• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1185-1201
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• 2022

Feller introduced an unfair-fair-game in his famous book [3]. In this game, at each trial, player will win 2^k yuan with probability p_k = 1/2^kk(k + 1), k ∈ ℕ, and zero yuan with probability p₀ = 1 - Σ^∞_k=1 p_k. Because the expected gain is 1, player must pay one yuan as the entrance fee for each trial. Although this game seemed "fair", Feller [2] proved that when the total trial number n is large enough, player will loss n yuan with its probability approximate 1. So it's an "unfair" game. In this paper, we study in depth its convergence in probability, almost sure convergence and convergence in distribution. Furthermore, we try to take 2^k = m to reduce the values of random variables and their corresponding probabilities at the same time, thus a new probability model is introduced, which is called as the related model of Feller's unfair-fair-game. We find out that this new model follows a long-tailed distribution. We obtain its weak law of large numbers, strong law of large numbers and central limit theorem. These results show that their probability limit behaviours of these two models are quite different.

• The Journal of Fisheries Business Administration
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• v.45 no.3
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• pp.55-69
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• 2014

We try to test the pecking order theory of Korean fisheries firm's capital structure using debt capacity. At first, we estimate the debt capacity as the probability of assigning corporate bond rating from credit-rating agencies. We use logit regression model to estimate this probability as a proxy of debt capacity. The major results of this study are as follows. Firstly, we can confirm the fisheries firm's financing behaviour which issues new debt securities for financial deficit. Empirical test of SSM model indicates that the higher probability of assigning corporate bond rating, the higher the coefficient of financial deficit. Especially, high probability group follows this result exactly. Therefore, the pecking order theory of fisheries firm's capital structure applies well for high probability group which means high debt capacity. It also applies for medium and low probability group, but their significances are not good. Secondly, the most of fisheries firms in high probability group issue new debt securities for their financial deficit. Low probability group's fisheries firms also issue new debt securities for their financial deficit within the limit of their debt capacity, but beyond debt capacity they use equity financing for financial deficit. Therefore, the pecking order theory on debt capacity come into existence well in high probability group.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.15 no.6
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• pp.138-149
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• 2016

The study reviewed the effects of the variable speed limit under adverse weather conditions by using a driving simulator. The study assumed that the display of the reduced speed limit without any change of the weather condition and the display of the same speed limit under the change of the weather conditions violate the expectancy of drivers, so it brings the negative effects on the safety. The study regards drivers conformance as the index of the degree of the compliance of driver expectancy, and utilizes the cumulative probability density within the certain range of the speed including displayed speed limit as the quantitative measure of effectiveness. The study reviewed this assumptions by using a driving simulator. As the results, the cases assumed to violate the expectancy of drivers showed the negative effects on the driving behaviour of driver relatively.