• Asian Pacific Journal of Cancer Prevention
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• 제13권5호
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• pp.1829-1831
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• 2012

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.

• 물과 미래
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• 제18권4호
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• pp.317-325
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• 1985

본 연구에서는 낙동강, 한강 및 금강의 중요관측지점의 월평균 유출량을 분석에 사용하였으며, 먼저 일정유량(Truncation level) 별로 Run-length와 Run-sum에 대한 2-변수 Gamma 분포 및 대수정규분포의 적합성 여부를 검토하였던 바 Gamma 모델이 적합한 것으로 판명된 자료와 실측치와 비교하였다. 그리고 Run-length 및 Run-sum에 대한 일정유량별로 평균치의 변화에 대한 성질을 구명하였다.

• Asian Pacific Journal of Cancer Prevention
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• 제17권sup3호
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• pp.311-316
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• 2016

Breast cancer is one of the most common causes of cancer mortality in Iran. Social determinants of health are among the key factors affecting the pathogenesis of diseases. This cross-sectional study aimed to determine the social determinants of breast cancer survival time with parametric and semi-parametric regression models. It was conducted on male and female patients diagnosed with breast cancer presenting to the Cancer Research Center of Shohada-E-Tajrish Hospital from 2006 to 2010. The Cox proportional hazard model and parametric models including the Weibull, log normal and log-logistic models were applied to determine the social determinants of survival time of breast cancer patients. The Akaike information criterion (AIC) was used to assess the best fit. Statistical analysis was performed with STATA (version 11) software. This study was performed on 797 breast cancer patients, aged 25-93 years with a mean age of 54.7 (${\pm}11.9$) years. In both semi-parametric and parametric models, the three-year survival was related to level of education and municipal district of residence (P<0.05). The AIC suggested that log normal distribution was the best fit for the three-year survival time of breast cancer patients. Social determinants of health such as level of education and municipal district of residence affect the survival of breast cancer cases. Future studies must focus on the effect of childhood social class on the survival times of cancers, which have hitherto only been paid limited attention.

• 대한기계학회논문집A
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• 제36권2호
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• pp.223-230
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• 2012

취성이 큰 재료의 강도는 일반적으로 정규분포 또는 와이블분포로 설명되어 왔으나 감마분포도적합할 수 있다. 재료의 파손이 가해진 응력의 연속된 값 중 가장 큰 값에 좌우된다면 극치분포를 적용하는 것이 합당하다. 본 논문에서는 재료강도가 감마분포를 따르며 극치분포하는 응력이 작용할 경우 응력-강도 간섭이론에 기반하여 신뢰도 계산식을 제시하였으며, 확률분포 파라미터별 신뢰도와 안전율 및 변동계수와의 관계를 통하여 신뢰도 계산식의 유효성을 입증하였다. 안전율과 변동계수에 기반한 신뢰도 예측방법으로 목표 신뢰도가 설정되었을 때 최소한 요구되는 안전율과 최대로 허용되는 응력의 변동계수를 예측할 수 있다.

• 기술사
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• 제20권3호
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• pp.15-25
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• 1987

Statistical control charts are useful tools to monitor and control the manufacturing processes and are widely used in most Korean industries. Many Korean companies, however, do not always obtain desired results from the traditional control charts by Shewhart such as the X-chart, X-chart, X-chart, etc. This is partly because the quality charterstics of the process are not distributed normally but are skewed due to the intermittent production, small lot size, etc. In Shewhart X-chart, which is the most widely used one in Korea, such skewed distributions make the plots to be inclined below or above the central line or outside the control limits although no assignable causes can be found. To overcome such shortcomings in nonnormally distributed processes, a distribution-free type of confidence interval can be used, which should be based on order statistics. This thesis is concerned with the design of control chart based on a sample median which is easy to use in practical situation and therefore properties for nonnormal distributions may be easily analyzed. Control limits and central lines are given for tile more famous nonnormal distributions, such as Gamma, Beta, Lognormal, Weibull, Pareto, Truncated-normal distributions. Robustness of the proposed median control chart is compared with that of the X-chart, the former tends to be superior to the latter as the probability distribution of the process becomes more skewed. The average run length to detect the assignable cause is also compared when the process has a Normal or a Gamma distribution for which the properties of X are easy to verify, the proposed chart is slightly worse than the X-chart for the normally distributed product but much better for Gamma-distributed products. Average Run Lengths of the other distributions are also computed. To use the proposed control chart, the probability distribution of the process should be known or estimated. If it is not possible, the results of comparison of the robustness force us to use the proposed median control chart based on a normal distribution. To estimate the distribution of the process, Sturge's formula is used to graph the histogram and the method of probability plotting, $X^2$-goodness of fit test and Kolmogorov-Smirnov test, are discussed with real case examples. A comparison of the propose4 median chart and the X chart was also performed with these examples and the median chart turned out to be superior to the X-chart.

