A subset selection procedure for multinomial distributions |
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Authors: | Saad T Bakir |
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Institution: | College of Business Administration, Alabama State University , 915 South Jackson St., Montgomery , AL , 36104 , USA |
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Abstract: | A subset selection procedure is developed for selecting a subset containing the multinomial population that has the highest value of a certain linear combination of the multinomial cell probabilities; such population is called the ‘best’. The multivariate normal large sample approximation to the multinomial distribution is used to derive expressions for the probability of a correct selection, and for the threshold constant involved in the procedure. The procedure guarantees that the probability of a correct selection is at least at a pre-assigned level. The proposed procedure is an extension of Gupta and Sobel's 14] selection procedure for binomials and of Bakir's 2] restrictive selection procedure for multinomials. One illustration of the procedure concerns population income mobility in four countries: Peru, Russia, South Africa and the USA. Analysis indicates that Russia and Peru fall in the selected subset containing the best population with respect to income mobility from poverty to a higher-income status. The procedure is also applied to data concerning grade distribution for students in a certain freshman class. |
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Keywords: | income mobility large sample approximation selection procedures singular multivariate normal distribution |
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