• 제목/요약/키워드: Gamma Family Distribution

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Gamma 및 비Gamma군 분포모형에 의한 강우의 지점 및 지역빈도 비교분석 (I) (Comparative Analysis of Regional and At-site Analysis for the Design Rainfall by Gamma and Non-Gamma Family (I))

  • 류경식;이순혁
    • 한국농공학회논문집
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    • 제46권4호
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    • pp.25-36
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    • 2004
  • This study was conducted to derive the design rainfall by the consecutive duration using the at-site frequency analysis. Using the errors, K-S tests and LH-moment ratios, Log Pearson type 3 (LP3) and Generalized Extreme Value (GEV) distributions of Gamma and Non-Gamma Family, respectively were identified as the optimal probability distributions among applied distributions. Parameters of GEV and LP3 distributions were estimated by the method of L and LH-moments and the Indirect method of moments respectively. Design rainfalls following the consecutive duration were derived by at-site frequency analysis using the observed and simulated data resulted from Monte Carlo techniques. Relative root-mean-square error (RRMSE) and relative efficiency (RE) in RRMSE for the design rainfall derived by at-site analysis in the observed and simulated data were computed and compared. It has shown that at-site frequency analysis by GEV distribution using L-moments is confirmed as more reliable than that of GEV and LP3 distributions using LH-moments and Indirect method of moments in view of relative efficiency.

Families of Distributions Arising from Distributions of Ordered Data

  • Ahmadi, Mosayeb;Razmkhah, M.;Mohtashami Borzadaran, G.R.
    • Communications for Statistical Applications and Methods
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    • 제22권2호
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    • pp.105-120
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    • 2015
  • A large family of distributions arising from distributions of ordered data is proposed which contains other models studied in the literature. This extension subsume many cases of weighted random variables such as order statistics, records, k-records and many others in variety. Such a distribution can be used for modeling data which are not identical in distribution. Some properties of the theoretical model such as moment, mean deviation, entropy criteria, symmetry and unimodality are derived. The proposed model also studies the problem of parameter estimation and derives maximum likelihood estimators in a weighted gamma distribution. Finally, it will be shown that the proposed model is the best among the previously introduced distributions for modeling a real data set.

The Marshall-Olkin generalized gamma distribution

  • Barriga, Gladys D.C.;Cordeiro, Gauss M.;Dey, Dipak K.;Cancho, Vicente G.;Louzada, Francisco;Suzuki, Adriano K.
    • Communications for Statistical Applications and Methods
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    • 제25권3호
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    • pp.245-261
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    • 2018
  • Attempts have been made to define new classes of distributions that provide more flexibility for modelling skewed data in practice. In this work we define a new extension of the generalized gamma distribution (Stacy, The Annals of Mathematical Statistics, 33, 1187-1192, 1962) for Marshall-Olkin generalized gamma (MOGG) distribution, based on the generator pioneered by Marshall and Olkin (Biometrika, 84, 641-652, 1997). This new lifetime model is very flexible including twenty one special models. The main advantage of the new family relies on the fact that practitioners will have a quite flexible distribution to fit real data from several fields, such as engineering, hydrology and survival analysis. Further, we also define a MOGG mixture model, a modification of the MOGG distribution for analyzing lifetime data in presence of cure fraction. This proposed model can be seen as a model of competing causes, where the parameter associated with the Marshall-Olkin distribution controls the activation mechanism of the latent risks (Cooner et al., Statistical Methods in Medical Research, 15, 307-324, 2006). The asymptotic properties of the maximum likelihood estimation approach of the parameters of the model are evaluated by means of simulation studies. The proposed distribution is fitted to two real data sets, one arising from measuring the strength of fibers and the other on melanoma data.

다년간 계속되는 갈수의 크기 및 심도에 관한 빈도분석 방안 (An Approach for Frequency Analysis of Multiyear Drought Magnitude and Severity)

  • 이길성
    • 대한토목학회논문집
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    • 제7권1호
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    • pp.111-120
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    • 1987
  • 부족량의 지속기간에 따른 성질을 관측하여, 다년간 계속되는 가뭄의 크기와 심도에 관한 빈도분석 방안을 개발하였다. 평균 부족량의 변화를 식별하기 위하여, 월 부족량의 통계치에 의한 표준화와 자료의 통합과정이 시행되었다. 가뭄의 크기와 심도에 관한 매개변수를 추정하기 위하여, Gamma 분포함수의 재생산성이 부족량에 대하여 적용되었다. 이들 분포와 지속기간 분포와의 복합화 맞 연구 결과가 실시간 예측에 관하여 의미하는 바를 논의하였다.

