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Article
Minimax Estimation Of The Parameter Of The Maxwell Distribution Under Quadratic Loss Function
تقدير Minimax لمعلمة توزيع ماكسويل تحت دالة الخسارة التربيعية

Author: Huda, A. Rasheed هدى عبدالله رشيد
Journal: Al-Rafidain University College For Sciences مجلة كلية الرافدين الجامعة للعلوم ISSN: 16816870 Year: 2013 Issue: 31 Pages: 43-56
Publisher: Rafidain University College كلية الرافدين الجامعة

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Abstract

This paper is concerned with the problem of finding the minimax estimators of the parameter θ of the Maxwell distribution (MW) for quadratic loss functions by applying the theorem of Lehmann [1950]. Through simulation study the performance of this method compared with the classical methods containing the Maximum Likelihood and moment Estimators with respect to Mean squared-errors (MSEs) .We reach to that the Minimax estimator with small positive values of c gives the best results, followed by the Maximum likelihood estimator

يهتم هذا البحث بمشكلة إيجاد مقدرات Minimax للمعلمة θ لتوزيع ماكسويل (MW) لدوال الخسارة التربيعية من خلال تطبيق نظرية Lehmann [1950]. من خلال دراسة المحاكاة تم مقارنة أداء هذه الطريقة مع الطرائق التقليدية المتضمنة تقديرات الإمكان الأعظم والعزوم بالإعتماد على متوسط مربعات الخطأ (MSEs) وقد تم التوصل إلى أن مقدر Minimax مع قيم صغيرة موجبة الى c يعطي أفضل تقدير، يليه مقدر الإمكان الأعظم.


Article
Electronic excitation produced by proton moving inside polystyrene using Drude model
الاثارة الالكترونية بواسطة بروتونات متحركة داخل البوليسترين باستخدام نموذج درود

Author: Sahar Mezher Mutashar سحر مزهر مطشر
Journal: JOURNAL OF THI-QAR SCIENCE مجلة علوم ذي قار ISSN: 19918690 Year: 2015 Volume: 5 Issue: 3 Pages: 142-149
Publisher: Thi-Qar University جامعة ذي قار

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Abstract

The electronic response of target is characterized by its energy-loss function (ELF) , which it described by several models that fit the available experimental data (at zero momentum transfer), but use different approaches to obtain the Bethe surface so that is to extend the (ELF) to include any energy and momentum transferred. In the present research the Drude dielectric formalism had been used to calculate the probability for an energetic proton to produce electronic excitations in target, Target material used in this research is a polymeric material which is polystyrene. And calculate the effects of ionization fraction of Partial Stopping Power Effective Charge (PSPEC) of polystyrene have been studied and taking into consideration the electronic excitation in the target. Drude Energy Loss Function DELF has been used to take in the consideration the charge exchange, screening length and charge density. FORTRAN-90 program has been written for the mathematical equations using software Compaq visual Fortran90 V 6.6, for linking and execute.

تتميز الاستجابة الإلكترونية للهدف بدالة فقدان الطاقة (ELF) والتي وصفها العديد من النماذج التي تناسب البيانات التجريبية المتاحة (عند الزخم المنتقل الصفري w=0) ولكن استخدام مناهج مختلفة للحصول على سطح بيث (Bethe surface) بحيث يتم توسيع دالة فقدان الطاقة (ELF) لتشمل أي طاقة وزخم منتقل. في هذا البحث تم استخدام دالة العازلة لدرود لحساب احتمالية انتاج الإثارات الإلكترونية بواسطة بروتون فعال في مادة الهدف. مادة الهدف المستخدمة في هذا البحث هي مادة بوليمرية وهي البوليسترين . وقد تم دراسة تاثير الكسر الايوني للشحنة المؤثرة لطاقة الايقاف الجزيئي (PSPEC) من البوليسترين ومع الأخذ بعين الاعتبار الإثارة الإلكترونية في الهدف. وقد اخذت دالة فقدان الطاقة لدرود DELF بنظر الاعتبار تغير الشحنات والكثافة الشحنات. لقد كتب FORTRAN-90 برنامج المعادلات الرياضية باستخدام برنامج Compaq visual Fortran90 V 6.6 للربط والتنفيذ.