• 산업경영시스템학회지
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• 제10권16호
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• pp.101-106
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• 1987

Statistical control charts are useful tools to monitor and control the manufacturing processes and are widely used in most Korean industries. Many Korean companies, however, do not always obtain desired results from the traditional control charts by Shewhart such as the $\bar{X}$-chart, $\bar{X}$-chart, $\bar{X}$-chart, etc. This is partly because the quality charterstics of the process are not distributed normally but are skewed due to the intermittent production, small lot size, etc. In Shewhart $\bar{X}$-chart. which is the most widely used one in Kora, such skewed distributions make the plots to be inclined below or above the central line or outside the control limits although no assignable causes can be found. To overcome such shortcomings in nonnormally distributed processes, a distribution-free type of confidence interval can be used, which should be based on order statistics. This thesis is concerned with the design of control chart based on a sample median which is easy to use in practical situation and therefore properties for nonnormal distributions may be easily analyzed. Control limits and central lines are given for the more famous nonnormal distributions, such as Gamma, Beta, Lognormal, Weibull, Pareto, Truncated-normal distributions. Robustness of the proposed median control chart is compared with that of the $\bar{X}$-chart; the former tends to be superior to the latter as the probability distribution of the process becomes more skewed. The average run length to detect the assignable cause is also compared when the process has a Normal or a Gamma distribution for which the properties of X are easy to verify, the proposed chart is slightly worse than the $\bar{X}$-chart for the normally distributed product but much better for Gamma-distributed products. Average Run Lengths of the other distributions are also computed. To use the proposed control chart, the probability distribution of the process should be known or estimated. If it is not possible, the results of comparison of the robustness force us to use the proposed median control chart based oh a normal distribution. To estimate the distribution of the process, Sturge's formula is used to graph the histogram and the method of probability plotting, $\chi$$^2$-goodness of fit test and Kolmogorov-Smirnov test, are discussed with real case examples. A comparison of the proposed median chart and the $\bar{X}$ chart was also performed with these examples and the median chart turned out to be superior to the $\bar{X}$-chart.

• 한국환경보건학회지
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• 제30권5호
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• pp.432-439
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• 2004

Korean certification regulation for particulate filtering respirators requires inward leakage (IL) test as European Standards (EN) and the standard levels of regulation are the same as those of EN. This study was conducted to evaluate particulate filtering respirators being commercially used in the market by using IL and assess the characteristics of IL. The study began with discussing the concept of IL, comparison of IL with fit test, and IL measurement method. Three brands of half masks and 10 brands of filtering facepieces (two top class, four 1st class and four 2nd class), total 13 brands respirators, and 10 test panels (subjects) who were classified in 9 facial grids in accordance with face length and lip length, were selected for IL test. IL tests were conducted in the laboratory of 3M Innovation Center which was established by EN standard. As expected ILs of half masks were lower than those of filtering facepiece mask. ILs of half masks and some filtering facepieces were significantly different in manufacturers. ILs of 1st class filtering facepieces were found to be much more than those of 2nd class and thus the result would cause wearers to get confused to select a mask. Four of six brands being no compliance with standards were thought that they should be tested again for certification because of a lot of differences from standards. There were no significant differences among ILs of five exercises. In 6 out of 13 brands lognormal distribution of ILs may be a better fit distribution and in 7 brands both lognormal and normal distributions were rejected. The result indicates that geometric mean may be better than arithmetic mean to establish standard.

