• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.311-320
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• 2005

Studies in the evolutionary biology of aging require good estimates of the age-dependent mortality rate coefficient (one of the Gompertz parameters). In this paper we introduce an alternative algorithm for estimating this parameter. And we discuss the sensitivity of the estimates to changes in the other model parameters.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.153-161
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• 1997

A Korean exporience life table(male) is constructed by using a mixture of weighted moving average(WMA) model and Gompertz' parametric survival model based on 25,000,000 insured of major 6 life insurance companies from 1988 to 1992. The graduated values are taken as those which minimize the composite measure of fittness and smoothness. Moreover, we propose closed form estimators for three parameters of Gompertz' model.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.32 no.4
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• pp.184-191
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• 2009

In a technological driven environment, a depreciation estimate which is based on traditional life analysis results in a decelerated rate of capital recovery. This time pattern of technological growths models needs to be incorporated into life analysis framework especially in those industries experiencing fast technological changes. The approximation technique for calculating the variance can be applied to the six growth models that were selected by the degree of skewness and the transformation of the functions. For the Pearl growth model, the Gompertz growth model, and the Weibull growth model, the errors have zero mean and a constant variance over time. However, transformed models like the linearized Fisher-Pry model, the linearized Gompertz growth model, and the linearized Weibull growth model have increasing variance from zero to that point at which inflection occurs. It can be recommended that if the variance of error over time is increasing, then a transformation of observed data is appropriate.

• Journal of Preventive Medicine and Public Health
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• v.56 no.1
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• pp.59-66
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• 2023

Objectives: The aim of this study was to evaluate the effect of body weight status and sleep duration on the discrete-time hazard of menarche in Korean schoolgirls using multiple-point prospective panel data. Methods: The study included 914 girls in the 2010 Korean Children and Youth Panel Study who were in the elementary first-grader panel from 2010 until 2016. We used a Gompertz regression model to estimate the effects of weight status based on age-specific and sex-specific body mass index (BMI) percentile and sleep duration on an early schoolchild's conditional probability of menarche during a given time interval using general health condition and annual household income as covariates. Results: Gompertz regression of time to menarche data collected from the Korean Children and Youth Panel Study 2010 suggested that being overweight or sleeping less than the recommended duration was related to an increased hazard of menarche compared to being average weight and sleeping 9 hours to 11 hours, by 1.63 times and 1.38 times, respectively, while other covariates were fixed. In contrast, being underweight was associated with a 66% lower discrete-time hazard of menarche. Conclusions: Weight status based on BMI percentiles and sleep duration in the early school years affect the hazard of menarche.

• Journal of Preventive Medicine and Public Health
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• v.52 no.2
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• pp.140-144
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• 2019

Objectives: Investigating the survival of patients with cancer is vitally necessary for controlling the disease and for assessing treatment methods. This study aimed to compare various statistical models of survival and to determine the survival rate and its related factors among patients suffering from lung cancer. Methods: In this retrospective cohort, the cumulative survival rate, median survival time, and factors associated with the survival of lung cancer patients were estimated using Cox, Weibull, exponential, and Gompertz regression models. Kaplan-Meier tables and the log-rank test were also used to analyze the survival of patients in different subgroups. Results: Of 102 patients with lung cancer, 74.5% were male. During the follow-up period, 80.4% died. The incidence rate of death among patients was estimated as 3.9 (95% confidence [CI], 3.1 to 4.8) per 100 person-months. The 5-year survival rate for all patients, males, females, patients with non-small cell lung carcinoma (NSCLC), and patients with small cell lung carcinoma (SCLC) was 17%, 13%, 29%, 21%, and 0%, respectively. The median survival time for all patients, males, females, those with NSCLC, and those with SCLC was 12.7 months, 12.0 months, 16.0 months, 16.0 months, and 6.0 months, respectively. Multivariate analyses indicated that the hazard ratios (95% CIs) for male sex, age, and SCLC were 0.56 (0.33 to 0.93), 1.03 (1.01 to 1.05), and 2.91 (1.71 to 4.95), respectively. Conclusions: Our results showed that the exponential model was the most precise. This model identified age, sex, and type of cancer as factors that predicted survival in patients with lung cancer.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.25 no.1
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• pp.29-36
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• 1992

This paper deals with the estimation of population ecological parameters, including growth parameters, survival rates, instantaneous coefficient of natural mortality and age at first capture, of the small yellow-croaker, Pseudosciaena Polyactis in Korean waters, which determine fluctuations in stock abundance. For describing the growth of the small yellow croaker, von Bertalanffy growth equation was recommended for the purpose of stock assessment, although the Gompertz model yielded the closest fit. The survival rate (S) of the croaker was estimated to be 0.219 (variance=0.0000262), and the instantaneous coefficient of natural mortality (M) was 0.4 $year^{-1}$. From the estimates of S and M, the instantaneous coefficient of fishing mortality (F) was calculated to be 1.11$year^{-1}$ implying an impact from fishing three times that of natural mortality. Finally, the age at first capture $(t_{c})$ was estimated to be 0.602.

• Communications for Statistical Applications and Methods
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• v.21 no.1
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• pp.23-43
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• 2014

We study the dependence between the insureds in multiple-life insurance contracts. With the future lifetimes of the insureds modeled as correlated random variables, both premium and reserve are different from those under independence. In this paper, Gaussian copula is used to impose the dependence between the insureds with Gompertz marginals. We analyze the change of the reserves of standard multiple-life insurance contracts at various dependence levels. We find that the reserves based on the assumption of dependent lifetimes are quite different for some contracts from those under independence as its correlation increase, which elucidate the importance of the dependence model in multiple-life contingencies in both theory and practice.

• Food Science and Biotechnology
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• v.15 no.5
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• pp.715-720
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• 2006

This study was performed to develop a predictive model for the growth kinetics of Listeria monocytogenes in tryptic soy broth (TSB) using a response surface model with a combination of potassium lactate (PL), temperature, and pH. The growth parameters, specific growth rate (SGR), and lag time (LT) were obtained by fitting the data into the Gompertz equation and showed high fitness with a correlation coefficient of $R^2{\geq}0.9192$. The polynomial model was identified as an appropriate secondary model for SGR and LT based on the coefficient of determination for the developed model ($R^2\;=\;0.97$ for SGR and $R^2\;=\;0.86$ for LT). The induced values that were calculated using the developed secondary model indicated that the growth kinetics of L. monocytogenes were dependent on storage temperature, pH, and PL. Finally, the predicted model was validated using statistical indicators, such as coefficient of determination, mean square error, bias factor, and accuracy factor. Validation of the model demonstrates that the overall prediction agreed well with the observed data. However, the model developed for SGR showed better predictive ability than the model developed for LT, which can be seen from its statistical validation indices, with the exception of the bias factor ($B_f$ was 0.6 for SGR and 0.97 for LT).