Likelihood-based inference for the ratio of shape parameters of generalized exponential distributions

이재운,이우동,강상길 한국데이터정보과학회 2018 한국데이터정보과학회지 Vol.29 No.3

This article deals with the likelihood-based inference for the ratio of the shape parameters of the generalized exponential distribution. When the parameter of interest is the ratio of the shape parameters, we develop the likelihood-based inference based on the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic for the parameter of interest. To show the performances of the proposed likelihood-based methods, we perform simulations and compare the two likelihood-based statistics when the sample size is small. An example based on simulated data is given. From the numerical results, we can see that the modified signed log-likelihood ratio statistic has good performances in terms of coverage probabilities of confidence intervals and power, and gives desirable results even with a small sample size.

Likelihood-based inference for the ratio of shape parameters of generalized exponential distributions

Jaeun Lee,Woo Dong Lee,Sang Gil Kang 한국데이터정보과학회 2018 한국데이터정보과학회지 Vol.29 No.3

This article deals with the likelihood-based inference for the ratio of the shape parameters of the generalized exponential distribution. When the parameter of interest is the ratio of the shape parameters, we develop the likelihood-based inference based on the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic for the parameter of interest. To show the performances of the proposed likelihood-based methods, we perform simulations and compare the two likelihood-based statistics when the sample size is small. An example based on simulated data is given. From the numerical results, we can see that the modified signed log-likelihood ratio statistic has good performances in terms of coverage probabilities of confidence intervals and power, and gives desirable results even with a small sample size.

Small sample likelihood based inference for the normal variance ratio

Lee, Woo Dong The Korean Data and Information Science Society 2013 한국데이터정보과학회지 Vol.24 No.4

This study deals with the small sample likelihood based inference for the ratio of two normal variances. The small sample likelihood inference is an approximation method. The signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic, which converge to standard normal distribution, are proposed for the normal variance ratio. Through the simulation study, the coverage probabilities of confidence interval and power of the exact, the signed log-likelihood and the modified signed log-likelihood ratio statistic will be compared. A real data example will be provided.

Small sample Likelihood based inference for the normal variance ratio

Woo Dong Lee 한국데이터정보과학회 2013 한국데이터정보과학회지 Vol.24 No.4

This study deals with the small sample likelihood based inference for the ratio of two normal variances. The small sample likelihood inference is an approximation method. The signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic, which converge to standard normal distribution, are proposed for the normal variance ratio. Through the simulation study, the coverage probabilities of confidence interval and power of the exact, the signed log-likelihood and the modified signed log-likelihood ratio statistic will be compared. A real data example will be provided.

Small sample likelihood based inference for the normal variance ratio

이우동 한국데이터정보과학회 2013 한국데이터정보과학회지 Vol.24 No.4

This study deals with the small sample likelihood based inference for the ratio of two normal variances. The small sample likelihood inference is an approximation method. The signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic, which converge to standard normal distribution, are proposed for the normal variance ratio. Through the simulation study, the coverage probabilities of confidence interval and power of the exact, the signed log-likelihood and the modified signed log-likelihood ratio statistic will be compared. A real data example will be provided.

Likelihood-based inference for the ratio of the parameters of the inverse exponential distributions

Sang Gil Kang,Hong Kyung Park,Woo Dong Lee 한국데이터정보과학회 2019 한국데이터정보과학회지 Vol.30 No.6

In this article, two likelihood-based methods are developed to make a statistical inference of the ratio of the parameters of the inverse exponential distributions. The exact method and the likelihood-based methods under the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic are developed. The confidence intervals of the ratio and the test of the ratio of the parameters of two independent inverse exponential distributions are studied by proposed statistics. For comparing the accuracy of the proposed methods, we investigate the coverage probability, the bilateral symmetry and length of the confidence intervals in the small sample size. Also, the power of the test statistics are compared. And a real data example is provided.

