thompson-Type Shrinkage and Single Stage Shrinkage methods. Comparisons among the suggestion estimators were made using Monte Carlo Simulation based on statistical indicter mean squared error (MSE).
In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The p... more In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The paper has estimated the parameters (shape and scale) using (Maximum likelihood, Modified moment, Lindley (1980) Bayesian approximation technique and Shrinkage Bayesian) methods, and then computing the value of the above-mentioned. We consider the Bayesian estimators for the unknown parameters of the Birnbaum_Saunders distribution under the reference prior. The Bayesian estimators cannot be obtained in closed forms. An approximate Bayesian approach is proposed using the idea of Lindley to obtain the Bayesian estimators. We then calculated and estimated all previous parameters, and compared the numerical estimation using statistical indicators mean absolute percentage error among the four considered estimation methods. Results are compared using Monte Carlo simulations studies carried out showed that the Shrinkage method gave us the best estimator.
The stress-strength S-S method employs a variety of estimation techniques, including maximum like... more The stress-strength S-S method employs a variety of estimation techniques, including maximum likelihood, shrinkage and least square, to determine and estimate the reliability of a particular system R = P (Y 1 < X < Y 2 ) while the system contains a single component with strength X subject to two stresses, Y 1 and Y 2 . With the consumption of Monte Carlo simulation and the statistical measurement Mean Squared Error (MSE), the various estimation methods have been evaluated according to the Restricted Generalized Weibull Distribution (RGWD), the stresses Y 1 and Y 2 and the strength X constitute independent, non-identical random variables in our S-S model.
The stress-strength S-S method employs a variety of estimation techniques, including maximum like... more The stress-strength S-S method employs a variety of estimation techniques, including maximum likelihood, shrinkage and least square, to determine and estimate the reliability of a particular system R = P (Y 1 < X < Y 2) while the system contains a single component with strength X subject to two stresses, Y 1 and Y 2. With the consumption of Monte Carlo simulation and the statistical measurement Mean Squared Error (MSE), the various estimation methods have been evaluated according to the Restricted Generalized Weibull Distribution (RGWD), the stresses Y 1 and Y 2 and the strength X constitute independent, non-identical random variables in our S-S model.
In this paper, we use a variety of nonparametric estimation techniques, based on a sample from co... more In this paper, we use a variety of nonparametric estimation techniques, based on a sample from complete real data, to estimate the survival function of lung cancer patients. This function describes the time a patient with lung cancer is expected to live after receiving a diagnosis of the disease or entering a hospital. The mean squared error was used to compare the aforementioned estimation techniques, and it was found that the shrinkage approach produced the best survival function for lung cancer.
This paper deal with estimate the reliability system which contains one component for the strengt... more This paper deal with estimate the reliability system which contains one component for the strength random variable x subject to the stress random y; R=p(y&lt;x) when the two random variable x and y follow the inverted exponential distribution (IED), using different estimation methods like; maximum likelihood method, least square method, weighted least square method, rank set sampling method, Modified Thompson type shrinkage estimation method. A comparison of the proposed estimation methods by using Monte-carle simulation depend on the mean square error indicator.
The purpose of this article to find and derive the formula of the system reliability in stress-st... more The purpose of this article to find and derive the formula of the system reliability in stress-strength model when the strength x and stress y are independent and follows Chen distribution (GD) with two shapes parameters. After this we concern with estimation the system reliability via different estimation methods namely; Maximum likelihood method (MLE), Least square method (LS), Weighted least square (WLS), Rank regression method (RR), Rank set sampling method (RS) and Percentile estimation method. Finally, the comparisons among the proposed estimation methods through Mote Carle simulation based on mean square error criteria will be made to obtain the best method.
In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The p... more In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The paper has estimated the parameters (shape and scale) using (Maximum likelihood, Modified moment, Lindley (1980) Bayesian approximation technique and Shrinkage Bayesian) methods, and then computing the value of the above-mentioned. We consider the Bayesian estimators for the unknown parameters of the Birnbaum_Saunders distribution under the reference prior. The Bayesian estimators cannot be obtained in closed forms. An approximate Bayesian approach is proposed using the idea of Lindley to obtain the Bayesian estimators. We then calculated and estimated all previous parameters, and compared the numerical estimation using statistical indicators mean absolute percentage error among the four considered estimation methods. Results are compared using Monte Carlo simulations studies carried out showed that the Shrinkage method gave us the best estimator.
