• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.311-320
• /
• 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
• /
• 제8권2호
• /
• pp.153-161
• /
• 1997

본 연구에서는 우리나라 6대 생명보험회사의 모든 남자의 개인보험 계약자를 대상으로 조사한 1988년부터 1992년까지 25,000,000건의 자료를 가중이동평균모형을 이용한 보간법과 곰페 르츠모형을 이용한 보외법을 적용하여 경험생명표를 작성하였다. 적합성 및 평활성 기준에서 가중이동평균모형의 차분수와 항수, 곰페르츠모형의 모수 및 두 모형이 접촉하는 접점의 연령을 산출하였다. 특히 연립방정식을 이용하여 곰페르츠 모형의 모수를 폐쇄형으로 추정하는 방법을 제안하였다.

• 산업경영시스템학회지
• /
• 제32권4호
• /
• pp.184-191
• /
• 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
• /
• 제56권1호
• /
• pp.59-66
• /
• 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
• /
• 제52권2호
• /
• pp.140-144
• /
• 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.

• 한국수산과학회지
• /
• 제25권1호
• /
• pp.29-36
• /
• 1992

한국 근해 참조기 자원의 양적인 변동에 관련되는 자원 특성치인 개체의 성장식과 개체군의 생잔율, 순간사망계수 및 어획개시연령 등을 추정하였다. 참조기의 연령과 성장 관계는 Gompertz 성장 모델의 선형화 방법에 의한 이론적인 적합도가 가장 높았으나 실용적인 면을 고려하여 von Bertalanffy 성장식의 이용이 권고되었다. 생잔율은 0.219(분산: 0.0000262), 순간자연사망계수는 0.4/년으로 추정되었다. 최근의 순간어획사망계수는 1.11/년으로 추정되어 순간자연사망계수의 약 3배 정도로 높게 나타났다. 어획개시연령은 0.602세로 추정되었다

• Communications for Statistical Applications and Methods
• /
• 제21권1호
• /
• pp.23-43
• /
• 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
• /
• 제15권5호
• /
• pp.715-720
• /
• 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).