• Research in Mathematical Education
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• v.15 no.2
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• pp.127-140
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• 2011

"Statistical literacy" is important to be an effective citizen ([Gal, I. (2005). Towards "probability literacy" for all citizens: Building blocks and instructional dilemmas. In: G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39-63). New York: Springer]). Probability and statistics has been connected with real context and can be used to stimulate students' creative abilities. This study aims at identifying the extent that textbooks in three countries include experimental probability concepts and non-routine, open-ended, application and contextual problems. How well textbooks reflect real application situations is important in the sense that students can employ probability concepts when solving real world problems. Results showed that three textbook series did not mention experimental probability. Furthermore, all of text-books had more routine, close-ended, knowing, and non-contextual problems.

• Water Engineering Research
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• v.4 no.3
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• pp.155-173
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• 2003

Parameters and quantiles of the 2-parameter generalized Pareto distribution were estimated using the methods of regular moments, modified moments, probability weighted moments, linear moments, maximum likelihood, and entropy for Monte Carlo-generated samples. The performance of these seven estimators was statistically compared, with the objective of identifying the most robust estimator. It was found that in general the methods of probability-weighted moments and L-moments performed better than the methods of maximum likelihood estimation, moments and entropy, especially for smaller values of the coefficient of variation and probability of exceedance.

• Ocean Systems Engineering
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• v.1 no.3
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• pp.249-261
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• 2011

The stochastic nonlinear dynamic behavior and probability density function of ship rolling are studied using the nonlinear dynamical systems approach and probability theory. The probability density function of the rolling response is evaluated through solving the Fokker Planck Equation using the path integral method based on a Gauss-Legendre interpolation scheme. The time-dependent probability of ship rolling restricted to within the safe domain is provided and capsizing is investigated from the probability point of view. The random differential equation of ships' rolling motion is established considering the nonlinear damping, nonlinear restoring moment, white noise and colored noise wave excitation.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.30 no.2
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• pp.51-57
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• 2007

The expected busy period for the controllable M/G/1 queueing model operating under the triadic policy is derived by using the pseudo probability density function which is totally different from the actual probability density function. In order to justify the approach using the pseudo probability density function to derive the expected busy period for the triadic policy, well-known expected busy periods for the dyadic policies are derived from the obtained result as special cases.

• 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 Korean Statistical Society
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• v.19 no.2
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• pp.122-127
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• 1990

Consider the following problem in the large deviation theory. For constants $a_1, \cdots, a_p$ the tail probability $P(M_1 > a_1, \cdots, M_p > a_p)$ of the sample medians $(M_1, \cdots, M_p)$ is supposed to converge to zero as sample size increases. This paper shows that this probability converges to zero exponentially fast and estimates the convergence rates of the above tail probability of the sample medians. Also compare with the rates about the sample means.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.529-534
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• 2007

We obtain an explicit expression of the loss probability for the PR/M/1/K queue when the offered load is strictly less than one.

• Journal of Korean Society of Disaster and Security
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• v.6 no.2
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• pp.23-30
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• 2013

A dynamic analysis of random vibration processes is concerned with the first excursion probability based on first passage time during some specified lifetime or duration of the excitation. This study is concerned with the estimation of first-passage probability for hazard fluctuate wind velocity in the major cities reflecting the recent meteorological with largest data samples (yearly 2003-2012). The basic wind speeds were standardized homogeneously to the surface roughness category C, and to 10m above the ground surface. In this paper, the hazard fluctuate wind velocities are treated as a time-independent (stationary) random process and Gaussian random processes. The first excursion probability were calculated from Poisson model based on the independent event of level crossing & two-state Markov model based on the envelopes of level crossing.

• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.377-385
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• 2013

We consider a compound Poisson risk model in which the premium rate changes when the surplus exceeds a threshold. The explicit form of the ruin probability for the risk model is obtained by deriving and using the overflow probability of the workload process in the corresponding M/G/1 queueing model.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.393-401
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• 1997

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.