• Title, Summary, Keyword: Lognormal distribution

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Noninformative priors for linear function of parameters in the lognormal distribution

  • Lee, Woo Dong;Kim, Dal Ho;Kang, Sang Gil
    • Journal of the Korean Data and Information Science Society
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    • v.27 no.4
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    • pp.1091-1100
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    • 2016
  • This paper considers the noninformative priors for the linear function of parameters in the lognormal distribution. The lognormal distribution is applied in the various areas, such as occupational health research, environmental science, monetary units, etc. The linear function of parameters in the lognormal distribution includes the expectation, median and mode of the lognormal distribution. Thus we derive the probability matching priors and the reference priors for the linear function of parameters. Then we reveal that the derived reference priors do not satisfy a first order matching criterion. Under the general priors including the derived noninformative priors, we check the proper condition of the posterior distribution. Some numerical study under the developed priors is performed and real examples are illustrated.

Estimation on composite lognormal-Pareto distribution based on doubly censored samples (결합 로그노말-파레토 분포에서 추출된 양쪽 중도 절단된 표본을 이용한 모수추정)

  • Lee, Kwang-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.2
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    • pp.171-177
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    • 2011
  • With the development of the actuarial and insurance industries, the distributions of the insurance payments data are deeply studied by many authors. It is known that theses types of distribution are very highly positively skewed and have a long thick upper tail such as Pareto or lognormal distribution. In 2005, Cooray and Ananda proposed a new model which is composed lognormal distribution and Pareto distribution. They said it as composite lognormal-Preto distribution. They showed that the proposed distribution was better fitted than lognormal or Pareto distribution. On the other hand many agreements about the insurance payment have some options for a trivially small payment or extremely large one because of the limits of total payment. Appling these cases, in this paper we consider the parameter estimation on the composite lognormal-Pareto distribution based on doubly censored samples.

Statistical Analysis for Fatigue Lifetime of Ceramics (세라믹스의 피로수명에 대한 통계적 분석)

  • 박성은;김성욱;이홍림
    • Journal of the Korean Ceramic Society
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    • v.34 no.9
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    • pp.927-934
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    • 1997
  • Static and cyclic fatigue tests were carried out for alumina specimen to study the statistical analyses (normal, lognormal and Weibull distribution) of fatigue lifetime data and nominal initial crack length data. Fatigue lifetime data followed Weibull distribution better than normal or lognormal distribution, for the shape parameter of the notched specimen was larger than that of the unnotched specimen. The nominal initial crack length data obtained from fatigue lifetime followed the lognormal and Weibull distribution better than normal distribution, for the coefficient of variation of the unnotched specimen was larger than that of the notched specimen, and shape parameter of unnotched specimen was smaller than that of the notched specimen.

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A Robust Estimation for the Composite Lognormal-Pareto Model

  • Pak, Ro Jin
    • Communications for Statistical Applications and Methods
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    • v.20 no.4
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    • pp.311-319
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    • 2013
  • Cooray and Ananda (2005) proposed a composite lognormal-Pareto model to analyze loss payment data in the actuarial and insurance industries. Their model is based on a lognormal density up to an unknown threshold value and a two-parameter Pareto density. In this paper, we implement the minimum density power divergence estimation for the composite lognormal-Pareto density. We compare the performances of the minimum density power divergence estimator (MDPDE) and the maximum likelihood estimator (MLE) by simulations and an example. The minimum density power divergence estimator performs reasonably well against various violations in the distribution. The minimum density power divergence estimator better fits small observations and better resists against extraordinary large observations than the maximum likelihood estimator.

On UMVU Estimator of Parameters in Lognormal Distribution

  • Lee, In-Suk;Kwon, Eun-Woo
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.1
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    • pp.11-18
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    • 1999
  • To estimate the mean and the variance of a lognormal distribution, Finney (1941) derived the uniformly minimun variance unbiased estimators(UMVUE) in the form of infinite series. However, the conditions ${\sigma}^{2}\;>\;n\;and\;{\sigma}^{2}\;<\;\frac{n}{4}$ for computing $E(\hat{\theta}_{AM})\;and\;E(\hat{\eta}^{2}_{AM})$ are necessary. In this paper, we give an alternative derivation of the UMVUE's.