Likelihood-based inference for the ratio of the parameters of the inverse exponential distributions

강상길,박홍경,이우동 한국데이터정보과학회 2019 한국데이터정보과학회지 Vol.30 No.6

In this article, two likelihood-based methods are developed to make a statistical inference of the ratio of the parameters of the inverse exponential distributions. The exact method and the likelihood-based methods under the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic are developed. The confidence intervals of the ratio and the test of the ratio of the parameters of two independent inverse exponential distributions are studied by proposed statistics. For comparing the accuracy of the proposed methods, we investigate the coverage probability, the bilateral symmetry and length of the confidence intervals in the small sample size. Also, the power of the test statistics are compared. And a real data example is provided.

Comparison of two tests for seasonal variation

Marrero Osvaldo 한국통계학회 2023 Journal of the Korean Statistical Society Vol.52 No.1

Statistical analyses of seasonal variation are important in the medical and social sciences because the results from such analyses can help elucidate the environment’s impact on human activity, behavior, and health. Generally, we are concerned with a data set of just 12 frequencies over a one-year period, and both the sample size and the variation’s amplitude are small, features that complicate the analysis; to assist in these situations, statisticians have created specialized tests for such data. One of those tests is an optimal-power likelihood-ratio test, whose application can fail because of computational complications. We are interested in the practical application of the said likelihood-ratio test, and so we present previously unknown information about the following: (1) When is the likelihood-ratio test likely to fail, and what are the chances for such failure to happen? (2) If the likelihood-ratio test does fail, what other test should the researcher use? Also, we provide new insights as to when and why the likelihood-ratio test would fail. Thus, in this study, we round out and complete important information about the performance of the optimal-power likelihood-ratio test for seasonality. Our results are useful to researchers who plan to do an analysis of seasonal variation.

샴 신경망 출력값의 우도비 기반 동일인 필적 여부에 관한 분석

이미경,진경원,이의철 국제차세대융합기술학회 2021 차세대융합기술학회논문지 Vol.5 No.4

필적 정보를 통한 생체 인식은 유서, 계약서 등의 진위 여부 판별을 통해 중요한 법적 증거가 될 수 있 다. 그러나 일반적으로 필기 쌍의 동일인 여부는 전문가의 경험과 주관에 의해 결정된다. 인공지능을 통한 생체인 식이 법정 증거력을 확보하기 위해서는 판정에 대한 신뢰도 값이 제시될 필요가 있다. 확률 분포 및 최소오류 결 정이론 기반의 이진 분류 문제에서는 판정에 대한 신뢰도를 우도비로 산출할 수 있다. 본 논문에서는 샴 신경망 기반 필적 생체정보의 동일인 및 타인 매칭 점수 분포를 확률분포 형태로 구축하고, 비교되는 필적 쌍의 점수를 통해 본인 여부 및 우도비 값을 산출한다. 동일인 분포와 타인 분포가 겹쳐지는 구간에서는 판정에 대한 우도비가 급격하게 작아진다. 실제로 우도비가 작게 산출되는 경우가 인간의 육안으로도 판정의 모호성을 가지는지 정성적 으로 분석해본다. 분석 결과, 우도비가 큰 경우에는 육안으로도 판정이 명확한 경우가 대부분이었으며, 우도비가 작은 경우에는 실제로 육안 판정이 어려운 것으로 나타났다. Handwriting biometrics can be important legal evidence through determination of the authenticity of wills and contracts. However, in general, whether handwriting pairs are genuinity is determined by the expert's experience and subjectivity. In order for biometric recognition through artificial intelligence to secure legal evidence, it is necessary to present a reliability value for the genuinity decision. In binary classification problem based on probability distribution and least-error decision theory, the reliability of the decision can be calculated as a likelihood ratio. In this paper, genuine and imposter matching score distributions of handwriting biometrics based on Siamese neural network is constructed in the form of probability distribution, and the identity and likelihood ratio values are calculated through the scores of handwriting pairs compared. In the ovelapped section between the genuine and the imposter distributions , the likelihood ratio for the judgment decreases sharply. Qualitatively analyze whether the case in which the likelihood ratio is actually calculated has ambiguity in the judgment even with the human eye. As a result of the analysis, it was found that, in most cases, when the likelihood ratio was large, the determination was clear even with the naked eye, and when the likelihood ratio was small, it was actually difficult to determine visually.

