• Title, Summary, Keyword: Gompertz growth model

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A Software Reliability Growth Model Based on Gompertz Growth Curve (Gompertz 성장곡선 기반 소프트웨어 신뢰성 성장 모델)

  • Park Seok-Gyu;Lee Sang-Un
    • The KIPS Transactions:PartD
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    • v.11D no.7
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    • pp.1451-1458
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    • 2004
  • Current software reliability growth models based on Gompertz growth curve are all logarithmic type. Software reliability growth models based on logarithmic type Gompertz growth curve has difficulties in parameter estimation. Therefore this paper proposes a software reliability growth model based on the logistic type Gompertz growth curie. Its usefulness is empirically verified by analyzing the failure data sets obtained from 13 different software projects. The parameters of model are estimated by linear regression through variable transformation or Virene's method. The proposed model is compared with respect to the average relative prediction error criterion. Experimental results show that the pro-posed model performs better the models based on the logarithmic type Gompertz growth curve.

A Gompertz Model for Software Cost Estimation (Gompertz 소프트웨어 비용 추정 모델)

  • Lee, Sang-Un
    • The KIPS Transactions:PartD
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    • v.15D no.2
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    • pp.207-212
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    • 2008
  • This paper evaluates software cost estimation models, and presents the most suitable model. First, we transformed a relevant model into variables to make in linear. Second, we evaluated model's performance considering how much suitable the cost data of the actual development software was. In the stage of model performance evaluation criteria, we used MMRE which is the relative error concept rather than the absolute error. Existing software cost estimation model follows Weibull, Gamma, and Rayleigh function. In this paper, Gompertz function model is suggested which is a kind of growth curve. Additionally, we verify the compatability of other different growth curves. As a result of evaluation of model's performance, Gompertz function was considered to be the most suitable for the cost estimation model.

Bayesian Inference of the Stochastic Gompertz Growth Model for Tumor Growth

  • Paek, Jayeong;Choi, Ilsu
    • Communications for Statistical Applications and Methods
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    • v.21 no.6
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    • pp.521-528
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    • 2014
  • A stochastic Gompertz diffusion model for tumor growth is a topic of active interest as cancer is a leading cause of death in Korea. The direct maximum likelihood estimation of stochastic differential equations would be possible based on the continuous path likelihood on condition that a continuous sample path of the process is recorded over the interval. This likelihood is useful in providing a basis for the so-called continuous record or infill likelihood function and infill asymptotic. In practice, we do not have fully continuous data except a few special cases. As a result, the exact ML method is not applicable. In this paper we proposed a method of parameter estimation of stochastic Gompertz differential equation via Markov chain Monte Carlo methods that is applicable for several data structures. We compared a Markov transition data structure with a data structure that have an initial point.

Analysis of Growth in Intersubspecific Crossing of Mice Using Gompertz Model

  • Kurnianto, E.;Shinjo, A.;Suga, D.
    • Asian-Australasian Journal of Animal Sciences
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    • v.11 no.1
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    • pp.84-88
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    • 1998
  • The aim of this study was to describe growth patterns of mice using Gompertz model. Two distinct types of mice, laboratory mouse $CF_{\sharp1}$ (Mus musculus domesticus) and Yonakuni wild mouse (Yk, Mus musculus molossinus yonakuni) were used. From all possible crosses, there were two parental types and two reciprocal $F_1$ crosses obtained. Individual body weights were measured weekly from birth to ten weeks of age on 321 mice. Standardization to six mice was conducted and only first litters were used. Growth curve parameters were estimated to fit growth data. The results showed that growth among genetic groups were significantly different (p < 0.05) for both sexes, in which parental type of $CF_{\sharp1}$ and Yk had the highest and the smallest values, respectively. Meanwhile, reciprocal $F_1$ crosses were intermediate between parental types. It was concluded that Gompertz model provided and excellent fit for the growth data with a high coefficient determination $(R^2 = 0.999)$.

Modeling Growth of Canopy Heights and Stem Diameters in Soybeans at Different Groundwater Level (지하 수위가 다른 조건에서 콩의 초장과 경태 모델링)

