عنوان البحث(Papers / Research Title)
bayesian fixed sample size procedure for selecting the least prbable event in multinomial distribution
الناشر \ المحرر \ الكاتب (Author / Editor / Publisher)
كوثر فوزي حمزة الحسن
Citation Information
كوثر,فوزي,حمزة,الحسن ,bayesian fixed sample size procedure for selecting the least prbable event in multinomial distribution , Time 5/12/2011 5:23:29 PM : كلية التربية للعلوم الصرفة
وصف الابستركت (Abstract)
bayesian fixed sample size procedure for selecting the least prbable event in multinomial distribution, bayesian dection -theoretical approach is used
الوصف الكامل (Full Abstract)
Bayesian Fixed Sample Size Procedure for Selecting the Least Probable Event in Multinomal Distribution
By
Saad A.Madhi and Kawther F .Hamza
Dept .of Mathematics College of Education.
ABSTRACT
In this paper, a fixed sample size prosedure for selecting the least probable event (i.e ,the cell with smallest probability ) in multinomial distribution is given .Bayesian decision –theoretic approach is used to construct this procedure.Bayes risks of taking decisions under linear losses and Dirichelet priors are derived .
1. Introduction
Consider the multinomial distribution with k cells and unknown probabilities of an observation in the ith cell ,(i=1,2,….,k),where . It is required to find the cell with the smallest (least) probability (best cell in this sense).There are many practical situations where a solution to this problem is required . For example ,we have a sample of blood from each of a large number of populations in a certain city ,and each person is classifed as type A, type B, type AB, or type O,since we wish to identify the blood type that is more rare ,the goal is to determine which blood type occurs least frequently among these persons .
The problem of selecting the smallest cell probability has been considered by Alam and Thompson (1972) using indefference zone approach . According to this approach ,the cell with smallest count is selected as the least probable event ,with ties broken by randomization .
Let (1/k < <1) and c ,(0<c<1/k-1) by given .the smallest count should be determined for probability of correct select selection whenever , (i=1, 2, …, k).
This paper deals with Bayesian fixed sample size procedure for selecting the least cell probability in multinomial distribution whose parameters are distributed a prior according to a Dirichlet distribution. Section 2 contains the formulation of the problem .Section 3 ,presents the prior and posterior probabilities .In section 4 ,we develop a procedure for selecting the smallest cell probability in multinomial distribution using a Bayesian Decision – theoretic approach . Section 5 contains some concluding remarks and future works .
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