• Title/Summary/Keyword: Gompertz growth model

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Development of Market Growth Pattern Map Based on Growth Model and Self-organizing Map Algorithm: Focusing on ICT products (자기조직화 지도를 활용한 성장모형 기반의 시장 성장패턴 지도 구축: ICT제품을 중심으로)

  • Park, Do-Hyung;Chung, Jaekwon;Chung, Yeo Jin;Lee, Dongwon
    • Journal of Intelligence and Information Systems
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    • v.20 no.4
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    • pp.1-23
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    • 2014
  • Market forecasting aims to estimate the sales volume of a product or service that is sold to consumers for a specific selling period. From the perspective of the enterprise, accurate market forecasting assists in determining the timing of new product introduction, product design, and establishing production plans and marketing strategies that enable a more efficient decision-making process. Moreover, accurate market forecasting enables governments to efficiently establish a national budget organization. This study aims to generate a market growth curve for ICT (information and communication technology) goods using past time series data; categorize products showing similar growth patterns; understand markets in the industry; and forecast the future outlook of such products. This study suggests the useful and meaningful process (or methodology) to identify the market growth pattern with quantitative growth model and data mining algorithm. The study employs the following methodology. At the first stage, past time series data are collected based on the target products or services of categorized industry. The data, such as the volume of sales and domestic consumption for a specific product or service, are collected from the relevant government ministry, the National Statistical Office, and other relevant government organizations. For collected data that may not be analyzed due to the lack of past data and the alteration of code names, data pre-processing work should be performed. At the second stage of this process, an optimal model for market forecasting should be selected. This model can be varied on the basis of the characteristics of each categorized industry. As this study is focused on the ICT industry, which has more frequent new technology appearances resulting in changes of the market structure, Logistic model, Gompertz model, and Bass model are selected. A hybrid model that combines different models can also be considered. The hybrid model considered for use in this study analyzes the size of the market potential through the Logistic and Gompertz models, and then the figures are used for the Bass model. The third stage of this process is to evaluate which model most accurately explains the data. In order to do this, the parameter should be estimated on the basis of the collected past time series data to generate the models' predictive value and calculate the root-mean squared error (RMSE). The model that shows the lowest average RMSE value for every product type is considered as the best model. At the fourth stage of this process, based on the estimated parameter value generated by the best model, a market growth pattern map is constructed with self-organizing map algorithm. A self-organizing map is learning with market pattern parameters for all products or services as input data, and the products or services are organized into an $N{\times}N$ map. The number of clusters increase from 2 to M, depending on the characteristics of the nodes on the map. The clusters are divided into zones, and the clusters with the ability to provide the most meaningful explanation are selected. Based on the final selection of clusters, the boundaries between the nodes are selected and, ultimately, the market growth pattern map is completed. The last step is to determine the final characteristics of the clusters as well as the market growth curve. The average of the market growth pattern parameters in the clusters is taken to be a representative figure. Using this figure, a growth curve is drawn for each cluster, and their characteristics are analyzed. Also, taking into consideration the product types in each cluster, their characteristics can be qualitatively generated. We expect that the process and system that this paper suggests can be used as a tool for forecasting demand in the ICT and other industries.

Genetic Aspects of the Growth Curve Parameters in Hanwoo Cows (한우 암소의 성장곡선 모수에 대한 유전적 경향)