Article
The Comparison Between the MLE and Standard Bayes Estimators of the Reliability Function of Exponential Distribution

Journal: Ibn Al-Haitham Journal For Pure And Applied Science مجلة ابن الهيثم للعلوم الصرفة والتطبيقية ISSN: 16094042/ 25213407 Year: 2019 Volume: 32 Issue: 1 Pages: 101-109
Publisher: Baghdad University جامعة بغداد

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Abstract

In this paper, a Monte Carlo Simulation technique is used to compare the performance ofMLE and the standard Bayes estimators of the reliability function of the one parameterexponential distribution. Two types of loss functions are adopted, namely, squared error lossfunction (SELF) and modified square error loss function (MSELF) with informative and noninformativeprior. The criterion integrated mean square error (IMSE) is employed to assessthe performance of such estimators.


Article
Weighted Exponential Distribution: Approximate Bayes Estimations with Fuzzy Data

Authors: Lamyaa K. Hussein --- Nadia Hashim Al-Noor
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2018 Volume: 00 Issue: 1 Pages: 174-185
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

This paper aims to focus on Bayes estimations for the shape and scale parameters along with the reliability function of weighted exponential distribution with fuzzy data. Bayes estimations have been obtained using symmetric and asymmetric loss functions. Lindley's approximation method has been used for the integrals that cannot be solved in closed form. At the end, some comparison for Bayes estimations are studied through a Monte Carlo simulation study.


Article
Comparison of the Suggested loss Function with Generalized Loss Function for One Parameter Inverse Rayleigh Distribution

Author: Emad Farhood AL-Shareefi
Journal: Ibn Al-Haitham Journal For Pure And Applied Science مجلة ابن الهيثم للعلوم الصرفة والتطبيقية ISSN: 16094042/ 25213407 Year: 2017 Volume: 30 Issue: 2 Pages: 224-232
Publisher: Baghdad University جامعة بغداد

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Abstract

The experiences in the life are considered important for many fields, such as industry, medical and others. In literature, researchers are focused on flexible lifetime distribution.In this paper, some Bayesian estimators for the unknown scale parameter of Inverse Rayleigh Distribution have been obtained, of different two loss functions, represented by Suggested and Generalized loss function based on Non-Informative prior using Jeffery's and informative prior represented by Exponential distribution. The performance of estimators is compared empirically with Maximum Likelihood estimator, Using Monte Carlo Simulation depending on the Mean Square Error (MSE). Generally, the preference of Bayesian method of Suggested loss function with Exponential informative prior are the best estimator compared to others.


Article
A NEW PROCEDURE : BAYESIAN SELECTION TO FIND THE BEST OF GEOMETRIC POPULATION UNDER GENERAL LOSS FUNCTION

Author: Samira Faisal Hathoot سميرة فيصل حطحوط
Journal: Journal of Kufa for Mathematics and Computer مجلة الكوفة للرياضيات والحاسوب ISSN: 11712076 Year: 2012 Volume: 1 Issue: 6 Pages: 49-56
Publisher: University of Kufa جامعة الكوفة

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Abstract

In many practical situations theexperimenter is confronted with the problem ofchoosing the best one of a number ofpopulations or categories or ranking themaccording to their performance . This paperderives a procedure for selecting the better ofTwo Geometric populations employing adecision-theoretic Bayesian framework withBeta prior under general loss function .the numerical results for this procedureare given by using Math Works Matlab ver 7.0.1with different loss functions constant , linear andquadratic , where in one equation we can obtainthe Bayes risk for the three types of the lossfunctions : constant , linear and quadratic .