• 한국수자원학회논문집
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• 제32권3호
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• pp.265-279
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• 1999

본 연구에서는, Markov 연쇄 모형에 의해 산정된 모의 일 강우량을 일 유출모형인 Tand 모형에 입력시켜 모의 일유출량을 산정함으로써 저수유량계열을 확장하는 방법을 개발하였다. 또한, 모의된 일 유량계열로부터 지속기간별 연 최저치 계열을 작성하였으며, 지속기간별 연 최저치계열에 대한 빈도분석을 시행하였다. 분석에 사용된 분포형은 Lognormal-2, Lognormal-3, Gamma-2, Gamma-3, LogGamma-3, Gumbel-2, Weibull-2 분포이었으며, 모수추정은 모멘트법과 최우도법을 사용하였다. Kolmogorov - Sminorv 검정방법으로 지속기간별 연 최저치 계열에 적합한 확률분포형을 결정하고, 용담댐 지점을 대상으로 하여 지속기간별 갈수 빈도곡선을 산정하였다. 본 연구에서 제안된 방법을 적용하면 과거 저수 유량계열의 통계적 특성을 잘 나타내는 일 유량의 모의가 가능 하여, 갈수유량계열 자료가 빈곤한 유역에서 확률 갈수량을 추정하는데 유용하리라고 판단된다.

• 한국운동역학회지
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• 제25권1호
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• pp.113-122
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• 2015

Objective : The purpose of this study was to analyze the foot-pressure distribution of 2D(2 dimensional form) & 3D(3 dimensional form; a customized arch-fit for posture correction) insoles for assessing their biomechanical functionality. Background : Recently there has been increased interest in both foot health and foot pain patients. Analysis of the plantar pressure was often used to solve the problems of the foot displayed by such people as rheumatoid arthritis patients. Method : Subjects who participated in this study were 17 female university students who had no previous injury experience in lower limbs and a normal gait pattern. The shoe size of all subjects was 240 mm. Two models of insoles of 2D(typical flat insole - 2 dimensional form) and 3D(special production - 3 dimensional form) were selected for the test. Using the Pedar-X system and Pedar-X insoles, 4.0 km/h of walking speed, and a compilation of 50 steps walking stages were used to analyze foot-pressure distribution. Results : Results of the foot-pressure distribution and biomechanical functionality on each insole were as follows; analyses of mean plantar pressure, maximum plantar pressure, maximum vertical GRF, and plantar pressure curve shape all showed overall low plantar pressure and GRF. Conclusion : This can be evaluated as an excellent insole for low levels on the plantar pressure and GRF. Therefore, it is possible to conclude that according to this analysis the 3D Customized Arch-fit Insole was better than 2D insole on the basis of these criteria.

• 한국ITS학회 논문지
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• 제22권4호
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• pp.35-47
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• 2023

그동안 차두시간분포를 나타내는 확률분포로 음지수분포, Erlang 분포, 정규분포 등 다양한 단일확률분포들이 사용되어져 왔다. 그러나, 실제 도로에서 차두시간분포의 조사결과는 단일확률분포로서 설명하기 어려운 경우가 있었다. 본 연구는 차량의 차두시간에 대해 두 개의 정규분포가 일정한 관련성을 가지고 결합된 복합확률분포의 파라메타에 대해 최우추정법 중 하나인 EM 알고리즘을 이용하여 추정하는 접근방법을 시도하였다. 이에 대한 분석결과 기존에 알려진 단일확률분포로서 잘 설명되기 어려웠던 차량도착 차두시간 분포를 EM 알고리즘을 이용하여 복합확률분포의 파라메타를 추정하여 설명하였다. χ² test 적합도 검정결과, 유의수준 1%에서 통계학적으로 유의성이 확보되어 EM 알고리즘을 이용한 복합확률분포의 파라메타 추정의 신뢰성이 입증되는 것으로 분석되었다.