• Korean Journal of Food Science and Technology
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• v.42 no.3
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• pp.373-376
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• 2010

The objective of this study was to present the proper probability distribution model based on the data obtained from surveys on domestic refrigerator food storage temperatures in home. Domestic refrigerator temperatures were determined as risk factors in foodborne disease outbreaks for microbial risk assessment (MRA). The temperature was measured by directly visiting 139 homes using a data logger from May to September of 2009. The overall mean temperature for all the refrigerators in the survey was $3.53{\pm}2.96^{\circ}C$, with 23.6% of the refrigerators measuring above $5^{\circ}C$. Probability distributions were also created using @RISK program based on the measured temperature data. Statistical ranking was determined by the goodness of fit (GOF, i.e., the Kolmogorov-Smirnov (KS) or Anderson-Darling (AD) test) to determine the proper probability distribution model. This result showed that the LogLogistic (-10.407, 13.616, 8.6107) distribution was found to be the most appropriate for the MRA model. The results of this study might be directly used as input variables in exposure evaluation for conducting MRA.

• Proceedings of the KAIS Fall Conference
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• 2011.05a
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• pp.176-178
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• 2011

본 연구에서는 소프트웨어 제품을 개발하여 테스팅을 거친 후 사용자에게 인도하는 시기를 결정하는 방출문제에 대하여 연구되었다. 인도시기에 관한 모형은 무한 고장수에 의존하는 비동질적인 포아송 과정을 적용하였다. 이러한 포아송 과정은 소프트웨어의 결함을 제거하거나 수정 작업 중에도 새로운 결함이 발생될 가능성을 반영하는 모형이다. 강도함수는 로그-로지스틱 패턴을 이용하였다. 따라서 소프트웨어 요구 신뢰도를 만족시키고 소프트웨어 개발 및 유지 총비용을 최소화 시키는 방출시간이 최적 소프트웨어 방출 정책이 된다.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.177-185
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• 2014

Under bivariate normal distribution assumptions, the interaction and quadratic terms are needed in the logistic regression model with two predictors. However, depending on the correlation coefficient and the variances of two conditional distributions, the interaction and quadratic terms may not be necessary. Although the need for these terms can be determined by comparing the two scatter plots, it is not as useful for interaction terms. We explore the structure and usefulness of the 3-D residual plot as a tool for dealing with interaction in logistic regression models. If predictors have an interaction effect, a 3-D residual plot can show the effect. This is illustrated by simulated and real data.

• Journal of Forest and Environmental Science
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• v.36 no.1
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• pp.7-16
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• 2020

Tree size distribution modelling is an integral part of forest management. Most distribution yield systems rely on some flexible probability models. In this study, a simple finite mixture of two components two-parameter Weibull distribution was compared with complex four-parameter distributions in terms of their fitness to predict tree size distribution of teak (Tectona grandis Linn f) plantations. Also, a system of equation was developed using Seemingly Unrelated Regression wherein the size distributions of the stand were predicted. Generalized beta, Johnson's SB, Logit-Logistic and generalized Weibull distributions were the four-parameter distributions considered. The Kolmogorov-Smirnov test and negative log-likelihood value were used to assess the distributions. The results show that the simple finite mixture outperformed the four-parameter distributions especially in stands that are bimodal and heavily skewed. Twelve models were developed in the system of equation-one for predicting mean diameter, seven for predicting percentiles and four for predicting the parameters of the finite mixture distribution. Predictions from the system of equation are reasonable and compare well with observed distributions of the stand. This simplified mixture would allow for wider application in distribution modelling and can also be integrated as component model in stand density management diagram.

• Journal of Food Hygiene and Safety
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• v.27 no.3
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• pp.312-316
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• 2012

This study was to present the proper probability distribution models that based on the data for surveys of food cold storage temperatures as the input variables to the further MRA (Microbial risk assessment). The temperature was measured by directly visiting 7 food plants. The overall mean temperature for food cold storages in the survey was $2.55{\pm}3.55^{\circ}C$, with 2.5% of above $10^{\circ}C$, $-3.2^{\circ}C$ and $14.9^{\circ}C$ as a minimum and maximum. Temperature distributions by space-locations was $0.80{\pm}1.69^{\circ}C$, $0.59{\pm}1.68^{\circ}C$, and $0.65{\pm}1.46^{\circ}C$ as an upper (2.4~4 m), middle (1.5~2.4 m), and lower (0.7~1.5 m), respectively. Probability distributions were also created using @RISK program based on the measured temperature data. Statistical ranking was determined by the goodness of fit (GOF) to determine the proper probability distribution model. This result showed that the LogLogistic (-4.189, 5.9098, 3.2565) distribution models was found to be the most appropriate for relative MRA conduction.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.15-27
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• 2018

Parametric method of flood frequency analysis involves fitting of a probability distribution to observed flood data. When record length at a given site is relatively shorter and hard to apply the asymptotic theory, an alternative distribution to the generalized extreme value (GEV) distribution is often used. In this study, we consider the beta-P distribution (BPD) as an alternative to the GEV and other well-known distributions for modeling extreme events of small or moderate samples as well as highly skewed or heavy tailed data. The L-moments ratio diagram shows that special cases of the BPD include the generalized logistic, three-parameter log-normal, and GEV distributions. To estimate the parameters in the distribution, the method of moments, L-moments, and maximum likelihood estimation methods are considered. A Monte-Carlo study is then conducted to compare these three estimation methods. Our result suggests that the L-moments estimator works better than the other estimators for this model of small or moderate samples. Two applications to the annual maximum stream flow of Colorado and the rainfall data from cloud seeding experiments in Southern Florida are reported to show the usefulness of the BPD for modeling hydrologic events. In these examples, BPD turns out to work better than $beta-{\kappa}$, Gumbel, and GEV distributions.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.43-60
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• 2018