  • Lee, Chang-U;Choe, Jae-Gwan;Jeon, Gi-Jun;Kim, Hyeong-Cheol
    • Journal of Animal Science and Technology
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    • v.48 no.1
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    • pp.29-38
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    • 2006
  • The objective of this study was to estimate genetic variances of growth curve parameters in Hanwoo cows. The data used in this study were records from 1,083 Hanwoo cows raised at Hanwoo Experiment Station, National Livestock Research Institute(NLRI). First evaluation model(Model I) fit year-season of birth and age of dam as fixed effects and second model(Model II) added age at the final weight as a linear covariate to Model I. Heritability estimates of A, b and k from Gompertz model were 0.22, 0.11 and 0.07 using modelⅠ and 0.28, 0.11 and 0.12 using modelⅡ. Those from Von Bertalanffy model were 0.22, 0.11 and 0.07 using modelⅠ, 0.28, 0.11 and 0.12 using modelⅡ. Heritability estimates of A, b and k from Logistic model were 0.14, 0.07 and 0.05 using modelⅠ, 0.18, 0.07 and 0.12 using modelⅡ. Heritability estimates of A from Gompertz model were higher than those from Von Bertalanffy model or Logistic model in both model Ⅰand model Ⅱ. Heritability estimates of b from Logistic model were higher than those from Gompertz model or Von Bertalanffy model in both modelⅠand model Ⅱ. Heritability estimates of birth weight, weaning weight, 3 month weight, 6 month weight, 9 month weight, 12 month weight, 18 month weight, 24 month weight, 36 month weight were after linear age adjustment 0.27, 0.11, 0.19, 0.14, 0.16, 0.23, 0.52 and 0.32, respectively. Heritability estimates of birth weight, weaning weight, 3 month weight, 6 month weight, 9 month weight and 24 month weight fit by Gompertz model were larger than those estimated from linearly adjusted data. Heritability estimates of 12 month weight, 18 month weight and 36 month weight fit by Von Bertalanffy model were larger than those estimated from linearly adjusted data. In the multitrait analyses for parameters from Gompertz model, genetic and phenotypic correlations between A and k parameters were -0.47 and -0.67 using modelⅠand -0.56 and -0.63 using model Ⅱ. Those between the A and b parameters were 0.69 and 0.34 using modelⅠand 0.72 and 0.37 using model Ⅱ. Those between the b and k parameters were -0.26 and 0.01 using modelⅠand -0.30 and 0.01 using model Ⅱ. In the multitrait analyses for parameters from Von Bertalanffy model, genetic and phenotypic correlations between A and k parameters were -0.49 and -0.67 suing model Ⅰ and -0.57 and -0.70 using modelⅡ. Those between the A and b parameters were 0.61 and 0.33 using modelⅠ and 0.60 and 0.30 using model Ⅱ. Those between the b and k parameters were -0.20 and 0.02 using modelⅠ and 0.16 and 0.00 using modelⅡ. In the multitrait analyses for parameters from Logistic model, genetic and phenotypic correlations between A and k parameters were -0.43 and -0.67 using model Ⅰ and -0.50 and -0.63 using modelⅡ. Those between the A and b parameters were 0.47 and 0.22 using modelⅠ and 0.38 and 0.24 using modelⅡ. Those between the b and k parameters were -0.09 and 0.02 using model Ⅰ and -0.02 and 0.13 using model Ⅱ.

Development of Site Index Curves and Comparison with National Scale for Cryptomeria japonica in Gyeongsang-do (경상도 지역 삼나무의 지위지수 곡선 개발 및 비교 검정)

  • Park, Hee-Jung;Choi, Suk-Won;Ko, Byung-Jun;Lee, Sang-Hyun
    • Journal of Korean Society of Forest Science
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    • v.110 no.4
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    • pp.658-664
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    • 2021
  • This study aimed to develop accurate status site index curves for C. japonica in Gyeongsang-do that reflect the regional characteristics. The development of high-growth models in Chapman-Richards, Schumacher, and Gompertz for 552 C. japonica growing in Gyeongsang-do. The Gompertz growth function is the most suitable for developing site index curves. The comparative test was analyzed using the F test at a significance level of 5% and the graph. As a result, compared with the national site index curves and site index curves under base age in Jeolla-do, the p-value was 0.05 or higher, and there was no statistically significant difference. The p-value was 0.05 or lower compared with site index curves over stand age in Jeolla-do, indicating a statistically significant difference. Therefore, it was determined that site index curves for C. japonica in Gyeongsang-do can be applied to the national site index curves and site index curves under base age in Jeolla-do, but not to site index curves over base age in Jeolla-do. Hence, based on the results of the study, it is possible to provide basic data on the forest management system for C. japonica in Gyeongsang-do and systematic and reasonable management through high field application reflecting regional characteristics.

Analysis of Software Reliability Growth Model with Gamma Family Distribution (감마족 분포를 이용한 소프트웨어 신뢰 성장 모형의 분석)

  • Kan, Kwang-Hyun;Jang, Byeong-Ok;Kim, Hee-Cheul
    • Journal of IKEEE
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    • v.9 no.2 s.17
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    • pp.143-151
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    • 2005
  • Finite failure NHPP models proposed in the literature exhibit is either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. For the sake of proposing shape parameter of the Gamma family distribution, used the special pattern. Data set, where the underlying failure process could not be adequately described by the knowing models, which motivated the development of the Gamma or Weibull model and Gompertz model. Analysis of failure data set that led us to the Gamma or Weibull model and Gompertz model using arithmetic and Laplace trend tests, bias tests was presented in this Paper.