Article
Use the Heavy Alpha Particles in Simulation Experiments to Find Energy Appropriate for Destruction Cancer Cells

Author: Alaa M. Hammadi1 , Khalid A. Ahmaed 2, Asmaa A. Hataem3, Jawad A. Al-Aboudi1
Journal: Iraqi Journal of Biotechnology المجلة العراقية للتقانات الحياتية ISSN: 18154794 Year: 2016 Volume: 15 Issue: 3 Pages: 8-16
Publisher: Baghdad University جامعة بغداد

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Abstract

The importance of using the heavy alpha particles in simulation experiments to find the appropriate energy for destruction cancer cells has multiple applications in physics and medical physics. It is found that the probability of destruction of cancer cells increased at energies lower than few 20 MeV and exponentially decreasing at high energies larger than 20 MeV. The programming language FORTRAN - 90 was used for a required calculation. Different kinetic energies of the incident alpha particle (T = 0.05, 1, 2, 2.5 MeV / u) to destroy cancer cells were employed. The energy loss of incident particle was calculated by dielectric formalism using model Plasmon pole approximation (PPA) model in two target , which are Liquid water and DNA , which more than one wavelength of the incident particle (Brandt and Kitagawa Model) and (Kaneko Model) Good agreement is with previous work was achieved.


Article
Bayesian Estimation for Two Parameters of Gamma Distribution Under Precautionary Loss Function

Journal: Ibn Al-Haitham Journal For Pure And Applied Science مجلة ابن الهيثم للعلوم الصرفة والتطبيقية ISSN: 16094042/ 25213407 Year: 2019 Volume: 32 Issue: 1 Pages: 187-196
Publisher: Baghdad University جامعة بغداد

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Abstract

In the current study, the researchers have been obtained Bayes estimators for the shape andscale parameters of Gamma distribution under the precautionary loss function, assuming thepriors, represented by Gamma and Exponential priors for the shape and scale parametersrespectively. Moment, Maximum likelihood estimators and Lindley’s approximation have beenused effectively in Bayesian estimation.Based on Monte Carlo simulation method, those estimators are compared depending on themean squared errors (MSE’s). The results show that, the performance of Bayes estimator underprecautionary loss function with Gamma and Exponential priors is better than other estimates inall cases.


Article
Estimate the Two Parameters of Gamma Distribution Under Entropy Loss Function

Authors: Loaiy F. Naji --- Huda A. Rasheed
Journal: Iraqi Journal of Science المجلة العراقية للعلوم ISSN: 00672904/23121637 Year: 2019 Volume: 60 Issue: 1 Pages: 127-134
Publisher: Baghdad University جامعة بغداد

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Abstract

AbstractIn this paper, Bayes estimators for the shape and scale parameters of Gammadistribution under the Entropy loss function have been obtained, assuming Gammaand Exponential priors for the shape and scale parameters respectively. Moment,Maximum likelihood estimators and Lindley’s approximation have been usedeffectively in Bayesian estimation. Based on Monte Carlo simulation method, thoseestimators are compared depending on the mean squared errors (MSE’s). The resultsshow that, the performance of the Bayes estimator under Entropy loss function isbetter than other estimates in all cases.


Article
Bayesian Estimators of the parameter and Reliability Function of Inverse Rayleigh Distribution"A comparison study”

Authors: Masooma Ali Abod --- Hazim Mansoor Gorgee
Journal: Ibn Al-Haitham Journal For Pure And Applied Science مجلة ابن الهيثم للعلوم الصرفة والتطبيقية ISSN: 16094042/ 25213407 Year: 2020 Volume: 33 Issue: 2 Pages: 128-139
Publisher: Baghdad University جامعة بغداد

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Abstract

In this paper, Bayesian estimator for the parameter and reliability function of inverseRayleigh distribution (IRD) were obtained Under three types of loss function, namely, squareerror loss function (SELF), Modified Square error loss function (MSELF) and Precautionaryloss function (PLF), taking into consideration the informative and non- informative prior. Theperformance of such estimators was assessed on the basis of mean square error (MSE)criterion by performing a Monte Carlo simulation technique.

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