• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.783-796
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• 2017

In the theory of probability, a Bernoulli trial is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted. In the successive games of scissors paper stone there exists the case of draw in each game. In this paper we are interested in the ultimate success probability of each participant and the expected number of the game till any one of the two has the ultimate victory. Using our results, we can calculate the ultimate winning probability of each player of the two players and the expected number of the game till any one of the two has the ultimate victory in any case whether there is draw or not in each game.

• Journal of the Korean Data and Information Science Society
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• v.27 no.3
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• pp.663-676
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• 2016

In Korean professional baseball the championship team of the year is determined by the four series of games: semi-semi-playoff, semi-playoff, playoff and korean series. To the top 5 teams in a regular season privileges are given to play the games at post season. At semi-semi playoff the winner of two teams which are ranked at 4th and 5th place in the regular season can advance to the game of semi playoff. The winner at semi playoff advances to the playoff to play with the second place team in the regular season. Finally, the championship team is to be determined in the Korean series between the winner of the playoff and the first ranked team in the regular season. We propose methods of how to calculate the winning probabilities of each of high ranked 5 teams advancing to Korean series. From our proposed methods we can estimate the championship probabilities of each of high ranked 5 teams advancing to the Korean series only if we know the winning probabilities between two teams in the regular season or the post season.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.507-516
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• 2011

Comparative studies on generalized binomial models (Moon, 2003; Ng, 1989; Paul, 1985; Kupper and Haseman, 1978; Griffiths, 1973) are restrictive in that the models compared are rather limited and MSE of the estimates is the only measure considered for the model adequacy. This paper is aimed to report simulation results which provide possible guidelines for selecting a proper model. We examine Pearson type of goodness-of-fit statistic to its degrees of freedom and AIC for the overall model quality. MSE and Bias of the individual estimates are also considered as the component fit measures. Performance of some models varies widely for a certain range of the parameter space while most of the models are quite competent. Our evaluation shows that the Extended Beta-Binomial model (Prentice, 1986) turns out to be particularly favorable in the point that it provides consistently excellent fit almost all over the values of the intra-class correlation coefficient and the probability of success.