An improvement on paulson s sequential ranking procedure

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Abstract
Using Jensen s inequality we obtain a tighter bound on the probability of making a correct selection in Paulson s procedure for selecting the normal population which has the largest population mean by replacing Boole s inequality by a geometric inequality As a consequence we are able to use a sharper value for the constant aλ in Paulson s procedure If more than two populations are involved this should lead to an improvement in the expected number of stages to termination and expected total number of observations which is uniform in {delta;∗ P∗}. We also use the same method to improve Swanepoel and Geertsema's procedure for selecting the normal population which has the largest population mean Hoel and Mazumdar s extension of Paulson's procedure for a class of distributions in the Koopman-Darmois family and Hoel and Sobel s elimination "play the winner" procedure for selecting the binomial population with the largest probability of success