This paper deal with estimate the reliability system which contains one component for the strengt... more This paper deal with estimate the reliability system which contains one component for the strength random variable x subject to the stress random y; R=p(y<x) when the two random variable x and y follow the inverted exponential distribution (IED), using different estimation methods like; maximum likelihood method, least square method, weighted least square method, rank set sampling method, Modified Thompson type shrinkage estimation method. A comparison of the proposed estimation methods by using Monte-carle simulation depend on the mean square error indicator.
The purpose of this article to find and derive the formula of the system reliability in stress-st... more The purpose of this article to find and derive the formula of the system reliability in stress-strength model when the strength x and stress y are independent and follows Chen distribution (GD) with two shapes parameters. After this we concern with estimation the system reliability via different estimation methods namely; Maximum likelihood method (MLE), Least square method (LS), Weighted least square (WLS), Rank regression method (RR), Rank set sampling method (RS) and Percentile estimation method. Finally, the comparisons among the proposed estimation methods through Mote Carle simulation based on mean square error criteria will be made to obtain the best method.
In this article, we introduce a new model that extends the inverse Gaussian distribution. This mo... more In this article, we introduce a new model that extends the inverse Gaussian distribution. This model is obtained when a parameter is incorporated into the logarithmic inverse Gaussian distribution producing great flexibility for fitting non-negative data. We present a comprehensive ...
In this study, we present different methods of estimating fuzzy reliability of a two-paramete... more In this study, we present different methods of estimating fuzzy reliability of a two-parameter Rayleigh distribution via the maximum likelihood estimator, median first-order statistics estimator, quartile estimator, L-moment estimator, and mixed Thompson-type estimator. The mean-square error MSE as a measurement for comparing the considered methods using simulation through different values for the parameters and unalike sample sizes is used. The results of simulation show that the fuzziness values are better than the real values for all sample sizes, as well as the fuzzy reliability at the estimation of the Maximum likelihood Method, and Mixed Thompson Method perform better than the other methods in the sense of MSE, so that we recommend to use this type of estimation.
This Research deals with estimation the reliability function of two-parameters Rayleigh distribut... more This Research deals with estimation the reliability function of two-parameters Rayleigh distribution, using different estimation methods like, Maximum likelihood, Median-First Order Statistics, Ridge Regression, Modified Thompson-Type Shrinkage and Single Stage Shrinkage methods. Comparisons among the suggestion estimators were made using Monte Carlo Simulation based on statistical indicter mean squared error (MSE).
In this study, we present different methods of estimating fuzzy reliability of a two-parameter Ra... more In this study, we present different methods of estimating fuzzy reliability of a two-parameter Rayleigh distribution via the maximum likelihood estimator, median first-order statistics estimator, quartile estimator, L-moment estimator, and mixed Thompson-type estimator. The mean-square error MSE as a measurement for comparing the considered methods using simulation through different values for the parameters and unalike sample sizes is used. The results of simulation show that the fuzziness values are better than the real values for all sample sizes, as well as the fuzzy reliability at the estimation of the Maximum likelihood Method, and Mixed Thompson Method perform better than the other methods in the sense of MSE, so that we recommend to use this type of estimation.
Ibn Al-Haitham Journal For Pure And Applied Science, Apr 24, 2017
In this paper we estimate the parameters and related probability functions, survival function, cu... more In this paper we estimate the parameters and related probability functions, survival function, cumulative distribution function , hazard function(failure rate) and failure (death) probability function(pdf) for two parameters Birnbaum-Saunders distribution which is fitting the complete data for the patients of lymph glands cancer. Estimating the parameters (shape and scale) using (maximum likelihood , regression quantile and shrinkage) methods and then compute the value of mentioned related probability functions depending on sample from real data which describe the duration of survivor for patients who suffer from the lymph glands cancer based on diagnosis of disease or the inter of patients in a hospital for period of three years ( start with 2010 to the end of 2012) .Calculating and estimating all previous probability functions , then comparing the numerical estimation by using statistical indicators mean squares error and mean absolute percentage error between the three considered estimation methods with respect to survival function. Concluding that, the survival function for the lymph glands cancer by using shrinkage method is the best.