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On Parameter Estimation of Growth Curves for Technological Forecasting by Using Non-linear Least Squares

  • Ko, Young-Hyun;Hong, Seung-Pyo;Jun, Chi-Hyuck
    • Management Science and Financial Engineering
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    • v.14 no.2
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    • pp.89-104
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    • 2008
  • Growth curves including Bass, Logistic and Gompertz functions are widely used in forecasting the market demand. Nonlinear least square method is often adopted for estimating the model parameters but it is difficult to set up the starting value for each parameter. If a wrong starting point is selected, the result may lead to erroneous forecasts. This paper proposes a method of selecting starting values for model parameters in estimating some growth curves by nonlinear least square method through grid search and transformation into linear regression model. Resealing the market data using the national economic index makes it possible to figure out the range of parameters and to utilize the grid search method. Application to some real data is also included, where the performance of our method is demonstrated.

Models Describing Growth Characteristics of Holstein Dairy Cows Raised in Korea

  • Vijayakumar, Mayakrishnan;Choy, Yun-Ho;Kim, Tae-Il;Lim, Dong-Hyun;Park, Seong-Min;Alam, Mahboob;Choi, Hee-Chul;Ki, Kwang-Seok;Lee, Hyun-Jeong
    • Journal of The Korean Society of Grassland and Forage Science
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    • v.40 no.3
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    • pp.167-176
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    • 2020
  • The objective of the present study was to determine the best model to describe and quantify the changes in live body weight, height at withers, height at rump, body length and chest girth of Holstein cows raised under Korean feeding conditions for 50 months. The five standard growth models namely polynomial linear regression models, regression of growth variables on the first and second-order of ages in days (model 1) and regression of growth variables on age covariates from first to the third-order (model 2) as well as non-linear models were fitted and evaluated for representing growth pattern of Holstein cows raised in Korean feeding circumstances. Nonlinear models fitted were three exponential growth curve models; Brody, Gompertz, and von Bertalanffy functional models. For this purpose, a total of 22 Holstein cows raised in Korea used in the period from April 2016 to May 2020. Each model fitted to monthly growth curve records of dairy cows by using PROC NLIN procedure in SAS program. On the basis of the results, nonlinear models showed the lower root mean square of error (RMSE) for live body weight, height at withers, height at rump, body length and chest girth (12.22, 1.95, 1.55, 4.04, 2.06) with higher correlation coefficiency (R2) values for live body weight, height at withers, height at rump, body length and chest girth (0.99, 0.99, 0.99, 1.00, 1.00). Overall, the evaluation of the different growth models indicated that the Gompertz model used in the study seemed to be the most appropriate one for standard growth of Holstein cows raised under Korean feeding system.

Estimation of Parameters for Individual Growth Curves of Cows in Bostaurus Coreanae (한우 암소의 개체별 성장곡선 모수 추정)

  • Lee, C.W.;Choi, J.G.;Jeon, G.J.;Na, K.J.;Lee, C.;Hwang, J.M.;Kim, B.W.;Kim, J.B.
    • Journal of Animal Science and Technology
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    • v.45 no.5
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    • pp.689-694
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    • 2003
  • Weight records of Hanwoo cows from birth to 36 months of age collected in Daekwanryeong branch, National Livestock Research Institute(NLRI) were fitted to Gompertz, von Bertalanffy and Logistic functions. For the growth curve parameters fitted on individual records using Gompertz model, the mean estimates of mature weight(A), growth ratio(b) and growth rate(k) were 383.42 ${\pm}$ 97.29kg, 2.374 ${\pm}$ 0.340 and 0.0037 ${\pm}$ 0.0012, respectively, and mean estimates of body weight, age and daily gain rate at inflection were 141.05 ${\pm}$ 35.79kg, 255.63 ${\pm}$ 109.09 day and 0.500 ${\pm}$ 0.123kg, respectively. For von BertalanfTy model, the mean estimates of A, b and k were 410.47 ${\pm}$ 117.98kg, 0.575${\pm}$0.057 and 0.003 ${\pm}$ 0.001, and mean estimates of body weight, age and daily gain at inflection were 121.62 ${\pm}$ 34.94kg, 211.02 ${\pm}$ 105.53 and 0.504 ${\pm}$ O.l24kg. For Logistic model, the mean estimates of A, b and k were 347.64 ${\pm}$ 97.29kg, 6.73 ${\pm}$ 0.34 and 0.006 ${\pm}$ 0.0018, and mean estimates of body weight, age and daily gain at inflection were 173.82 ${\pm}$ 37.25kg, 324.47 ${\pm}$ 126.85 and 0.508 ${\pm}$ 0.131kg. Coefficients of variation for the A, b and k parameter estimates were 25.3%, 14.3% and 32.4%, respectively, for Gompertz model, 28.70/0, 9.9% and 33.3% for von Bertalanffy model, and 27.9°/0, 5.0% and 30.0% for Logistic model.