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혈액투석 환자의 자기관리 수행도와 이에 영향을 미치는 요인 (Self-Care and Associating Factors in Hemodialysis Patients)

  • 전진호;강혜경
    • 보건교육건강증진학회지
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    • 제16권1호
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    • pp.149-166
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    • 1999
  • Self-care and the performance of their own role might be important for the prevention of complications and improvement of quality of life in hemodialysis patients with chronic renal failure(CRF). To improve well-being and quality of life for the patients, the author estimated the level of self-care and associating factors through a questionnaire. The information was composed of the knowledge for hemodialysis and renal disease, the level of self-care, health belief, supports from the family, disease-related stresses, personal characteristics, medical history, relationships with medical personnel, etc. The data was gathered from 126 hemodialysis patients who were undergoing hemodialysis in one university hospital and five hospitals in Kyungsangnam-Do area from December 1997 to January 1998, and was analyzed by PC SAS program(version 6.12) with the level of significance($\alpha$=0.05). The mean age of subjects was 47.0$\pm$13.5years with no significant difference in gender distribution. The mean duration of hemodialysis was 39.0 months, and their frequencies of hemodialysis were more than three times per week(77.0%). Only 21.4% had the specific education on hemodialysis and CRF. In the level which was expressed as the score out of 100, the mean of knowledge was 90.7$\pm$9.1 and the mean of self-care was 73.9$\pm$12.7, that means, they only partially carried their knowledge into practice. They showed a significant correlation between knowledge and health belief($\gamma$=0.282); self-care and health belief($\gamma$=0.357), family supports and knowledge($\gamma$=0.221), self-care($\gamma$=0.402), health belief($\gamma$=0.431); and health belief and stress($\gamma$=-0.361). Age, religion, marrital status, education, and relationships with medical personnel showed positive correlations, and smoking showed negative correlation with self-care. In the multiple regression with the level of self-care as dependent variable, and each of the characeristics as independent variables, supports from the family($\beta$=6.615=0.158), the experience of disease specific education($\beta$=4.959), relationships with medical personnel($\beta$=6.615), current smoking($\beta$=-6.986), and current drinking ($\beta$=-7.095) were detected as significant factors. The value of R-square was 34%. In summary, to promote the level self-care and to improve the well beings and Quality of life for the hemodialysis patients, it would be emphasized that they terminate smoking and drinking, and it would be recommended that the education programs and supports from the family be strengthened. And, because there was a considerable difference between the level of knowledge and self-care, it would also be emphasized to propose the education programs which focused on execution. In addition to that, there is a need to improve relationships between the patients and medical personnel through positive changes in the attitudes of the medical personnel.

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PROPERTIES ON q-DIFFERENCE RICCATI EQUATION

  • Huang, Zhi-Bo;Zhang, Ran-Ran
    • 대한수학회보
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    • 제55권6호
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    • pp.1755-1771
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    • 2018
  • In this paper, we investigate a certain type of q-difference Riccati equation in the complex plane. We prove that q-difference Riccati equation possesses a one parameter family of meromorphic solutions if it has three distinct meromorphic solutions. Furthermore, we find that all meromorphic solutions of q-difference Riccati equation and corresponding second order linear q-difference equation can be expressed by q-gamma function if this q-difference Riccati equation admits two distinct rational solutions and $q{\in}{\mathbb{C}}$ such that 0 < ${\mid}q{\mid}$ < 1. The growth and value distribution of differences of meromorphic solutions of q-difference Riccati equation are also treated.

ON THE EXISTENCE OF THE TWEEDIE POWER PARAMETER IMPLICIT ESTIMATOR

  • Ghribi, Abdelaziz;Hassin, Aymen;Masmoudi, Afif
    • 대한수학회보
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    • 제59권4호
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    • pp.979-991
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    • 2022
  • A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter p, a mean m and a dispersion parameter 𝜙. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter m, suggesting that the implicit estimator of the power parameter p exists, was established and we provided some asymptotic properties of this estimator.