Ibn AL- Haitham Journal For Pure and Applied Science, 2018
This Research deals with estimation the reliability function for two-parameters Exponenti... more This Research deals with estimation the reliability function for two-parameters Exponential distribution, using different estimation methods ; Maximum likelihood, Median-First Order Statistics, Ridge Regression, Modified Thompson-Type Shrinkage and Single Stage Shrinkage methods. Comparisons among the estimators were made using Monte Carlo Simulation based on statistical indicter mean squared error (MSE) conclude that the shrinkage method perform better than the other methods
This paper focuses on the use of censored data in survival analysis. Survival analysis is used mo... more This paper focuses on the use of censored data in survival analysis. Survival analysis is used most frequently in the case of cancer patients when the study is fi nished and a number of individuals are still alive. The original article cited 2 was declared recently to be the most cited statistical study in the biomedical area. The goal of this paper is to explain the basic principles and methods involved. The way survival analysis processes data and interprets outputs is presented using the clinical data of oncological patients. Methods and Results: Survival analysis is used to estimate survivor function from survival data, to compare survivor functions and to assess the relationship of explanatory variables to survival time. These methods were applied to the data of 176 patients with heamato-oncological diagnoses who had undergone bone marrow blood transplant. It is very important to use appropriate methods when processing statistical data. Standard statistical procedures used for incomplete data could not provide the correct estimation.
In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The p... more In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The paper has estimated the parameters (shape and scale) using (Maximum likelihood, Modified moment, Lindley (1980) Bayesian approximation technique and Shrinkage Bayesian) methods, and then computing the value of the above-mentioned. We consider the Bayesian estimators for the unknown parameters of the Birnbaum_Saunders distribution under the reference prior. The Bayesian estimators cannot be obtained in closed forms. An approximate Bayesian approach is proposed using the idea of Lindley to obtain the Bayesian estimators. We then calculated and estimated all previous parameters, and compared the numerical estimation using statistical indicators mean absolute percentage error among the four considered estimation methods. Results are compared using Monte Carlo simulations studies carried out showed that the Shrinkage method gave us the best estimator.
This Research deals with estimation the reliability function for two-parameters Exponential distr... more This Research deals with estimation the reliability function for two-parameters Exponential distribution, using different estimation methods ; Maximum likelihood, Median-First Order Statistics, Ridge Regression, Modified Thompson-Type Shrinkage and Single Stage Shrinkage methods. Comparisons among the estimators were made using Monte Carlo Simulation based on statistical indicter mean squared error (MSE) conclude that the shrinkage method perform better than the other methods .
This Research deals with estimation the reliability function of two-parameters Rayleigh distribut... more This Research deals with estimation the reliability function of two-parameters Rayleigh distribution, using different estimation methods like, Maximum likelihood, Median-First Order Statistics, Ridge Regression, Modified Thompson-Type Shrinkage and Single Stage Shrinkage methods. Comparisons among the suggestion estimators were made using Monte Carlo Simulation based on statistical indicter mean squared error (MSE).
In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The p... more In this paper we estimated the parameters for two parameter-Birnbaum−Saunders distribution. The paper has estimated the parameters (shape and scale) using (Maximum likelihood, Modified moment, Lindley (1980) Bayesian approximation technique and Shrinkage Bayesian) methods, and then computing the value of the above-mentioned. We consider the Bayesian estimators for the unknown parameters of the Birnbaum_Saunders distribution under the reference prior. The Bayesian estimators cannot be obtained in closed forms. An approximate Bayesian approach is proposed using the idea of Lindley to obtain the Bayesian estimators. We then calculated and estimated all previous parameters, and compared the numerical estimation using statistical indicators mean absolute percentage error among the four considered estimation methods. Results are compared using Monte Carlo simulations studies carried out showed that the Shrinkage method gave us the best estimator.
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