Prediction of Seedling Emergence and Early Growth of Eleocharis kuroguwai Ohwi under Evaluated Temperature (상승된 온도 조건에서 올방개(Eleocharis kuroguwai)의 출아 및 초기생장 예측)

  • Kim, Jin-Won;Moon, Byeong-Chul;Lim, Soo-Hyun;Chung, Ji-Hoon;Kim, Do-Soon
    • Korean Journal of Weed Science
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    • v.30 no.2
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    • pp.94-102
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    • 2010
  • Field and pot experiments were conducted to investigate seedling emergence and early growth of Eleocharis kuroguwai panted on different dates. Non-linear regression analyses of observed data against effective accumulated temperature (EAT) with the Gompertz model showed that the Gompertz model works well in describing seedling emergence and early growth of E. kuroguwai regardless of planting date and soil burial depth. EATs required for 50% of the maximum seedling emergence of E. kuroguwai planted at 1, 3 and 5 cm soil burial depth in the pot experiment were estimated to be 54.5, 84.0 and $118.0^{\circ}C$, respectively, and $56.7^{\circ}C$ when planted at 1 cm in the field experiment. EATs required for 50% of the maximum leaf number of E. kuroguwai planted at 1, 3 and 5 cm soil burial depth in the pot experiment were estimated to be 213.3, 249.0 and $291.6^{\circ}C$, respectively, and $239.5^{\circ}C$ when planted at 1 cm in the field experiment. Therefore, models developed in this study thus predicted that if rotary tillage with water is made on 27 May under $+2^{\circ}C$ elevated temperature condition, dates for 50% of the maximum seedling emergence, 5 leaf stage and 5 cm plant height of E. kuroguwai buried at 3 cm soil depth were predicted to be 2 June, 10 June and 12 June. These dates are 1 day earlier for the seedling emergence and 3 days earlier for the early growth as compared with current temperature condition, suggesting that earlier application of herbicides is required for effective control of E. kuroguwai.

Development of a Predictive Model Describing the Growth of Staphylococcus aureus in Ready-to-Eat Sandwiches (즉석섭취 샌드위치에서의 Staphylococcus aureus 성장예측모델 개발)

  • Park, Hae-Jung;Bae, Hyun-Joo
    • Journal of the FoodService Safety
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    • v.2 no.2
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    • pp.91-96
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    • 2021
  • This study was performed to provide fundamental data on hygiene and quality control of ready-to-eat sandwiches. Predictive models were developed to the kinetics of Staphylococcus aureus growth in these sandwiches as a function of temperature (10, 15, 25, and 35℃). The result of the primary model that used the Gompertz equation showed that the lag phase duration (LPD) and generation time (GT) decreased and the exponential growth rate (EGR) increased with increasing storage temperature. The secondary model showed an R2 for M and B of 0.9967 and 09916, respectively. A predictive growth model of the growth degree as a function of temperature was developed. L(t)=A+Cexp(-exp(-B(t-M))) (A=Initial contamination level, C=MPD-A, B=0.473166-0.045040*Temp-0.001718*Temp*Temp, M=19.924824-0.627442*Temp-0.004493*Temp*Temp, t=time, Temp=temperature). This model showed an R2 value of 0.9288. All the models developed in this study showed a good fit.

Assessing the Impact of Network Effects on Brand Choice in the Growth Market: A Multi-Brand Diffusion Model

  • Seungyoo Jeon
    • International Journal of Internet, Broadcasting and Communication
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    • v.15 no.4
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    • pp.279-293
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    • 2023
  • This study investigates network effects to measure how strongly the early adopters affect the brand choice of the potential consumer. By using the Gumbel-Hougaard (GH) copula, this study checks the magnitude of network effects varied from country to country. To consider consumer heterogeneity and network effects in the growth market, this study proposes the multi-brand Gamma/Shifted-Gompertz (m-G/SG) model based on the GH copula. Out of eighteen Western European cellular phone market data and South Korea smartphone data sets, the m-G/SG model provides an improvement in the estimation accuracy over the Libai, Muller, and Peres model. The results show that network effects enhance (i) the polarization of brand choice probabilities as time elapses; (ii) the dominance of the more preferred and the earlier entered brand; and (iii) the deceleration of category-level diffusion. Potential followers can analyze their relationship with earlier entrants through the m-G/SG model and also establish an optimal market entry strategy.