Contributions to some "Stress-Strength" models in the presence of outliers
Yostina Shehata Morgan Shehata,
Contributions to some "Stress-Strength" models in the presence of outliers مساهمات لبعض نماذج " إجهاد-التحمل" في وجود القيم المتطرفة by Yostina Shehata Morgan Shehata ; Supervised Prof. Amal Soliman Hassan. - 166 Leaves : illustrations ; 30 cm. + CD.
Thesis (Ph.D)-Cairo University, 2025.
Bibliography: Pages 131-137
Outliers play a critical role in statistical analysis, as they can distort model parameters and reduce the accuracy of estimates and model fit. In reliability theory, the stress-strength reliability model is widely applied across disciplines due to its flexibility in modeling real-world systems. In this thesis, the estimation of the stress-strength reliability for the exponentiated half-logistic distribution in the presence of outliers and homogenous case is discussed. The reliability estimator is obtained using the maximum likelihood and Bayesian estimation methods. Using the gamma prior of parameters along with the symmetric and asymmetric loss functions, the Bayesian estimator of R is produced. A simulation study is implemented to compute and compare the performance of estimates in both methods. Application to two real-world datasets from the insurance and physical studies is provided to confirm the results of study. The estimation the stress-strength reliability for the inverted Kumaraswamy distribution in the presence of outliers and homogenous case is discussed as the second contribution. For the traditional method, maximum likelihood estimator and asymptotic confidence interval estimator based on delta method are computed. Furthermore, with independent gamma priors, a Bayesian estimator for R is provided. One could obtain the Bayesian estimator with independent gamma priors for stress-strength parameter using symmetric and asymmetric loss functions. Credible intervals with the highest posterior densities are established. Advanced computations are performed using Markov chain Monte Carlo techniques. Monte Carlo procedure using simulations is designed to implement the precision of estimates for different sample sizes and number of outliers. The performance of estimates is planned by experiments with real data. Furthermore, estimation of stress-strength reliability model for the inverted Kumaraswamy distribution in the presence of outliers and homogenous case, is considered. The maximum likelihood estimator for reliability R* is computed, and a Bayesian estimator employing independent gamma priors is also explored. The outcomes of the numerical study show that both techniques' reliability estimates were enhanced by larger sample numbers in scenarios with and without outliers. Also, three real data sets are applied to the proposed methodology. يعد نموذج "الاجهاد-التحمل" أحد أبرز وأهم نماذج دراسات وقياسات الصلاحية وذلك لتعدد الإستخدامات والتطبيقات لهذا النموذج في مختلف المجالات الهندسية والفيزيائية والطبية وغيرها، وطبقا لهذا النموذج والذي يستخدم لقياسصلاحية مكون واحد يكون له قوة معينة يعمل من خلالها ويتاثر أو يعمل غالبا في ظل مستويمعين من الضغط(الاجهاد) ويظل المكون يعمل بكفاءة طالما أن الضغط الذى يؤثر فيه لم يزد بأى حال عن قوة هذا المكون.قام العديد من الباحثين بدراسة اهمية القيم المتطرفة ودراسة اثرهذة القيم علي النتائج وتعتبر القيم المتطرفة مشكلة بالنسبة للعديد من الإحصائينلانها تتسبب في تشوية النتائج الحقيقية وبالتالي فانها توثر علي اتخاذ القرارات. فيهذهالرسالةتمتقديم ثلاثإسهاماتوهم:تناولالإسهام الأول والذيتمعرضهفي تقدير قيمة صلاحية النموذج R=Pr(Z
Text in English and abstract in Arabic & English.
Mathematical statistics
الإحصاء الرياضي
outliers stress-strength reliability exponentiated half-logistic distribution inverted Kumaraswamy distribution Markov chain Monte Carlo Bayesian estimators القيم المتطرفة الاجهاد-التحمل
519.505
Contributions to some "Stress-Strength" models in the presence of outliers مساهمات لبعض نماذج " إجهاد-التحمل" في وجود القيم المتطرفة by Yostina Shehata Morgan Shehata ; Supervised Prof. Amal Soliman Hassan. - 166 Leaves : illustrations ; 30 cm. + CD.
Thesis (Ph.D)-Cairo University, 2025.
Bibliography: Pages 131-137
Outliers play a critical role in statistical analysis, as they can distort model parameters and reduce the accuracy of estimates and model fit. In reliability theory, the stress-strength reliability model is widely applied across disciplines due to its flexibility in modeling real-world systems. In this thesis, the estimation of the stress-strength reliability for the exponentiated half-logistic distribution in the presence of outliers and homogenous case is discussed. The reliability estimator is obtained using the maximum likelihood and Bayesian estimation methods. Using the gamma prior of parameters along with the symmetric and asymmetric loss functions, the Bayesian estimator of R is produced. A simulation study is implemented to compute and compare the performance of estimates in both methods. Application to two real-world datasets from the insurance and physical studies is provided to confirm the results of study. The estimation the stress-strength reliability for the inverted Kumaraswamy distribution in the presence of outliers and homogenous case is discussed as the second contribution. For the traditional method, maximum likelihood estimator and asymptotic confidence interval estimator based on delta method are computed. Furthermore, with independent gamma priors, a Bayesian estimator for R is provided. One could obtain the Bayesian estimator with independent gamma priors for stress-strength parameter using symmetric and asymmetric loss functions. Credible intervals with the highest posterior densities are established. Advanced computations are performed using Markov chain Monte Carlo techniques. Monte Carlo procedure using simulations is designed to implement the precision of estimates for different sample sizes and number of outliers. The performance of estimates is planned by experiments with real data. Furthermore, estimation of stress-strength reliability model for the inverted Kumaraswamy distribution in the presence of outliers and homogenous case, is considered. The maximum likelihood estimator for reliability R* is computed, and a Bayesian estimator employing independent gamma priors is also explored. The outcomes of the numerical study show that both techniques' reliability estimates were enhanced by larger sample numbers in scenarios with and without outliers. Also, three real data sets are applied to the proposed methodology. يعد نموذج "الاجهاد-التحمل" أحد أبرز وأهم نماذج دراسات وقياسات الصلاحية وذلك لتعدد الإستخدامات والتطبيقات لهذا النموذج في مختلف المجالات الهندسية والفيزيائية والطبية وغيرها، وطبقا لهذا النموذج والذي يستخدم لقياسصلاحية مكون واحد يكون له قوة معينة يعمل من خلالها ويتاثر أو يعمل غالبا في ظل مستويمعين من الضغط(الاجهاد) ويظل المكون يعمل بكفاءة طالما أن الضغط الذى يؤثر فيه لم يزد بأى حال عن قوة هذا المكون.قام العديد من الباحثين بدراسة اهمية القيم المتطرفة ودراسة اثرهذة القيم علي النتائج وتعتبر القيم المتطرفة مشكلة بالنسبة للعديد من الإحصائينلانها تتسبب في تشوية النتائج الحقيقية وبالتالي فانها توثر علي اتخاذ القرارات. فيهذهالرسالةتمتقديم ثلاثإسهاماتوهم:تناولالإسهام الأول والذيتمعرضهفي تقدير قيمة صلاحية النموذج R=Pr(Z
Text in English and abstract in Arabic & English.
Mathematical statistics
الإحصاء الرياضي
outliers stress-strength reliability exponentiated half-logistic distribution inverted Kumaraswamy distribution Markov chain Monte Carlo Bayesian estimators القيم المتطرفة الاجهاد-التحمل
519.505