• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.483-498
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• 1994

Suppose that a stationary process ${X_t}$ has a marginal distribution whose support consists of sufficiently large integers. We are concerned with some analogous law of large numbers for such distribution function F. In particular, we determine a weak law of large numbers for maximum queueing length in $M/M\infty$ system. We also present a limiting behavior for the maxima based on AR(1) process with binomial thining and poisson marginals (INAR(1)) introduced by E. Mckenzie. It turns out that the result of AR(1) process is the same as that of $M/M/\infty$ queueing process in limit when we observe the queues at regularly spaced intervals of time.

• 응용통계연구
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• 제28권3호
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• pp.583-592
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• 2015

영-과잉(zero-inflation) 현상은 최근 계수(count) 시계열 분석의 주요토픽으로 다루어지고 있다. 본 논문에서는 영-과잉 계수 시계열의 변동성을 연구하고 있다. 기존의 정수형 모형인 INGARCH(integer valued GRACH) 모형에 조건부 포아송 및 조건부 음이항 분포를 사용하여 변동성에 영-과잉 현상을 추가하였다. 모수 추정 방법으로 EM알고리즘을 사용하였으며 국내 콜레라 발생건수에 적용시켜 보았다.

• 응용통계연구
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• 제23권4호
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• pp.777-781
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• 2010

Yates' continuity correction of the chi-squared test for testing the homogeneity of two binomial proportions in $2{\times}2$ contingency tables is developed to lower the value of the test statistic slightly. The effect of continuity correction is expected to decrease as the sample size increases. However, in extremely unbalanced $2{\times}2$ contingency tables, we find some cases where the effect of continuity correction is eccentric and is larger than expected. In such cases, we conclude that the chi-squared test with continuity correction should not be employed as a test statistic in both asymptotic tests and exact tests.

• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.493-502
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• 2017

We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

• 호남수학학술지
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• 제5권1호
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• pp.251-260
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• 1983

• 응용통계연구
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• 제28권1호
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• pp.75-82
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• 2015

본 연구에서는 민감한 이항특성에 대한 신뢰구간 추정에 직접질문법과 간접질문법을 사용한다. 간접질문법으로 응답자들의 응답부담을 줄여주기 위해서 확률장치를 사용하는 Warner (1965)의 확률화응답기법(RRT)을 고려한다. 두 방법에 의한 신뢰구간을 비교하기 위해서 평가기준으로 평균포함확률(MCP), 평균제곱오차의 제곱근(RMSE), 그리고 평균기대폭(MEW)을 사용한다. 수치적 비교 결과 RRT의 MCP가 명목수준()을 크게 초과하여 보수적이고 MEW도 매우 크다. 따라서 이들을 보완해 주어야 실제적으로 간접질문법의 유용성을 높일 수 있다.

• Journal of the Korean Statistical Society
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• 제21권2호
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• pp.167-177
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• 1992

In this paper, we investigate the limiting distribution of $M_n = max (X_1, X-2, \cdots, X_n)$ in the infinite moving average process ${X_t = \sum c_i Z_{t-i}}$ generated from i.i.d. negative binomial variables $Z_i$'s. While no limit result is possible, nonetheless asymptotic bounds are derived. We also present the tail behavior of $X_t$, i.e., weighted sum of i.i.d. random variables. This continues a study made by Rootzen (1986) for discrete innovation sequences.

• Communications for Statistical Applications and Methods
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• 제7권3호
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• pp.859-869
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• 2000

In this paper, various methods for finding confidence intervals for p of binomial parameter are reviewed. Also we introduce tow bootstrap confidence intervals for p. We compare the performance of bootstrap methods with other methods in terms of average coverage probability by Monte Carlo simulation. Advantages of these bootstrap methods are discussed.

• Communications for Statistical Applications and Methods
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• 제19권6호
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• pp.761-770
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• 2012

We frequently encounter outcomes of count that have extra variation. This paper considers several alternative models for overdispersed count responses such as a quasi-Poisson model, zero-inflated Poisson model and a negative binomial model with a special focus on a generalized linear mixed model. We also explain various goodness-of-fit criteria by discussing their appropriateness of applicability and cautions on misuses according to the patterns of response categories. The overdispersion models for counts data have been explained through two examples with different response patterns.

• Communications for Statistical Applications and Methods
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• 제17권3호
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• pp.309-318
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• 2010

The construction of asymptotic confidence intervals is considered for the difference of binomial proportions in two doubly sampled data subject to false-positive error. The coverage behaviors of several likelihood based confidence intervals and a Bayesian confidence interval are examined. It is shown that a hierarchical Bayesian approach gives a confidence interval with good frequentist properties. Confidence interval based on the Rao score is also shown to have good performance in terms of coverage probability. However, the Wald confidence interval covers true value less often than nominal level.