• Title/Summary/Keyword: log-normal distribution

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A Fundamental Study of Probability Functions and Relationship of Wave Heights. -On the Wave Heights of the East Coast of Korea- (파고의 확률분포 및 상관에 관한 기초적 연구 - 동해안의 파고를 중심으로 하여 -)

  • 윤해식;이순탁
    • Water for future
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    • v.7 no.2
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    • pp.99-106
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    • 1974
  • The records of wave heights which were observed at Muk ho and Po hang of the East Coast of Korea were analized by several probility functions. The exponential 2 parameter distribution was found as the best fit probability function to the historical distribution of wave heights by the test of goodness of fit. But log-normal 2 parameter and log-extremal type A distributions were also fit to the historical distribution, especially in the Smirnov-Kolmogorov test. Therefore, it can't be always regarded that those two distributions are not fit to the wave heiht's distribution. In the test of goodness of fit, the Chi-Square test gave very sensitive results and Smirnov-Kolmogorov test, which is a distribution free and non-parametric test, gave more inclusive results. At the next stage, the inter-relationship between the mean and the one-third wave heights, the mean and the one-=tenth wave heights, the one-third and the one-tenth wave heights, the one-third and the highest wave heights were obtained and discussed.

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Re-Transformation of Power Transformation for ARMA(p, q) Model - Simulation Study (ARMA(p, q) 모형에서 멱변환의 재변환에 관한 연구 - 모의실험을 중심으로)

  • Kang, Jun-Hoon;Shin, Key-Il
    • The Korean Journal of Applied Statistics
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    • v.28 no.3
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    • pp.511-527
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    • 2015
  • For time series analysis, power transformation (especially log-transformation) is widely used for variance stabilization or normalization for stationary ARMA(p, q) model. A simple and naive back transformed forecast is obtained by taking the inverse function of expectation. However, this back transformed forecast has a bias. Under the assumption that the log-transformed data is normally distributed. The unbiased back transformed forecast can be obtained by the expectation of log-normal distribution; consequently, the property of this back transformation was studied by Granger and Newbold (1976). We investigate the sensitivity of back transformed forecasts under several different underlying distributions using simulation studies.

An Alternative Parametric Estimation of Sample Selection Model: An Application to Car Ownership and Car Expense (비정규분포를 이용한 표본선택 모형 추정: 자동차 보유와 유지비용에 관한 실증분석)

  • Choi, Phil-Sun;Min, In-Sik
    • Communications for Statistical Applications and Methods
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    • v.19 no.3
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    • pp.345-358
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    • 2012
  • In a parametric sample selection model, the distribution assumption is critical to obtain consistent estimates. Conventionally, the normality assumption has been adopted for both error terms in selection and main equations of the model. The normality assumption, however, may excessively restrict the true underlying distribution of the model. This study introduces the $S_U$-normal distribution into the error distribution of a sample selection model. The $S_U$-normal distribution can accommodate a wide range of skewness and kurtosis compared to the normal distribution. It also includes the normal distribution as a limiting distribution. Moreover, the $S_U$-normal distribution can be easily extended to multivariate dimensions. We provide the log-likelihood function and expected value formula based on a bivariate $S_U$-normal distribution in a sample selection model. The results of simulations indicate the $S_U$-normal model outperforms the normal model for the consistency of estimators. As an empirical application, we provide the sample selection model for car ownership and a car expense relationship.

Anomalous Pattern Analysis of Large-Scale Logs with Spark Cluster Environment

  • Sion Min;Youyang Kim;Byungchul Tak
    • Journal of the Korea Society of Computer and Information
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    • v.29 no.3
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    • pp.127-136
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    • 2024
  • This study explores the correlation between system anomalies and large-scale logs within the Spark cluster environment. While research on anomaly detection using logs is growing, there remains a limitation in adequately leveraging logs from various components of the cluster and considering the relationship between anomalies and the system. Therefore, this paper analyzes the distribution of normal and abnormal logs and explores the potential for anomaly detection based on the occurrence of log templates. By employing Hadoop and Spark, normal and abnormal log data are generated, and through t-SNE and K-means clustering, templates of abnormal logs in anomalous situations are identified to comprehend anomalies. Ultimately, unique log templates occurring only during abnormal situations are identified, thereby presenting the potential for anomaly detection.

Performance Comparison of Cumulative Incidence Estimators in the Presence of Competing Risks (경쟁위험 하에서의 누적발생함수 추정량 성능 비교)

  • Kim, Dong-Uk;Ahn, Chi-Kyung
    • The Korean Journal of Applied Statistics
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    • v.20 no.2
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    • pp.357-371
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    • 2007
  • For the time-to-failure data with competing risks, cumulative incidence functions (CIFs) are commonly estimated using nonparametric methods. If the cases of events due to the cause of primary interest are infrequent relative to other cause of failure, nonparametric methods may result in rather imprecise estimates for CIF. In such cases, Bryant et al. (2004) suggested to model the cause-specific hazard of primary interest parametrically, while accounting for the other modes of failure using nonparametric estimator. We represented the semiparametric cumulative incidence estimator and extended to the model of Weibull and log-normal distribution. We also conducted simulations to access the performance of the semiparametric cumulative incidence estimators and to investigate the impact of model misspecification in log-normal cause-specific hazard model.

