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a new approach

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 كوثر فوزي حمزة الحسن
5/8/2011 12:20:44 PM
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ABSTRACT
 
Median finding is an essential problem in statistics, it is provides a more robust notion of average than the mean. The measure location median was suggested to find the middle among collection multinomial ordered values. Bayesian procedure to select the median population is presented .prior distribution and linear loss function to find the Bayes risk are used. When the number of observation is odd.
 
1- INTRODUCTION
 
Over the last twenty years there has been considerable effort expended to develop statistically valid ranking-and-selection (R&S) procedures to compare a finite number of simulated alternatives. There exist at least four classes of comparison problems that arise in simulation studies: selecting the system with the largest or smallest expected performance measure (selection of the best), comparing all alternatives against a standard (comparison with a standard), and selecting the system with the largest probability of actually being the best Performer (multinomial selection), and selecting the system with the largest probability of success (Bernoulli selection). The ranking and selection approach is different. It asks given the data on the distributions of these K populations, what is the probability that we can correctly rank them from worst to best?
 
What is the probability that we can choose the best population (perhaps the one with the largest population mean) or at least the best M out of the K populations? [9][5, 1].
 
Now, in many situations (or problems) we want to select the median value (alternative) from among the alternatives .then, How can we get something dose to the median, reasonably quickly? Just like the "quicker selection ", given an unsorted array, how quickly can one select the median element? Median finding is a special case of the more general selection problem which asks for the mth element in sorted order. The median provides a better measure of location than the mean when there are some extremely large or small observations (i.e., when the data are skewed to the right or the left) for this reason, median income is used as the measure of location for the U.S. hoursehold’s income and it is a special case of the more general selection problem which asks for the k th element in sorted order [6].
 
There are several works in the literature treating the exact median selection problem (cf. [BFPRT73], [DZ99], [FJ80], [FR75], [Hoa61], [HPM97]). Traditionally, the “comparison cost model” is adopted, where the only factor considered in the algorithm cost is the number of key-comparisons. The best upper bound on this cost found so far is nearly 3n comparisons in the worst case (cf. [DZ99]). The algorithm described here approximates the median with high precision and lends itself to an immediate implementation.
 
The usefulness of such an algorithm is evident for all applications where it is sufficient to find an approximate median for example in some heap sort variants or for median-filtering in image representation. In addition, the analysis of its precision is of independent interest. All the works mentioned above—as well as ours—assume the selection is from values stored in an array in main memory.

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