  • Choi, Jin-Young;Kim, Dong-Hyun;Kwon, Soon-Hong;Choi, Won-Sik;Kim, Jong-Soon
    • Journal of the Korean Society of Industry Convergence
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    • v.20 no.5
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    • pp.395-404
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    • 2017
  • Cultivating soybeans in rice paddy field reduces labor costs and increases the yield. Soybeans, however, are highly susceptible to excessive soil water in paddy field. Controlled drainage system can adjust groundwater level (GWL) and control soil moisture content, resulting in improvement soil environments for optimum crop growth. The objective of this study was to fit the soybean growth data (canopy height and stem diameter) using Gompertz model and Logistic model at different GWL and validate those models. The soybean, Daewon cultivar, was grown on the lysimeters controlled GWL (20cm and 40cm). The soil textures were silt loam and sandy loam. The canopy height and stem diameter were measured from the 20th days after seeding until harvest. The Gompertz and Logistic models were fitted with the growth data and each growth rate and maximum growth value was estimated. At the canopy height, the $R_2$ and RMSE were 0.99 and 1.58 in Gompertz model and 0.99 and 1.33 in Logistic model, respectively. The large discrepancy was shown in full maturity stage (R8), where plants have shed substantial amount of leaves. Regardless of soil texture, the maximum growth values at 40cm GWL were greater than the value at 20cm GWL. The growth rates were larger at silt loam. At the stem diameter, the $R_2$ and RMSE were 0.96 and 0.27 in Gompertz model and 0.96 and 0.26 in Logistic model, respectively. Unlike the canopy height, the stem diameter in R8 stage didn't decrease significantly. At both GWLs, the maximum growth values and the growth rates at silt loam were all larger than the values at sandy loam. In conclusion, Gompertz model and Logistic model both well fit the canopy heights and stem diameters of soybeans. These growth models can provide invaluable information for the development of precision water management system.

Comparison of Models to Describe Growth of Green Algae Chlorella vulgaris for Nutrient Removal from Piggery Wastewater (양돈폐수의 영양염류 제거를 위한 녹조류 Chlorella vulgaris 성장 모형의 비교)

  • Lim, Byung-Ran;Jutidamrongphan, Warangkana;Park, Ki-Young
    • Journal of The Korean Society of Agricultural Engineers
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    • v.52 no.6
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    • pp.19-26
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    • 2010
  • Batch experiments were conducted to investigate growth and nutrient removal performance of microalgae Chlorella vulgaris by using piggery wastewater in different concentration of pollutants and the common growth models (logistic, Gompertz and Richards) were applied to compare microalgal growth parameters. Removal of nitrogen (N) and phosphorus (P) by Chlorella vulgaris showed correlation with biomass increase, implying nutrient uptake coupled with microalgae growth. The higher the levels of suspended solids (SS), COD and ammonia nitrogen were in the wastewater, the worse growth of Chlorella vulgaris was observed, showing the occurrence of growth inhibition in higher concentration of those pollutants. The growth parameters were estimated by non-linear regression of three growth curves for comparative analyses. Determination of growth parameters were more accurate with population as a variable than the logarithm of population in terms of R square. Richards model represented better fit comparing with logistic and Gompertz model. However, Richards model showed some complexity and sensitivity in calculation. In the cases tested, both logistic and Gompertz equation were proper to describe the growth of microalgae on piggery wastewater as well as easy to application.

Development of a Predictive Model Describing the Growth of Listeria Monocytogenes in Fresh Cut Vegetable (샐러드용 신선 채소에서의 Listerio monocytogenes 성장예측모델 개발)

  • Cho, Joon-Il;Lee, Soon-Ho;Lim, Ji-Su;Kwak, Hyo-Sun;Hwang, In-Gyun
    • Journal of Food Hygiene and Safety
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    • v.26 no.1
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    • pp.25-30
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    • 2011
  • In this study, predictive mathematical models were developed to predict the kinetics of Listeria monocytogenes growth in the mixed fresh-cut vegetables, which is the most popular ready-to-eat food in the world, as a function of temperature (4, 10, 20 and $30^{\circ}C$). At the specified storage temperatures, the primary growth curve fit well ($r^2$=0.916~0.981) with a Gompertz and Baranyi equation to determine the specific growth rate (SGR). The Polynomial model for natural logarithm transformation of the SGR as a function of temperature was obtained by nonlinear regression (Prism, version 4.0, GraphPad Software). As the storage temperature decreased from $30^{\circ}C$ to $4^{\circ}C$, the SGR decreased, respectively. Polynomial model was identified as appropriate secondary model for SGR on the basis of most statistical indices such as mean square error (MSE=0.002718 by Gompertz, 0.055186 by Baranyi), bias factor (Bf=1.050084 by Gompertz, 1.931472 by Baranyi) and accuracy factor (Af=1.160767 by Gompertz, 2.137181 by Baranyi). Results indicate L. monocytogenes growth was affected by temperature mainly, and equation was developed by Gompertz model (-0.1606+$0.0574^*Temp$+$0.0009^*Temp^*Temp$) was more effective than equation was developed by Baranyi model (0.3502-$0.0496^*Temp$+$0.0022^*Temp^*Temp$) for specific growth rate prediction of L.monocytogenes in the mixed fresh-cut vegetables.

