Share
حول مقدرات التقلص لمعلمة الشكل لتوزيع رالي المعمم == On Shrinkage Estimator for the Shape Parameter of Generalized Rayleigh Distribution
Author name:
ميمونة محمد امين بكري
Supervisor name:
عباس نجم سلمان
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Master
University:
University of Baghdad - College Of Science - Department Of Mathematics
Language:
English
University location:
Baghdad
First pages:
27T996 - p.pdf
Abstract:
The present work is concerned with estimate the shape parameter α of Generalized Rayleigh Distribution when the scale parameter () is known (=1). And when a prior estimate about the actual value α is available by using some preliminary tests single and double stage shrinkage estimators as well as some Preliminary test Single and Double Stage Minimax Shrinkage Estimators and when select a suitable regions and shrinkage weight function as φ ( ̂) , whereφ ( ̂) , which may be constant or function depends on classical estimator ̂.Expressions for Bias, Mean squared error (MSE), Relative Efficiency, Expected sample size, Expected sample size proportion, probability for avoiding the second sample and percentage of overall sample saved for the proposed estimator are derived In order to study the behavior of the proposed estimators. Conclusions and Numerical results of the mentioned expressions of the propose estimators about deferent constant involved init were displayed in a table in the end of each chapter, using Mathcad program.Finally provide some Comparisons between the suggested estimators with each other’s , classical estimators and with some similar studies were demonstrated to showing the usefulness of the suggested estimators using some statistical indicators like Mean Squared Error, Relative Efficiency and Bias Ratio. The results concluded that the preliminary test single and preliminary test Minimax stage shrinkage estimators better than classical estimator and Minimax estimator, as well as, the preliminary test Double stage and preliminary test Double stage Minimax shrinkage estimators better in terms of Relative Efficiency and Bias Ratio in one hand and reduces the effort and cost of samples is very expensive or difficult to obtain in the others.