GIS 기반 우도비를 활용한 오름의 형태별 공간분포 특성 연구 -제주도 중산간지역을 대상으로-

윤혜연 ( Hye-yeon Yoon ),장동호 ( Dong-ho Jang ) 한국사진지리학회 2020 한국사진지리학회지 Vol.30 No.3

본 연구는 제주도 중산간지역 오름의 형태별(말굽형, 원추형, 원형, 복합형) 공간분포 특성을 GIS 기반 우도비(Likelihood)를 통해 분석하였다. 분석 결과, 모든 오름의 형태는 고도(DEM)와 경사도, 토양 배수도, 임상도, 토지피복도, 지형 습윤지수도(TWI) 등 모든 GIS 주제도에서 높은 상관관계가 나타났다. 종합해보면, 말굽형, 원추형, 원형, 복합형 오름은 각각 해발고도 350∼400m(18.6%), 250∼300m(42.6%), 300∼350m(28.4%), 450∼500m(23.4%) 등에 분포한다. 또한, 경사는 모두 20∼30° 구간에서 각각 50.8%, 43.5%, 48.9%, 43.1%가 분포한다. 토양배수는 모두 양호로, 각각 68.4%, 84.4%, 83.3%, 51.3%가 속하는 것으로 나타났다. 임상의 경우, 말굽형과 원추형 오름은 침엽수 인공림에 각각 30.0%, 45.2%, 원형과 복합형 오름은 활엽수림에 각각 26.9%, 31.1%가 분포하고 있었다. 또한 토지피복은 모두 산림지역에서 각각 85.8%, 78.2%, 72.7%, 72.9%가 분포하고, TWI는 모두 0.4∼5.9 구간에 각각 88.1%, 91.1%, 80.0%, 82.3%가 분포한다. 도출된 우도비 결과는 향후 GIS 공간통합 모델을 활용한 오름의 형태별 공간분포 특성 분석을 위한 기초 자료로 활용될 수 있을 것이다. This study analyzed the spatial distribution characteristics in the types of Oreum(Horse-shoses Type, Conical Shape, Ring Shape, Complex Type), located at the mid-mountain area of Jeju Island by using GIS-based likelihood ratio. The result of the analysis, high correlation was found in all thematic maps such as DEM(Digital Elevation Model), slope, soil drainage, forest type, land cover, and TWI(Topographic Wetness Index). Based on frequency ratio result, most of the Oreum of Horse-shoses Type, Conical Shape, Ring Shape, Complex Type are distributed in elevation of 350~400m(18.6%), 250~300m(42.6%), 300~350m(28.4%), 450~500m(23.4%). In addition, the slope distribution was contained for each type of 50.8%, 43.5%, 48.9%, and 43.1% at the angle of 20~30°. Furthermore, the soil drainage, highest frequency was found at well drained class and counted at 68.4%, 84.4%, 83.3%, 51.3% respectively. In terms of forest type, Horse-shoses Type, Conical Shape Oreum highest ratio were found in coniferous plantation at 30.0%, 45.2%, and Ring Shape, Complex Type Oreum highest ratio 26.9%, 31.1% were found in Broad-leaved forest. Also, Moreover, the land-cover was distributed of forest areas at 85.8%, 78.2%, 72.7%, 72.9%, as well as section 0.4∼5.9 of TWI was shown at 88.1%, 91.1%, 80.0%, 82.3% respectively. The likelihood ratio results to be calculated and would be used as basic data for analyzing the spatial distribution characteristics in the types Oreum using a GIS spatial integration model.