Comparative Study on Growth Patterns of 25 Commercial Strains of Korean Native Chicken

  • Manjula, Prabuddha;Park, Hee-Bok;Yoo, Jaehong;Wickramasuriya, Samiru;Seo, Dong-Won;Choi, Nu-Ri;Kim, Chong Dae;Kang, Bo-Seok;Oh, Ki-Seok;Sohn, Sea-Hwan;Heo, Jung-Min;Lee, Jun-Heon
    • Korean Journal of Poultry Science
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    • v.43 no.1
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    • pp.1-14
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    • 2016
  • Prediction of growth patterns of commercial chicken strains is important. It can provide visual assessment of growth as function of time and prediction body weight (BW) at a specific age. The aim of current study is to compare the three nonlinear functions (i.e., Logistic, Gompertz, and von Betalanffy) for modeling the growth of twenty five commercial Korean native chicken (KNC) strains reared under a battery cage system until 32 weeks of age and to evaluate the three models with regard to their ability to describe the relationship between BW and age. A clear difference in growth pattern among 25 strains were observed and classified in to the groups according to their growth patterns. The highest and lowest estimated values for asymptotic body weight (C) for 3H and 5W were given by von Bertalanffy and Logistic model 4629.7 g for 2197.8 g respectively. The highest estimated parameter for maturating rate (b) was given by Logistic model 0.249 corresponds to the 2F and lowest in von Bertalanffy model 0.094 for 4Y. According to the coefficient of determination ($R^2$) and mean square of error (MSE), Gompertz and von Bertalanffy models were suitable to describe the growth of Korean native chicken. Moreover, von Bertalannfy model was well described the most of KNC growth with biologically meaningful parameter compared to Gompertz model.

Predictive Growth Model of Native Isolated Listeria monocytogenes on raw pork as a Function of Temperature and Time (온도와 시간을 주요 변수로 한 냉장 돈육에서의 native isolated Listeria monocytogenes에 대한 성장예측모델)

  • Hong, Chong-Hae;Sim, Woo-Chang;Chun, Seok-Jo;Kim, Young-Su;Oh, Deog-Hwan;Ha, Sang-Do;Choi, Weon-Sang;Bahk, Gyung-Jin
    • Korean Journal of Food Science and Technology
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    • v.37 no.5
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    • pp.850-855
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    • 2005
  • Model was developed to predict the growth of Listeria monocytogenes in raw pork. Experiment condition for model development was full 5-by-7 factorial arrangements of temperature (0, 5, 10, 15, and $20^{\circ}C$) and time (0, 1, 2, 3, 18, 48, and 120 hr). Gompertz values A, C, B, and M, and growth kinetics, exponential growth rate (EGR), generation time (GT), lag phase duration (LPD), and maximum population density (MPD) were calculated based on growth increased data. GT and LPD values gradually decreased, whereas EGR value gradually increased with increasing temperature. Response surface analysis (RSA) was carried out using Gompertz B and M values, to formulate equation with temperature being main control factor. This equation was applied to Gompertz equation. Experimental and predictive values for GT, LPD, and EGR, compared using the model, showed no significant differences (p<0.01). Proposed model could be used to predict growth of microorganisms for exposure assessment of MRA, thereby allowing more informed decision-making on potential regulatory actions of microorganisms in raw pork.

Estimation of growth curve in Hanwoo steers using progeny test records

  • Yun, Jae-Woong;Park, Se-Yeong;Park, Hu-Rak;Eum, Seung-Hoon;Roh, Seung-Hee;Seo, Jakyeom;Cho, Seong-Keun;Kim, Byeong-Woo
    • Korean Journal of Agricultural Science
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    • v.43 no.4
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    • pp.623-633
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    • 2016
  • A total of 6,973 steer growth records of Hanwoo breeding bull's progeny test data collected from 1989 to 2015 were analyzed to identify the most appropriate growth curve among three growth curve models (Gompertz, Logistic and von Bertalanffy). The Gompertz growth curve model equation was $W_t=990.5e^{{-2.7479e}^{-0.00241t}}$, the Logistic growth curve model equation was $W_t=772(1+8.3314e^{-0.00475t})^{-1}$, and the von Bertalanffy growth curve model equation was $W_t=1,196.4(1-0.646e^{-0.00162t})^3$. The Gompertz model parameters A, b, and k were estimated to be $990.5{\pm}10.27$, $2.7479{\pm}0.0068$, and $0.00241{\pm}0.000028$, respectively. The inflection point age was estimated to be 421 days and the weight of inflection point was 365.3 kg. The Logistic model parameters A, b, and k were estimated to be $772.0{\pm}4.12$, $8.3314{\pm}0.0453$, and $0.00475{\pm}0.000033$, respectively. The inflection point age was estimated to be 445 days and the weight of inflection point was 385.0 kg. The von Bertalanffy model parameters A, b, and k were estimated to be $1196.4{\pm}18.39$, $0.646{\pm}0.0010$, and $0.00162{\pm}0.000027$, respectively. The inflection point age was estimated to be 405 days and the weight of inflection point was 352.0 kg. Mature body weight of the von Bertalanffy model was 1196.4 kg, the Gompertz model was 990.5 kg, and the Logistic model was 772.0 kg. The difference between actual and estimated weights was similar in the Logistic model and the von Bertalanffy model. The difference between market weight and estimated market weight was the lowest in the Gompertz model. The growth curve using the von Bertalanffy model showed the lowest mean square error.