• The Korean Journal of Applied Statistics
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• v.18 no.2
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• pp.453-469
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• 2005

In Korea, mathematics education of 11-12 grade students has been taken according to the 7th national mathematics curriculum, which was renovated by the Ministry of Education and Human Resources Development announcement in 1997. The education of probability and statistics has been carried out as a part of this curriculum. We analyze mathematics textbooks-Practical mathematics and Mathematics I- and compare the 7th national mathematics curriculum with the 6th national mathematics curriculum.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.559-570
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• 2011

The role of jurisprudence is examined in the early history of probability and statistics. From the mid-17th to the early 18th century, Christiaan Huygens and Jacob Bernoulli used mathematical expectation to solve the problems that originated from games of chance. We demonstrate that their concept of expectation as a fair price for participating in a game came from the legal concept of 'fair trade'. In addition, we consider that the probability that Bernoulli defined in his Ars Conjectandi originated from the legal concept of 'degree of certainty'. After considering some contributions of Laplace and Poisson, we examined the history of census and statistical survey in the early 19th century. Contrary to the history of the 17th and 18th century, statistics influenced society and law in the 19th century.

• Journal for History of Mathematics
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• v.31 no.5
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• pp.251-269
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• 2018

Empirical probability and classical probability, which are two interpretations of Kolmogorov's axiom, are two ways to recognize the chances of events occurring in the real world. In this paper, I analyzed and suggested the contents of the high school textbooks ${\ll}$Probability and Statistics${\gg}$, associated with two interpretations of probability and experiments on which two interpretations are based. By presenting the cases required expressly stating what the experiment is for supporting students' understanding of some concepts, it was discussed that stating or not stating what the experiment is should be carefully determined by the educational intent. Especially, I suggested that in the textbooks we contrast the good idea of calculating the ratios of two possibilities in the imaginary world of the classical probability with the normal idea of grasping the chances of events through the frequencies in the real world of the empirical probability, with distinguishing the experiments in two interpretations of probability. I also suggested that in the textbooks we make it clear that the Weak Law of Large Numbers justifies our expectations of the frequencies' reflecting the chances of events occurring in the real world under ideal conditions. Teaching and learning about the aesthetic elements and the practicality of imaginary mathematical thinking supported by these textbooks statements could be one form of Humanities education in mathematics as STEAM education.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.333-339
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• 2003

In this paper, we develop the probability matching priors for the parameters of non-regular Pareto distribution. We prove the propriety of joint posterior distribution induced by probability matching priors. Through the simulation study, we show that the proposed probability matching Prior matches the coverage probabilities in a frequentist sense. A real data example is given.

• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.359-371
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• 2003

We consider the probability that the total population of a stable Jackson network reaches a given large value. By using the fluid limit of the reversed network, we derive new upper and lower bounds on this probability, which are sharper than those in Glasserman and Kou (1995). In particular, the improved lower bound is useful for analyzing the performance of an importance sampling estimator for the overflow probability in Jackson tandem networks. Bounds on the expected time to overflow are also obtained.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.433-443
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• 2011

We consider a compound Poisson risk model in which the premiums may depend on the state of the surplus process. By using the overflow probability of the workload process in the corresponding M/G/1 queueing model, we obtain the probability that the ruin occurs before the surplus reaches a given large value in the risk model. We also examplify the ruin probability in case of exponential claims.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.347-361
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• 2014

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto or Lomax distribution. In this paper, we established exact expressions and recurrence relations satised by the quotient moments of generalized order statistics for a generalized Pareto distribution. Further the results for quotient moments of order statistics and records are deduced from the relations obtained and a theorem for characterizing this distribution is presented.

• Proceedings of the Korean Reliability Society Conference
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• 2001.06a
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• pp.301-310
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• 2001

Lim et al.(1998) proposed the Bayesian Imperfect Repair Model, in which a failed system is perfectly repaired with probability P and is minimally repaired with probability 1 - P, where P is not fixed but a random variable with a prior distribution II(p). In this note, the steady state availability of the model is derived and the measure is obtained for several particular prior distribution functions.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.239-250
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• 1994

In this paper, we prove a strong large deviations theorem for the ratio of independent randoem variables with error rate of $O(n^{-1})$. To obtain our results we use the inversion formula for the tail probability and apply the Chaganty and Sethuraman's (1985) approach.

• Communications for Statistical Applications and Methods
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• v.20 no.2
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• pp.157-168
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• 2013

This paper deals with the history of one of the well-known and historically important problems in probability, "Gambler's ruin". This problem was first solved by Pascal and Fermat and published by Huygens in 1657. It was studied and extended by many probabilists in early years and thus, it became an important problem in probability history, introducing many new concepts. We would like to introduce the problem in detail to readers and share the ideas on how new problems are developed, relating to old problems.