This paper considers the use of classical and Bayesian inference methods to analyze data generated by variables whose natural behavior can be modeled using asymmetric distributions in the presence of left censoring. Our approach used a $L{\grave{e}}vy$ distribution in the presence of left censored data and covariates. This distribution could be a good alternative to model data with asymmetric behavior in many applications as lifetime data for instance, especially in engineering applications and health research, when some observations are large in comparison to other ones and standard distributions commonly used to model asymmetry data like the exponential, Weibull or log-logistic are not appropriate to be fitted by the data. Inferences for the parameters of the proposed model under a classical inference approach are obtained using a maximum likelihood estimators (MLEs) approach and usual asymptotical normality for MLEs based on the Fisher information measure. Under a Bayesian approach, the posterior summaries of interest are obtained using standard Markov chain Monte Carlo simulation methods and available software like SAS. A numerical illustration is presented considering data of thyroglobulin levels present in a group of individuals with differentiated cancer of thyroid.

• Proceedings of the Korea Water Resources Association Conference
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• 2019.05a
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• pp.151-151
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• 2019

Because drought is a complex and stochastic phenomenon in nature, statistical approaches for drought assessment receive great attention for water resource planning and management. Generally drought characteristics such as severity, duration and intensity are modelled separately. This study aims to develop a relationship between drought characteristics using a bivariate copula model. To achieve the objective, we calculated the Standardized Precipitation Index (SPI) using rainfall data at 6 rain gauge stations for the period of 1961-1999 in Jehlum River Basin, Pakistan, and investigated the drought characteristics. Since there is a significant correlation between drought severity and duration, they are usually modeled using different marginal distributions and joint distribution function. Using exponential distribution for drought severity and log-logistic distribution for drought duration, the Galambos copula was recognized as best copula to model joint distribution of drought severity and duration based on the KS-statistic. Various return periods of drought were calculated to identify time interval of repeated drought events. The result of this study can provide useful information for effective water resource management and shows superiority against univariate drought analysis.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.22
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• pp.9673-9678
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• 2014

Background: Breast cancer is a fatal disease and the most frequently diagnosed cancer in women with an increasing pattern worldwide. The burden is mostly attributed to metastatic cancers that occur in one-third of patients and the treatments are palliative. It is of great interest to determine factors affecting time from cancer diagnosis to secondary metastasis. Materials and Methods: Cure rate models assume a Poisson distribution for the number of unobservable metastatic-component cells that are completely deleted from the non-metastasis patient body but some may remain and result in metastasis. Time to metastasis is defined as a function of the number of these cells and the time for each cell to develop a detectable sign of metastasis. Covariates are introduced to the model via the rate of metastatic-component cells. We used non-mixture cure rate models with Weibull and log-logistic distributions in a Bayesian setting to assess the relationship between metastasis free survival and covariates. Results: The median of metastasis free survival was 76.9 months. Various models showed that from covariates in the study, lymph node involvement ratio and being progesterone receptor positive were significant, with an adverse and a beneficial effect on metastasis free survival, respectively. The estimated fraction of patients cured from metastasis was almost 48%. The Weibull model had a slightly better performance than log-logistic. Conclusions: Cure rate models are popular in survival studies and outperform other models under certain conditions. We explored the prognostic factors of metastatic breast cancer from a different viewpoint. In this study, metastasis sites were analyzed all together. Conducting similar studies in a larger sample of cancer patients as well as evaluating the prognostic value of covariates in metastasis to each site separately are recommended.

• Asian Pacific Journal of Cancer Prevention
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• v.16 no.17
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• pp.7923-7927
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• 2015

Background: The Cox PH model is one of the most significant statistical models in studying survival of patients. But, in the case of patients with long-term survival, it may not be the most appropriate. In such cases, a cure rate model seems more suitable. The purpose of this study was to determine clinical factors associated with cure rate of patients with breast cancer. Materials and Methods: In order to find factors affecting cure rate (response), a non-mixed cure rate model with negative binomial distribution for latent variable was used. Variables selected were recurrence cancer, status for HER2, estrogen receptor (ER) and progesterone receptor (PR), size of tumor, grade of cancer, stage of cancer, type of surgery, age at the diagnosis time and number of removed positive lymph nodes. All analyses were performed using PROC MCMC processes in the SAS 9.2 program. Results: The mean (SD) age of patients was equal to 48.9 (11.1) months. For these patients, 1, 5 and 10-year survival rates were 95, 79 and 50 percent respectively. All of the mentioned variables were effective in cure fraction. Kaplan-Meier curve showed cure model's use competence. Conclusions: Unlike other variables, existence of ER and PR positivity will increase probability of cure in patients. In the present study, Weibull distribution was used for the purpose of analysing survival times. Model fitness with other distributions such as log-N and log-logistic and other distributions for latent variable is recommended.