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The Effect of Scale Parameter in Designing Reliability Demonstration Test for Lognormal Lifetime Distribution (대수정규 수명분포를 갖는 제품에 대한 신뢰성 입증시험에서 척도모수의 영향분석)

  • Kwon, Young Il
    • Journal of Applied Reliability
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    • v.14 no.1
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    • pp.53-57
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    • 2014
  • In the fields of reliability application, the most commonly used test methods for reliability demonstration are zero-failure acceptance tests since they require fewer test samples and less test time compared to other test methods that guarantee the same reliability with a given confidence level. For products with lognormal lifetime distribution, the value of scale parameter is usually assumed to be known in designing reliability demonstration tests. It is important to select correct values of scale parameters to guarantee the specified reliability with given confidence level exactly. The effect of using wrong values of scale parameters in designing reliability demonstration test for products with lognormal lifetime distribution is examined and selecting proper values of scale parameters for conservative reliability demonstration is discussed.

Study on the flood frequency analysis for the annual exceedance series -Centering along the Geum River basin- (연초과치 계열의 홍수빈도 분석에 관한 연구 -금강유역을 중심으로-)

  • 박영근;이순혁
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.24 no.1
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    • pp.53-62
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    • 1982
  • This study was attempted to find best fitted distribution and the equations for probable maximum flow with the evaluation of parameters by the method of moment for the rat- ional design of hydraulic structures in the annual exceedance series. Six subwatersheds were selected as studying basins along Geum River basin. The results obtained through this study were analyzed and summarized as follows. 1. Fitted probability distribution was showed in the order of Three Parameter Lognorm al, Type 1 Extremal, Exponential, Pearson Type III, and Log Pearson Type I distribu- tion as the results of x$^2$ goodness of fit test. 2. Kolmogorov-Smirnov test showed in the order of Three Parameter Lognormal, Exp- onential' Pearson Type III, Log Pearson Type III and Type 1 Extremal distribution for the fitted probability distribution. 3. It can be concluded that Three parameter Lognormal distribution is a best fitted one among some other distributions out of respect for each both tests. An Exponential distribution was proposed as a suitable one by Chow, V.T. showeci lower fittness than that of Three Parameter Lognormal in Geum River basin. 5. Probable flood flow equations followins the return periods for each station were obt- ained by Three Parameter Lognormal distribution. 6. It is urgently essential that best fitted probability distribution should be established for the annual exceedance series in the main river systems of Korea.

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A Study on the Simulation of Monthly Discharge by Markov Model (Markov모형에 의한 월유출량의 모의발생에 관한 연구)

  • 이순혁;홍성표
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.31 no.4
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    • pp.31-49
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    • 1989
  • It is of the most urgent necessity to get hydrological time series of long duration for the establishment of rational design and operation criterion for the Agricultural hydraulic structures. This study was conducted to select best fitted frequency distribution for the monthly runoff and to simulate long series of generated flows by multi-season first order Markov model with comparison of statistical parameters which are derivated from observed and sy- nthetic flows in the five watersheds along Geum river basin. The results summarized through this study are as follows. 1. Both two parameter gamma and two parameter lognormal distribution were judged to be as good fitted distributions for monthly discharge by Kolmogorov-Smirnov method for goodness of fit test in all watersheds. 2. Statistical parameters were obtained from synthetic flows simulated by two parameter gamma distribution were closer to the results from observed flows than those of two para- meter lognormal distribution in all watersheds. 3. In general, fluctuation for the coefficient of variation based on two parameter gamma distribution was shown as more good agreement with the observed flow than that of two parameter lognormal distribution. Especially, coefficient of variation based on two parameter lognormal distribution was quite closer to that of observed flow during June and August in all years. 4. Monthly synthetic flows based on two parameter gamma distribution are considered to give more reasonably good results than those of two parameter lognormal distribution in the multi-season first order Markov model in all watersheds. 5. Synthetic monthly flows with 100 years for eack watershed were sjmulated by multi- season first order Markov model based on two parameter gamma distribution which is ack- nowledged to fit the actual distribution of monthly discharges of watersheds. Simulated sy- nthetic monthly flows may be considered to be contributed to the long series of discharges as an input data for the development of water resources. 6. It is to be desired that generation technique of synthetic flow in this study would be compared with other simulation techniques for the objective time series.

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Applying Conventional and Saturated Generalized Gamma Distributions in Parametric Survival Analysis of Breast Cancer

  • Yavari, Parvin;Abadi, Alireza;Amanpour, Farzaneh;Bajdik, Chris
    • Asian Pacific Journal of Cancer Prevention
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    • v.13 no.5
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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.