Gamma 및 비Gamma군 분포모형에 의한 강우의 지점 및 지역빈도 비교분석 (Ⅱ) (Comparative Analysis of Regional and At-site Analysis for the Design Rainfall by Gamma and Non-Gamma Family (Ⅱ))

  • 이순혁;류경식
    • 한국농공학회논문집
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    • 제46권5호
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    • pp.15-26
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    • 2004
  • This study was conducted to derive the regional design rainfall by the regional frequency analysis based on the regionalization of the precipitation. The optimal regionalization of the precipitation data were classified by the above mentioned regionalization for all over the regions except Jeju and Ulleung islands in Korea. Design rainfalls following the consecutive duration were derived by the regional analysis using the observed and simulated data resulted from Monte Carlo techniques. Relative root mean square error (RRMSE), relative bias (RBIAS) and relative reduction (RR) in RRMSE for the design rainfall were computed and compared between the regional and at-site frequency analysis. It has shown that the regional frequency analysis procedure can substantially more reduce the RRMSE, RBIAS and RR in RRMSE than those of at-site analysis in the prediction of design rainfall. Consequently, optimal design rainfalls following the classified regions and consecutive durations were derived by the regional frequency analysis using Generalized extreme value distribution which was identified to be more optimal one than the other applied distributions. Diagrams for the design rainfall derived by the regional frequency analysis using L-moments were drawn according to the regions and consecutive durations by GIS techniques.

수명분포가 감마족인 기록값 통계량에 기초한 무한고장 NHPP 소프트웨어 신뢰성장 모형에 관한 비교 연구 (A Study of Infinite Failure NHPP Software Reliability Growth Model base on Record Value Statistics with Gamma Family of Lifetime Distribution)

  • 김희철;신현철
    • 융합보안논문지
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    • 제6권3호
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    • pp.145-153
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    • 2006
  • 본 논문에서는 기록값 통계량을 이용한 무한 고장 NHPP 모형들이 제안되었다. 이 모형들은 결함당 고장 발생률이 단조 증가하거나 단조 감소하는 패턴을 가진다. 그리고 수명 분포에서는 어랑 분포, 랄리 분포와 굼벨를 이용한 소프트웨어 신뢰성 모형을 적용하여 비교연구에 초점을 두었다. 고장 간격 시간 자료를 이용한 무한 고장 NHPP 모형들에 대한 모수 추정법은 최우 추정법을 사용하였고 적용 분포들의 적용을 용이하게 하기 위하여 특수한 형태를 제시하였다. 고장 자료의 분석을 위하여 산술 및 라플라스 추세 검정과 적합도 및 치우침 검정을 실시하여 그 결과를 나열하였다.

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지수 및 비지수족 분포 모형에 근거한 소프트웨어 최적방출시기에 관한 비교 연구 (The Comparative Study of Software Optimal Release Time Based on Gamma Exponential and Non-exponential Family Distribution Model)

  • 김희철;신현철
    • 한국컴퓨터정보학회논문지
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    • 제15권5호
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    • pp.125-132
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    • 2010
  • 본 연구에서는 소프트웨어 제품을 개발하여 테스팅을 거친 후 사용자에게 인도하는 시기를 결정하는 방출문제에 대하여 연구 하였다. 방출문제의 분포는 소프트웨어의 결함을 제거하거나 수정 작업 중에도 새로운 결함이 발생될 가능성이 있는 무한고장수를 가진 비동질적인 포아송 과정에 기초하였다. 수명분포는 지수 족 분포와 비지수족 분포를 이용한 최적 방출시기에 관한 문제를 비교 제시하였다. 이러한 지수 및 비지수분포에 근거하여 소프트웨어 요구 신뢰도를 만족시키고 소프트웨어 개발 및 유지 총비용을 최소화 시키는 최적 소프트웨어 방출 정책에 대하여 논의 되었다. 본 논문의 수치적인 예에서는 고장 간격 시간 자료를 적용하고 모수추정 방법은 최우추정법을 이용하고 추세분석을 통하여 자료의 효율성을 입증한 후 최적 방출시기를 추정하였다.