Erlang Capacity of Cellular CDMA Mobile Communication System with soft Handoff (소프트 핸드오프를 갖는 셀룰러 CDMA 이동통신 시스템의 Erlang 용랑)

    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.25 no.3A
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    • pp.334-341
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    • 2000
  • This paper presents an analysis of the capacity, the interference of adjacent cells of a CDMA cellular system, depending on the soft handoff region and log-normal shadowing. The optimum soft handoff region is chosen by using Erlang capacity. It is shown that when the soft handoff region increases, the Erlang capacity increase due to a reduction of the interference power of adjacent cells. But if the region is increased above a certain value, there is no improvement in the system’s capacity. Furthermore as the standard deviation of the log-normal shadowing's normal distribution factor increases, the soft handoff region has to be increased linearly to achieve the same Erlang capacity.

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Linear regression under log-concave and Gaussian scale mixture errors: comparative study

  • Kim, Sunyul;Seo, Byungtae
    • Communications for Statistical Applications and Methods
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    • v.25 no.6
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    • pp.633-645
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    • 2018
  • Gaussian error distributions are a common choice in traditional regression models for the maximum likelihood (ML) method. However, this distributional assumption is often suspicious especially when the error distribution is skewed or has heavy tails. In both cases, the ML method under normality could break down or lose efficiency. In this paper, we consider the log-concave and Gaussian scale mixture distributions for error distributions. For the log-concave errors, we propose to use a smoothed maximum likelihood estimator for stable and faster computation. Based on this, we perform comparative simulation studies to see the performance of coefficient estimates under normal, Gaussian scale mixture, and log-concave errors. In addition, we also consider real data analysis using Stack loss plant data and Korean labor and income panel data.

Modeling of Suspended Sediment Transport Using Deep Neural Networks (심층 신경망 기법을 통한 부유사 이동 모델링)

  • Bong, Tae-Ho;Son, Young-Hwan;Kim, Kyu-Sun;Kim, Dong-Geun
    • Journal of The Korean Society of Agricultural Engineers
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    • v.60 no.4
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    • pp.83-91
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    • 2018
  • Land reclamation, coastal construction, coastline extension and port construction, all of which involve dredging, are increasingly required to meet the growing economic and societal demands in the coastal zone. During the land reclamation, a portion of landfills are lost from the desired location due to a variety of causes, and therefore prediction of sediment transport is very important for economical and efficient land reclamation management. In this study, laboratory disposal tests were performed using an open channel, and suspended sediment transport was analyzed according to flow velocity and grain size. The relationships between the average and standard deviation of the deposition distance and the flow velocity were almost linear, and the relationships between the average and standard deviation of deposition distance and the grain size were found to have high non-linearity in the form of power law. The deposition distribution of sediments was demonstrated to have log-normal distributions regardless of the flow velocity. Based on the experimental results, modeling of suspended sediment transport was performed using deep neural network, one of deep learning techniques, and the deposition distribution was reproduced through log-normal distribution.

Validation of the correlation-based aerosol model in the ISFRA sodium-cooled fast reactor safety analysis code

  • Yoon, Churl;Kim, Sung Il;Lee, Sung Jin;Kang, Seok Hun;Paik, Chan Y.
    • Nuclear Engineering and Technology
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    • v.53 no.12
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    • pp.3966-3978
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    • 2021
  • ISFRA (Integrated SFR Analysis Program for PSA) computer program has been developed for simulating the response of the PGSFR pool design with metal fuel during a severe accident. This paper describes validation of the ISFRA aerosol model against the Aerosol Behavior Code Validation and Evaluation (ABCOVE) experiments undertaken in 1980s for radionuclide transport within a SFR containment. ABCOVE AB5, AB6, and AB7 tests are simulated using the ISFRA aerosol model and the results are compared against the measured data as well as with the simulation results of the MELCOR severe accident code. It is revealed that the ISFRA prediction of single-component aerosols inside a vessel (AB5) is in good agreement with the experimental data as well as with the results of the aerosol model in MELCOR. Moreover, the ISFRA aerosol model can predict the "washout" phenomenon due to the interaction between two aerosol species (AB6) and two-component aerosols without strong mutual interference (AB7). Based on the theory review of the aerosol correlation technique, it is concluded that the ISFRA aerosol model can provide fast, stable calculations with reasonable accuracy for most of the cases unless the aerosol size distribution is strongly deformed from log-normal distribution.

A study on non-response bias adjusted estimation in business survey (사업체조사에서의 무응답 편향보정 추정에 관한 연구)

  • Chung, Hee Young;Shin, Key-Il
    • The Korean Journal of Applied Statistics
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    • v.33 no.1
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    • pp.11-23
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    • 2020
  • Sampling design should provide statistics to meet a given accuracy while saving cost and time. However, a large number of non-responses are occurring due to the deterioration of survey circumstances, which significantly reduces the accuracy of the survey results. Non-responses occur for a variety of reasons. Chung and Shin (2017, 2019) and Min and Shin (2018) found that the accuracy of estimation is improved by removing the bias caused by non-response when the response rate is an exponential or linear function of variable of interests. For that case they assumed that the error of the super population model follows normal distribution. In this study, we proposed a non-response bias adjusted estimator in the case where the error of a super population model follows the gamma distribution or the log-normal distribution in a business survey. We confirmed the superiority of the proposed estimator through simulation studies.